CBSE MATH STUDY

class 07 Maths half yearly Question paper

2023-09-27T08:05:00.000-07:00

Class 07 St Xebier's High school

Maths midterm (half -yearly) questions Paper 2023-24

CBSE Class 8th Maths ch.Probability formula and test paper

2018-03-03T22:56:00.000-08:00

Class X Mathematics SA 1 Question Paper (2015 – 2016)

2015-09-27T07:51:00.000-07:00

SA-1 Class 10th Maths 2015-16 Latest Original Question (Sept. 2015) Papers conducted in different CBSE schools
10th SA-1 CBSE Original Maths Paper 2015-2016 -1
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10th SA-1CBSE Original Maths Paper 2015-2016 -10
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CBSE Board 2014 SA-1 Original papers of mathematics for Class 10th conducted in different CBSE schools
10th SA-1 CBSE Original Maths Paper 2014_2015-1
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CBSE class 10 Board 2013 SA-1 Original papers of Maths
X Maths SA 01_Original_Question_Paper_2013-01
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Polynomial class 10 test yourself

2015-04-14T08:12:00.001-07:00

Section-A

1. The zeroes of the quadratic polynomial x² + 99x + 127 are

(A) both positive

(B) both negative

(D) both equal

2. The zeroes of the quadratic polynomial x²+ k x + k, k ≠ 0,

(A) cannot both be positive

(B) cannot both be negative

(D) are always equal

3. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then

(A) c and a have opposite signs

(B) c and b have opposite signs

(D) c and b have the same sign

4. If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.
(B) has no linear term and the constant term is positive.
(C) can have a linear term but the constant term is negative.
(D) can have a linear term but the constant term is positive.

5. The number of polynomials having zeroes as –2 and 5 is

(A) 1 (B) 2

Section-B

1. Find the zeroes of 2x³ – 11x² + 17x – 6.

2. Find the quadratic polynomial, the sum and the product of whose zeroes are ¹/₂, and –2 .3. Find the values of m and n for which x = 2 and –3 are zeroes of the polynomial: 3x² – 2mx + 2n.4. Check whether x² + 4 is factor of x⁴ + 9x² + 20

Section-C

5. Divide the polynomial (x⁴ + 1) by (x – 1) and verify the division algorithm.

6. Find all zeroes of x⁴ – 3x³ – 5x² + 21x – 14, if two of its zeroes are √7 and – √7 7. On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4 respectively, find g(x).

Section-D

8. Given that √2 is a zero of the cubic polynomial 6x³ + √2 x² – 10x – 4 √2 , find its other two zeroes.

9. Find k so that x²+ 2x + k is a factor of 2x⁴ + x³ – 14 x² + 5x + 6. Also find all the zeroes of the two polynomials.

10. Given that x – √5 is a factor of the cubic polynomial x³ – 3√ 5x² + 13x – 3 √5 , find all the zeroes of the polynomial.

9th class Maths NCERT Solution and previous Question

2014-10-06T18:31:00.000-07:00

X Chapter For Science

Test Paper And Study Materials

1 Matter in Our Surroundings

2 Is Matter Around Us Pure

3 Atoms and Molecules

4 Structure of the Atom

5 The Fundamental Unit of Life

6 Tissues

7 Diversity in Living Organisms

8 Motion

9 Force and Laws of Motion

10 Gravitation

10. Thrust and Pressure

11 Work and Energy

12 Sound

13 Why Do We Fall Ill

14 Natural Resources

15 Improvement in Food Resources

CBSE Class IX Chapters for Mathematics

Test Paper And Study Materials

IX Number System

IX Polynomial(Algebra)

IX Introduction to Euclid Geometry

IX Lines and Angles (Geometry)

IX Triangle(Geometry)

IX CO-Ordinate Geometry

IX Area of Triangle(Heron Formula)

IX Linear equations in two variables

IX Quadrilaterals

IX Area of Parallelogram

IX Geometry: Circles

IX Constructions

IX Surface Areas and Volumes

IX Statistics

IX Probability

DAV and DPS Question Papers for class 9 and 10 SA-1 September 2014 - 2015

2014-08-30T22:24:00.000-07:00

Click here to download latest DPS and DAV Sample Question paper

Class IX
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Geetha told her classmate radha that (root2 - 1 upon root root2 + 1) is an irrational number. Radha told Geetha that she was wrong and further claimed that if there is a number x such that x3 is irrational then x5 is also irrational. Geetha said that Radha was wrong. Radha accepted her mistake.justify both these statements.

2014-07-29T07:39:00.001-07:00

CBSE Class IX Chapters for Mathematics

Test Paper And Study Materials

IX Number System

IX Polynomial(Algebra)

IX Introduction to Euclid Geometry

IX Lines and Angles (Geometry)

IX Triangle(Geometry)

IX CO-Ordinate Geometry

IX Area of Triangle(Heron Formula)

IX Linear equations in two variables

IX Quadrilaterals

IX Area of Parallelogram

IX Geometry: Circles

IX Constructions

IX Surface Areas and Volumes

IX Statistics

IX Probability

9th[IX] Sample papers for Summative Assessment – 1 [links]
Mathematics	Science
Social Science	English, Hindi and Sanskrit
9th[IX] Sample papers for Summative Assessment – 2 [links]
Mathematics	Science
Social Science	English, Hindi and Sanskrit

PRACTICE QUESTIONS CLASS VIII: CHAPTER – 15_ INTRODUCTIONS TO GRAPH

2014-02-20T04:25:00.000-08:00

QUESTIONS CLASS VIII

PRACTICE CHAPTER – 15_ INTRODUCTIONS TO GRAPH

1. If y – coordinate of a point is zero, then this point always lies:

(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis

2. If x – coordinate of a point is zero, then this point always lies:

(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis

3. Point (–6, 4) lies in the quadrant:

(a) I (b) II (c) III (d) IV

4. The point (–4, –3) means:

(a) x = –4, y = –3 (b) x = –3, y = –4 (c) x = 4, y = 3 (d) None of these

5. Point (0, 4) lies on the:

(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis

6. Point (5, 0) lies on the:

(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis

7. On joining points (0, 0), (0, 2), (2,2) and (2, 0) we obtain a:

(a) Square (b) Rectangle (c) Rhombus (d) Parallelogram

8. Point (–2, 3) lies in the:

(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

9. Point (0, –2) lies:

(a) on the x-axis (b) in the II quadrant (c) on the y-axis (d) in the IV quadrant

10. Abscissa of the all the points on x – axis is:

(a) 0 (b) 1 (c) –1 (d) any number

11. Ordinate of the all the points on x – axis is:

(a) 0 (b) 1 (c) –1 (d) any number

12. Abscissa of the all the points on y – axis is:

(a) 0 (b) 1 (c) –1 (d) any number

13. Ordinate of the all the points on y – axis is:

(a) 0 (b) 1 (c) –1 (d) any number

14. The point whose ordinate is 4 and which lies on y – axis is:

(a) (4, 0) (b) (0, 4) (c) (1, 4) (d) (4, 2)

15. The perpendicular distance of the point P(3,4) from the y – axis is:

(a) 3 (b) 4 (c) 5 (d) 7

2 or 3 marks

11. Draw the graph of y = 3x. From the graph, find the value of y when (i) x = 4 and (ii) x =5.

12. Consider the relation between the perimeter and the side of a square, given by P = 4a. Draw a graph to show this relation. From the graph, find the value of P when (i) a = 4 and (ii) a =5.

13. Consider the relation between the area and the side of a square, given by A = x². Draw a graph to show this relation. From the graph, find the value of P when x = 4.

14. Simple interest on a certain sum is Rs. 40 per year then S = 40x, where x is the number of years. Draw a graph of this relation. From the graph, find the value of S when (i) x = 5 and (ii) x =6.

15. Plot the points (0, 2), (3, 0), (–3, 0) and (0, –2) in the graph sheet. Join these points. Name the figure obtained and find the area of the figure so obtained.

1.(c)	2.(d)	3. (b)	4. (a)	5. (d)
6. (c)	7. (a)	8. (b)	9. (c)	15. (a)
10. (a)	11.	12. (d)	13. (a)	14. (d)

Class 8 paper: click Here

sample paper class 8 dav board

2014-02-08T23:39:00.000-08:00

source: Summative Assessment-II, Sample Papers for Practice
DAV SA-II Board Paper Mathematics [2013-14]	DAV SA-II Board Paper Science [2013-14]
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DAV SA-II Board Paper Mathematics [2012-13]	DAV SA-II Board Paper Science [2012-2013]
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DAV SA-II Board Paper Mathematics [2011-12]	DAV SA-II Board Paper Science [2011-2012]
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9th SA-2 Solved Practice paper [Physics and Chemistry] 2014

2014-01-16T09:52:00.001-08:00

9^th SA-2 Solved Practice paper [Physics and Chemistry] 2014

1. Name the anion and cation which constitute the molecule of magnesium oxide [1]

2. A cube of side 5cm is immersed in water and then in saturated salt solution. In which case will it experience a greater buoyant force. If each side of the cube is reduced to 4cm and then immersed in water compare the force experienced by the cube, as compared to the first case. Give reasons for each case. 2

3. The kinetic energy of an object of mass `m’ moving with a velocity of 5ms-1 is 25J. Calculate its kinetic energy when its velocity is doubled. 2

4. The percentage of three elements calcium, carbon and oxygen in a sample of calcium carbonate is given as : [3]

Calcium =40% ; Carbon =12.0% ; Oxygen = 48%

If the law of constant proportion is true, what weights of these elements will be present in 1.5 g of another sample of calcium. Carbonate ? (Atomic mass of Ca = 40 u, C = 12 u, O = 16 u)

5. The description of atomic particles of two elements X and Y is given below[3]

	X	Y
Protons	8	8
neutrons	8	9
electrons	8	8

(i) What is the atomic number of Y?

(ii) What is the mass number of X?

(iii) What is the relation between X and Y?

(iv) Which element/elements do they represent?

(v) Write the electronic configuration of X?

(vi) Write the cation/anion formed by the element

6. Which of the following are isotopes and which are isobars?

Argon, Protium, Calcium, Deuterium. Explain why the isotopes have similar chemical properties but they differ in physical properties? [3]

7.What do you mean by buoyancy? Why does an object float or sink when placed on the surface of water?[3]

8. When is the work done by a force said to be negative? Give one situation in which one of the forces acting on the object is doing positive work and the other is doing negative work. [3]

9. Define one Joule of work. Calculate the work done in lifting a box weighting 150 kg through a vertical height of 7 meters (take g=10 ms2) [3]

10. A construction worker’s helmet slips and falls when he is 78.4 m above the ground. He hears the sound of the helmet hitting the ground 4.23 seconds after it slipped. Find the speed of sound on air. [3]

11. Answer these questions[5]

(i) Define mole

(ii) How is it related to Avogadro constant, relative mass and molecular mass?

(iii) What is the number of molecules in 0.25 moles of oxygen ? Avogadro’s no. = 6 .22 x10²³.

(i) Define atomicity

(ii) Give an example each of a polyatomic element and a polyatomic ion.

(iii) How many atoms are present in CaCl2 molecule and ion? SO₄^-2

(iv) Write down the formulae of

(a) sodium carbonate

(b) Ammonium chloride

(d) Aluminium hydroxide

12. (i) An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expressions.

(ii) Certain force acting on 20kg mass changes its velocity from 5ms-1 to 2ms-1 calculates the work done by the force. [5]

OR,

(i) Define kinetic energy. Derive an expression for the kinetic energy of an object.

(ii) The power of a motor pump is 5kW. How much water per minute the pump can raise to height of 20m? Take g=10ms^-2

Solution:

1.		Magnesium oxide – MgO Anion – O-2 Cation – Mg+2		½ ½
2		We know buyant force = V.P g V = Volume of body P = density of liquid g = acceleration Since density of saturated salt solutions is more than water the cube will experience greater upthrust. In second case as volume of cube is less then first so in 2nd case it will experience less upthrust		½ ½ ½ ½
3		Initial K.E = 25J Since K.E = ½ mv2 D as velocity doubles K.S becomes 4 times K.E = 4x25=100J		1 1
4		Mass of calcium in 1.5 g of sample = 40 x [1.5/100] = 9.6 g Mass of carbon in 1.5 g of sample = 12x [1.5/100] = 0.18 g Mass of oxygen in 1.5 g of sample = 48x[1.5/100] = 0.72 g		1 1 1
5		(i) Atomic number of y – 8 (ii) Mass number of x – 16 (iii) x and y are isotopes (iv) x and y represent – oxygen (v) ¹⁶₈O - 2, 6 (vi) It will form an anion – O^-²		1 1 1
6		Isotopes – Protium, Diuterium Isobars – Argon and calcium Since isotopes have identical electronic configuration containing same number of valence electrons they have similar chemical properties. Since the masses are slightly different the physical properties (density, melting pt, boiling pt, etc) are different		1 1
7		When a body is immersed in a fluid, it experiences an upward force. This upward force is the force of buoyancy. Forces acting an the body inside water are buoyant force weight of body and if the buoyant force is greater than the gravitational force it floats, otherwise it sinks.		1 2
8		Negative work – When the force is acting opposite to the direction of the displacement, the work done by the force is taken as negative. When we lift an object two forces act on the object. Muscular force – Doing positive work in the direction of the displacement. Gravitational force – doing negative work opposite to the direction of the displacement.		1 1 1
9		One Joule is the amount of work done on an object when a force of 1N displaces it by 1 m along the line of action of force m = 150kg ; G = 10m/s² ;h = 7m P.E = mgh P.E = 150 x 10 x7 = 10500J		1 2
10		We know, h = ut + 1/2 gt² u = 0, h = 78.4, g = 9.8 m/s² using these t² = 16 Þ t = 4 s time taken by the helmet reach the ground = 4 s Þ time taken by sound to reach the height = 4.23 – 4 = 0.23s ÞSpeed of sound = 78.4 /0.23 = 340.87 m/s		1 1 1
11		(i) Mole – one mole of any species (atoms, molecules, ions or particles) is that quantity in number having a mass equal to its atomic or molecular mass in grams (ii) 1 mole = 6.022 x 1023 in number – Relative mass in g. (iii) 1 mole of oxygen contain 6.022 x 1023 molecules 0.25 mole of oxygen contain 6.022 x1023 x 0.25 = 1.505 x 1023 molecules		1 2 2
OR		(i) Atomicity – Number of atoms constituting a molecule (ii) Polyatomic element – sulphur Polyatomic ion – NH4^-, OH^-, SO₄^-2 (any one) (iii) Cacl2 – atomicity – 3 SO4-2 – atomicity - 5 (iv) (a) Na2CO3 Sodium carbonate (b) NH4Cl Ammonium chloride (c) ZnO zinc oxide (d) Al(OH)3 Aluminium hydroxide	1 ½+½ ½+½ ½+½+ ½+½
12.		(i) Work done = mgh Difference in height of initial and final position is zero. Work done = mg ( h2 - h1) = mg(o) = O (ii) Work done = change in K.E Work done = 1/2 m (v₁²– v₂²) = ½ x 20(5² ^-2²) = 210 J		1 ½ 1 1 ½
OR
(i) Energy posesed by a body by virtue of motion. F = ma W = F.S = mas But u² - v² = 2as Þ as = ½ (v2-u2) w = energy Þ S = v²/2a m. a x x v² x 2a = 1/2mv²				½ ½ ½ ½
(ii) Energy = power x time = 5kw x 1 min = 3 x 10⁵ J mgh = E /gh = (3 x 10⁵)/ 10x 20 = 1.5 x 10³ kg volume of water = mass/ density = (1.5 x 10³ )/10³ = 1.5 m3				½ ½ 1
13	(i)
(ii)	Eardrum moves inwards when compression reaches it and moves outwards when rarefaction reaches it thus the ear drum vibrates. (ii) Audible rang 20Hz to 20,000 Hz OR
(i)	Ceiling and walls are made curved so that sound after reflection reaches the target audience. (ii) Reflection The sound goes to the obstacle and reaches back the ear of the listeners on reflection after 0.1s. If speed of sound in air is 344 m/s then the minimum distance of obstacle from the source of sound must be 17.2 cm (iii) Repeated reflection of sound that results in persistence of sound- Reverberation. sound is blurred, distorted, confusing sound absorbent material on roof, walls, seats

CBSE SUMMATIVE ASSESSMENT-II SAMPLE PAPER 2014 Class Xth [Links]	CBSE SUMMATIVE ASSESSMENT-II SAMPLE PAPER 2014 Class IXth [Links]
Sample Paper Mathematics	Sample Paper Mathematics
Sample Paper Science	Sample Paper Science
Sample Paper Hindi, English and Sanskrit	Sample Paper Hindi, English and Sanskrit
Sample Paper Social Science	Sample Paper Social Science

CBSE class 10th Guess paper for the for 2014 board examination.

2014-01-13T04:39:00.002-08:00

Find CBSE class 10th Guess paper for the for 2014 board examination. Question has been framed as per the analysis and facts that came from the previous year question papers

Find CBSE class 10th Science Sample paper for the second term examination. Question has been framed as per the syllabus covered in the second term examination

10th class solved Sample Question paper For SA2

2014-01-13T04:21:00.001-08:00

Xth ENGLISH COMMUNICATIVE SA_II_Question Paper [61005]

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Xth ENGLISH COMMUNICATIVE SA_II_Question Paper Solution [61005]

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Xth ENGLISH COMMUNICATIVE SA_II__Question Paper [2018]

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Xth ENGLISH COMMUNICATIVE SA_II_Question Paper Solution [2018]

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10th Sample Paper for Sanskrit Set-01

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10th Sample Paper for Sanskrit Set-01[Solution]

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10th Sample Paper for Sanskrit Set-02

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10th Sample Paper for Sanskrit Set-02[Solution]

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Xth SAMPLE PAPER SOCIAL SC. SOLVED 2014-1

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10th Maths Solved Sample Paper 2014 - 1

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10th Science Solved sample guess SA-II-paper -

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March 2014 boards Exam: Break between each paper for Class X students[TOI]

2013-12-24T09:07:00.000-08:00

Students appearing for the Class X board exams in March next year are set to get a break between each paper thanks to the scheduling.

Since the public exam will be conducted parallel to the Class XII board exams, the papers for Class X will be scheduled on alternate days, offering students some valuable extra study time.

The scheduling of Class XII papers is everyday from March 1 to 15.

On days when 'minor' Class XII papers-to be answered by a smaller number of students-are scheduled, the students of Classes X and XII will answer from common centres. The past practice of pairing seniors and juniors during such exams will however not be adopted.

"Some years ago, some papers of the two public exams were answered from common centres and the students would be made to sit together in each class. Though students of Classes X and XII will share centres during the 2014 exams, we will see to it that they are not made to sit together in a class," said Jose Remedios Rebello, chairperson, Goa board of secondary and higher secondary education.

He said schools that serve as centres will remain shut, at least during the morning session, when the public exams are in progress.

"Mostly city schools serve as board exam centres and will give their students a break when the board exams are on," said Rebello.

He added that other schools will also have to give their students a break during the exams-scheduled from March 1 to 15-as "we require their teachers as supervisors etc during the exams".

Schools will however have the liberty to call their students, especially their weaker ones, during the second half of the day "so that they may not be completely shut", said Rebello.

He said that though the Classes X and XII exams are being held earlier than usual due to the revised academic calendar to allow schools to attain minimum instructional days, the results of the public exams will be announced on dates similar to the last academic year.

"The results will be announced in the first and second week of May. The results will take time, although the exams are being held earlier, because the teachers will be called in batches and not all at once for paper corrections. This is to enable them to conduct classes at their respective schools," said Rebello.

CBSE SUMMATIVE ASSESSMENT-II SAMPLE PAPER "2014" CLASS X

X CBSE NCERT Board Questions Chapter Probability

2013-11-23T09:52:00.002-08:00

1. Which of the following can be the probability of an event ?

(A) 0.05 (B) 1.005 (C) 18/ 23 (D) 9/7

2. The probability of getting 53 Fridays in a leap year is :

(A) 1/7 (B) 2/7 (C) 4/7 (D) 5/7

3. If an event occurs surely, then its probability is (A) 0 (B) 1 (C) 1/2 (D) 3/4

4.Two dice are thrown at the same time. Find the probability of getting an even number on the first die.

5. A coin is tossed two times. Find the probability of getting at least one tail.

6.If there are 2 children in a family, find the probability that there is at least one boy in the family.

6. Two dice are thrown together. Find the probability that a multiple of 2 occurs on one dice and a multiple

of 3 occurs on the other.

7.A card is drawn from a well shuffled pack of 52 playing cards. What is the probability that the card drawn

is : (i) either a red or a king (ii) a black face card

8. A bag contains 6 red, 3 black and 6 white balls. A ball is selected at random from the bag. Find the

probability that the selected ball is : (a) red or black (b) not black

9. A coin is tossed three times. Find the probability of getting exactly two tails

10. Two dice are thrown together. What is the probability of getting a doublet ?

11. A coin is tossed 3 times. Find the probability of getting : (i) at least 2 heads (ii) not getting the same result in all the tosses (iii) exactly 1 tail

12. A card is drawn at random from a well – shuffled deck of 52 playing cards. Find the probability that the card drawn is : (i) either a spade or an ace (ii) a black king

13.One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting : (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) a queen of diamonds

14. Cards marked with numbers 5, 6, 7, ……., 30 are placed in a box and mixed thoroughly and one card is drawn at random from the box. What is the probability that the number on the card is (i) a prime number ? (ii) a multiple of 3 or 5 ? (iii) neither divisible by 5 nor by 10 ?

15. One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting :

(i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) a queen of diamonds

Assignment 9th Class Topic:- Linear equation in two variable CBSE/NCERT (For CPS and SDV Samastipur )

2013-11-11T07:47:00.002-08:00

1. Draw the graphs of 2x + y = 6 and 2x – y + 2 = 0 . Shade the region bounded by these lines and x-axis. Find the area of the shaded region.

2.       Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines y – axis. Also determine this area.

3.       A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs x and per day charge are Rs y. Write the linear equation representing the above information.

4. A number is 27 more than number obtained by reversing its digits. If is unit’s and ten’s digit are x and y respectively, write the linear equation representing the above statement.

5. Plot the points (3, 5) and (-1, 3) on a graph paper and verify that the straight line passing through these points also passes through the point (1, 4).

6. A three – wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

7. The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are x and y respectively, then write the linear equation representing the above statement.

8. If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of K.

9. Draw the graph of y = |x| .

10. Draw the graph of the equation 2x + y = 6. Shaded the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.

11. Ravish tells his daughter Aarushi, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. If present ages of Aarushi and ravish are x and y years respectively, represent this situation algebraically as well as graphically

12. Aarushi was driving a car with uniform speed of 60 km/h. Draw distance – time graph. From the graph, find the distance travelled by Aarushi in (a) 2and 1/2Hours (b) 1/2 hours

13. Solve the equation 2x + 1 = x – 3, and represent the solution (s) on (i) the number line (ii) the Cartesian plane.

14. Draw the graph of each of the following linear equations in Cartesian plane x + 5 = 0

15. Draw a graph of the equation (i) y = -3 (ii) 2y + 3 = 9

Answer

1.8 sq. units

2. 13.5 sq. units

3. X + 4y = 27

4. X – y + 3 = 0

6. Y = 8x + 7

7. X + y = 11

8. K=3

10. 9 sq. units

12. (i) 150 km (ii) 30 km

CBSE Board Test Paper Chapter_Coordinate Geometry

2013-11-09T06:18:00.000-08:00

CBSE TEST PAPER UNIT: 4 (coordinate geometry)

The method of describing the location of points in this way was proposed by the French mathematician René Descartes (1596 - 1650). (Pronounced "day CART"). He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. In honor of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane.

A system of geometry where the position of points on the plane is described using an ordered pair of numbers.

In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero.

Section-A

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2 (B) 3 (C) 1 (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6 (B) 8 (C) 4 (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8 (B) 2 √7 (C) 10 (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5 (B) 5√ 2 (C) 2 √5 (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5 (B) 3 (C) √ 34 (D) 4

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the

ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If he coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q.

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability

CBSE/NCERT 10th Ch:14 -Statistics – Mean, Mode and Median and Ogive Guess Question for SA-1

2013-08-14T08:23:00.001-07:00

10th Math's Chapter 14 -Statistics – Mean, Mode and Median of Grouped Data and Graphical Representation of Cumulative Frequency Distribution

"Mean, median, mode and draw cumulative frequency curves (ogives)"

The numerical representation of the ungrouped data called measures of central tendency, namely, mean, median and mode. we shall extend the study of these three measures, i.e., mean, median and mode from ungrouped data to that of grouped data. We shall also discuss the concept of cumulativ e frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives.

Set-01

1. The class mark of the class 10 – 25 is: (A) 17 (B) 18 (C) 17.5 (D) 15

2. Find the mean of the following frequency distribution [by assumed mean method]

Class :	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	7	5	10	12	6

3. Find the mode of the following frequency distribution

Class :	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	7	5	10	12	6

4. If the mean of the following distribution is 27, find the value of p

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	8	p	12	13	10

5. Find mean, and median for the following data :

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	8	16	36	34	6

6. Draw ‘less than’ and ‘more than’ ogives for the following distribution:

Scores :	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80
Frequency :	8	10	14	12	4	2

7. Find the value of f1 from the following data if its mode is 65:

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	6	8	f1	12	6	5

Set-02

1. If the „less than‟ type ogive and „more than‟ type ogive intersect each other at (20.5, 15.5), then the median of the given data is : (A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5 [01]

2. Find the sum of lower limit of mediun class and the upper limit of model class : [02]

Classes :	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency :	1	3	5	9	7	3

3. Convert the following data into more than type distribution :[02]

Class :	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80
Frequency :	2	8	12	24	38	16

4. Draw the less than type ogive for the following data and hence find the median from it.[03]

Classes :	50 – 60	60 – 70	70 – 80	80 – 90	90 – 100
Frequency :	6	5	9	12	6

5. The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Find the values of „p‟ and „q‟ : [03]

Classes :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency :	5	p	20	15	q	5

6. Calculate the average daily income (in `) of the following data about men working in a company :[05]

Daily income (in `)	< 100	< 200	< 300	< 400	< 500
Number of men	12	28	34	41	50

7. The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean n umber of wickets by choosing a suitable method. What does the mean signify? [Hint: Here, the class size varies, and the x ^,s are large. Let us still apply the stepdeviation method with a = 200 and h = 20]

Number of wickets	20 - 60	60 - 100	100 - 150	150 – 250	250 – 350	350 - 450
Number of bowlers	7	5	16	12	2	3

8. Draw a more than ogive for the following distribution and hence find its median.

Class	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90
Frequency	25	15	10	6	24	12	8

SET-03

1. Relationship among mean, median and mode is :

(A) 3 Median =Mode +2 Mean (B) 3 Mean = Median + 2 Mode

2 . Calculate the median for the following distribution :

Marks obtained	Number of students
Below 10	6
Below 20	15
Below 30	29
Below 40	41
Below 50	60
Below 60	70

3. Compute the arithmetic mean for the following data :

Marks obtained	No. of students
Less than 10	14
Less than 20	22
Less than 30	37
Less than 40	58
Less than 50	67
Less than 60	75

4. Find the missing frequencies f1 and f2 in the following frequency distribution table, if N =100 and median is 32.

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	Total
Frequency	10	f1	25	30	f2	10	100

5. For the following frequency distribution, draw a cumulative frequency curve of less than type.

Class :	200 – 250	250 – 300	300 – 350	350 – 400	400 – 450	450 – 500	500 – 550	550 – 600
Frequency:	30	15	45	20	25	40	10	15

6. The median class for the following data is

Class	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	10	12	20	22

(A) 20 - 40 (B) 40 - 60 (C) 60 - 80 (D) 80 – 100

7. Write the following frequency distribution as “more than type” and “less than type” cumulative frequency distribution.

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	5	15	20	23	17

8. Find the median for the following table which shows the daily wages drawn by 200 workers in a factory.

Daily wages (in Rs.)	Less than 100	Less than 200	Less than 300	Less than 400	Less than 500
No. of workers	40	82	154	184	200

9. The mean of the data in the following table is 50. Find the missing frequencies f1 and f2.

Class :	10 – 30	30 – 50	50 – 70	70 – 90	90 – 110	Total
Frequency :	90	f1	30	f2	40	200

10. Find the unknown entries a, b, c, d, e and f in the following distribution and hence find their mode.

Height (in cm) :	150–155	155–160	160–165	165–170	170–175	175–180	Total
Frequency :	12	b	10	d	e	2	50
Cumulative frequency :	a	25	c	43	48	f

For more paper visit: websiteof : jsuniltutorial

Polynomial MCQ Assignments class 10 Mathematics

2013-04-02T03:31:00.001-07:00

X Polynomial MCQ Assignments in Mathematics Class X

1. If α,β are zeroes of the polynomial f(x) = x2 + px + q, then polynomial having 1/α and 1/β as its zeroes is

(a) x2 + qx + p (b) x2 – px + q (c) qx2 + px + 1 (d) px2 + qx + 1

2. If α and β are zeroes of x2 – 4x + 1, then 1/α + 1/β – αβ is

(a) 3 (b) 5 (c) –5 (d) –3

3. The quadratic polynomial having zeroes as 1 and –2 is :

(a) x2 – x + 2 (b) x2 – x – 2 (c) x2 + x – 2 (d) x2 + x + 2

4. If α, β are zeroes of x2 – 6x + k, what is the value of k if 3α+2β=20 ?

(a)–16 (b) 8 (c) 2 (d) –8

5. If one zero of 2x2 – 3x + k is reciprocal to the other, then the value of k is

(a) 2 (b) −23 (c) −32 (d) –3

6. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is

(a) x2 + 3x – 2 (b) x2 – 2x + 3 (c) x2 – 3x + 2 (d) x2 – 3x – 2

7. If (x + 1) is a factor of x2 – 3ax + 3a – 7, then the value of a is :

(a)1 (b) –1 (c) 0 (d) –2

8. The number of polynomials having zeroes –2 and 5 is :

(a)1 (b) 2(c)3 (d) more than 3

9. The quadratic polynomial p(y) with –15 and–7 as sum and one of the zeroes respectively is :

(a) y2 – 15y – 56 (b) y2 – 15y + 56 (c) y2+ 15y + 56 (d) y2 + 15y – 56

10.The value of p for which the polynomial x3 + 4x2 – px + 8 is exactly divisible by (x – 2) is :

(a) 0 (b) 3 (c) 5 (d) 16

11. If 1 is a zero of the polynomial p(x) = ax2– 3(a – 1)x – 1, then the value of a is :

(a) 1 (b) –1 (c) 2 (d) –2

12. If –4 is a zero of the polynomial x2 – x – (2 + 2k), then the value of k is :

(a) 3 (b) 9 (c) 6 (d) –9

13.The degree of the polynomial (x + 1)(x2 – x – x4 + 1) is :

(a) 2 (b) 3 (c) 4 (d) 5

14. If (x + 1) is a factor of x2– 3ax + 3a – 7, then the value of a is :

(a) 1 (b) –1 (c) 0 (d) –2

15. If sum of the squares of zeroes of the quadratic polynomial f(x) = x2 – 8x + k is 40, the value of k is :
(a) 10 (b) 12 (c) 14 (d) 16

X math's Chapter: 02 Polynomials CBSE Test paper New
Class X Polynomial Test Paper-1 Download File

Class X Polynomial Test Paper-2 Download File

Class X Polynomial Test Paper-3 Download File

Class X Polynomial Test Paper-4 Download File

9th Linear Equation in two Variable [Guess paper] 2013

2013-02-26T06:35:00.002-08:00

9th Linear Equation in two Variable [Sample Guess paper] 2013

[1 Mark Questions]

1. Which of the following is not a linear equation?

(a) ax + by + c = 0 (b) 0x + 0y + c = 0

2. Age of ‘x’ exceeds age of ‘y’ by 7 yrs. This statement can be expressed as linear equation as

(a) x + y + 7 = 0 (b) x – y + 7 = 0

3. Linear equation in one variable is :

(a) 2x = y (b) y2 = 3y + 5 (c) 4x – y = 5 (d) 3t + 5 = 9t – 7

4. The condition that the equation ax + by + c = 0 represent a linear equation in two variables is

(a) a ≠ 0, b = 0 (b) b ≠ 0, a = 0

c) a = 0, b = 0 (d) a ≠ 0, b ≠ 0

5. How many linear equations in x and y can be satisfied by x = 1 and y = 2?

(a) only one (b) two (c) infinitely many (d) three

6. The general form of a linear equation in two variables is :

(a) ax + by + c = 0, where a, b, c are real umbers and a, b ≠ 0

(b) ax + b = 0, where a, b are real numbers and a ≠0

(d) none of these

7. The equation of the line whose graph passes through the origin, is :

(a) 2x + 3y = 1 (b) 2x + 3y = 0

[(b){form x = my}]

8. The equation of y-axis is :

(a) y = 0 (b) x = 0(c) y = a (d) x = a

[ (b) The equation of y-axis is x = 0 ]

9. The equation of x-axis is :

(a) y = 0 (b) x = 0 (c) y = a (d) x = a

[(a) The equation of x-axis is y = 0 ]

10. Any point on the x-axis is of the form:

(a) (x, y) (b) (0, y) (c) (x, 0) (d) (x, x)

[(c) On x-axis y-coordinate will be 0].

11. Any point on the line y = x is of the form :

(a) (a, a) (b) (0, a) (c) (a, 0) (d) (a, – a)

[(a) Any point on the line y = x is of the form (a, a).

12. The point of the form (a, – a) always lies on the line :

(a) x = a (b) y = – a (c) y = x (d) x + y = 0

[d) The point (a, – a) always lies on the line x + y = 0.]

13. Equation of the line y = 0 represents:

(a) y-axis (b) x-axis (c) both x-axis and y-axis (d) origin

[(b) The equation of x-axis is y = 0]

14. The graph of the linear equation 2x + 3y = 9 cuts y-axis at the point :

(a) 9/2 , 0 (b) (0, 9) (c) (0, 3) (d) (3,1) [C]

15. The point of the form (a, a) always lies on:

(a) x-axis(b) y-axis(c) on the line y = x(d) on the line x + y = 0 [C]

9th Linear Equation in two Variable [Guess paper] 2013 [2 Marks Questions]

1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

2. Which one of the following options is true, and why? y = 3x + 5 has (i) a unique solution (ii) only two solutions (iii) infinitely many solutions.

[ infinitely many solutions. It is because a linear equation in two variables has infinitely many solutions. We keep changing the value of x and solve the linear equation for the corresponding value of y]

3. Write any four solutions for (i) 2x + y = 7 or, (ii) x = 4y

4. Check (4, 0) is a solution For the equation x – 2y = 4

5. If (2, 0) is a solution of linear equation 2x + 3y = k, then find the value of k.

6. If the point (2 – 1) lies on the graph of the equation 3x + ky = 4, then find the value of k.

7. Give the geometric representations of y = 3 as an equation

(i) in one variable (ii) in two variables

8. Check whether the graph of the linear equation x + 2y = 7 passes through the point (0, 7).

9. Mayank and Sujata two students of class IX together contributed Rs 1000 towards PM Relief fund. Write a linear equation satisfying the data

10. The cost of a table exceeds the cost of the chair by Rs 150. Write a linear equation in two variables to represent this statement. Also, find two solutions of the same equation.

8th Polygons Solved Questions Paper[CBSE Maths]

2013-02-16T00:16:00.003-08:00

1.Q. Find the number of diagonals in an octagon?

Ans: Number Of Diagonals Of Polygon = n(n-3) / 2

Where n is Number Of Sides

Here n = 8

Diagonals= [8(8-3)5]/2 = 20

2.Q. Find the number of sides of a polygon whose each exterior angle is 45⁰ .

Ans: Measure of Each Exterior Angle of a Polygon = 360/n

Each Exterior Angle = 45

45 = 360/n

Number of Sides = 360/45 =8

So Number of Sides = 8

3. Q. The sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles. Determine the number of sides of the polygon.

Ans: sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles.

We know that in a regular polygon sum of all the exterior angles = 360°

Therefore, sum of interior angles = 3 × 360° = 1080°

Again, we have sum of interior angles, S = (n - 2)180°, where n is the number of sides of the polygon

⇒ (n - 2)180° = 1080°
⇒ n - 2 = 6
⇒ n = 8
4. Q. (a) What is the minimum interior angle possible for a regular polygon? Why?

(b) What is the maximum exterior angle possible for a regular polygon?

Answer: The polygon with minimum number of sides is a triangle, and each angle of an equilateral triangle measures 60°, so 60° is the minimum value of the possible interior angle for a regular polygon. For an equilateral triangle the exterior angle is 180°-60°=120° and this is the maximum possible value of an exterior angle for a regular polygon.
The sum of the exterior angles of any polygon= 360⁰
Hence, the polygon of 8 sides is octagon.

5. Q. Find the measure of each exterior angle of a regular polygon of 9 sides.

Ans: Total measure of all exterior angles = 360

No. of sides = 9

Measure of each exterior angle = 360/9 = 40

6.Q. If the sum of the measures of the interior angles of a polygon equals the sum of the measures of the exterior angles, how many sides does the polygon have?

Ans:The sum of the measures of the interior angles of a polygon with n sides =(n-2)x180⁰

(n-2) x180⁰= 360⁰Þ n=2+2=4

7.Q. The sum of the interior angles of a regular polygon is:(n - 2) × 180° where n is the number of sides of the polygon.

Solution: The sum of its exterior angles of regular polygon= 360°

The exterior angle of a regular polygon

Interior angle of a regular polygon = sum of interior angles ÷ number of sides

8. Q.What is the measure of the each angle of regular Hexagon?

Ans: No. of sides in regular hexagon = 6

The measure of the each angle =[(2n – 4)x90⁰/n ]=[2x6-4]x90⁰/6 =720⁰/6 =120⁰

9. Q. Find the number of sides of a polygon whose each interior angle is 156⁰ .

Ans each exterior angle = 180 - 1560 = 24⁰

Measure of Each Exterior Angle of a Polygon = 360/n

Þ 24⁰= 360/n Þ n = 360/24 =15

10.Q. Two regular polygons are such that the ratio between their no. of sides is 1:2 and the ratio of measures of their interior angle is 3:4. Find the number of sides of each polygon.

Ans: let the number of sides are x and 2x

then their interior angles will be [{(2n-4)/n}x90⁰] and [{(4n-4)/n}x90⁰]

A/Q, the ratio of measures of their interior angle = 3:4

Þ [{(2n-4)/n}x90⁰] ¸ [{(4n-4)/n}x90⁰] = ¾

On solving this we get , n=5

So, the numbers of sides are 5 and 2x5=10

8th Polygons Solved Questions Paper Download File

8th Maths Practice Paper-1

2013-02-11T07:18:00.000-08:00

1. An altitude of a triangle is 5/3 of its corresponding base. If the altitude were increased by 4 cm and the base decreased by 2 cm, the area of the triangle would remain the same.Find the base and altitude of the triangle.

2. Some toffees are bought at the rate of 11 for Rs. 10 and same numbers are bought at the rate of 9 for Rs 10. If the whole lot is sold at one rupee per toffee, find the gain or loss percent.

3. Chandu purchased a watch at 20% discount on its marked price but sold it at marked price. Find the gain percent of Chandu on this transaction.

4. A motorboat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in five hours and half. The speed of water is 1.5 km/hr. Find the speed of the boat in still water.

5. Factorize: x6 – 3x4y2 +3x2y4 –y6

6. Evaluate: (367/2 –369/2)/ 365/2

7. Divide 34x-22x3-12x4-10x2-75 by (3x+7) and check your answer.

8. The digit in the tens place of a number is three times that in the ones place. If the digits are reversed, the new number will be 36 less than the original number. Find the number.

9. A well is dug 20m deep and it has a diameter 7m. The earth, which is so dug out, is spread out on a rectangular plot 22m long and 14m broad. What is the height of the platform so formed?

10. The total surface area of a hollow cylinder open at both ends is 4620 sqcm, area of the base ring is 115.5sqcm and height 7cm. find the thickness of the cylinder.

11. A hemispherical bowl is made of steel 0.5cm thick. The inside radius of the bowl is 4cm. Find the volume of steel used in making the bowl.

12. A circus tent is cylindrical up to a height of 3m and conical above it .If the radius of the base is 49m and the slant height of the conical part is 53m, find the total canvas required to make the tent.

13. A storage tank consists of a circular cylinder with hemispherical ends on both the sides. If the external diameter of the cylinder be 1.4m and length be 5m. What will be the cost of painting it on the outside at the rate of Rs10 per sq. cm?

14. The difference between the compound interest and simple interest on a certain sum of money for two years at 7.5% per annum is Rs 360. Find the sum.

15. At what rate % per annum will a sum of Rs 4000 yield compound interest of Rs 410 in two years?

16. Diagonal of a parallelogram bisect at the point O . XY is a line segment passing through O such that X lies on AD and Y lies on BC. Give reasons for each of the following
(i) OB=OD ((ii)DBOYcongruent DDOX.

8th Maths Practice Paper-1 Download full Question paper pdf

8th Direct and Inverse Variation and Profit, Loss ... - cbse math study

cbsemathstudy.blogspot.com/.../8th-direct-and-inverse-variation-and....
These were sold at 8%gain and 4% loss respectively. Find his gain orloss percent in the whole transaction. Q-11. Some toffees are bought at the rate of11 per Rs.10 and sold at the rate of 9 per Rs.10. If the whole lot is sold at one rupee per toffee, find his gain or loss percent on the whole transaction.

Model Answers By Students of Secondary School Certificate (X) 2012-Mathematics

2013-01-22T07:23:00.000-08:00

Best Answers of Board Examination 2012 (Main)

Best attempted answer by the Candidates of Secondary School/Sr.School Certificate Exam.2012
Class-XII	Class-X
1.Physics	1.Science
2.Chemistry	2.Social Science
3.Biology	3.Mathematics
4.Math	4.Hindi-A
5.Business Study	5.Hindi-B
6.Accountancy	6.Eng.Lang & Litrature
7.Economics	7.Eng.communicative
8.Eng(Core)
9.Eng(Elective)
10.Functional English
11.Hindi(Core)
12.Hindi(Elective)

Previous Year Question Papers for Class X/XII (Board Examination 2012)

Q.P. CLASS X

Q.P. CLASS XII

Sample Question Paper for SA-I (Septmeber 2012)

For More Information http://www.cbse.nic.in

Optional Exercise – 13.5 - 10th Mathematics –Surface area and Volume

2013-01-21T06:52:00.003-08:00

Question 1: A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm³.

Solution: It can be observed that 1 round of wire will cover 3 mm height of cylinder.

Length of wire required in 1 round = Circumference of base of cylinder= 2pr = 2p × 5 = 10p

Number of round = Height of cylinder/Demeter of wire = 12/0.3= 40 round

Length of wire in 40 rounds = 40 × 10p = 40x10 x3.14=1256cm=12.56m

Radius of wire = 0.3/2 = 0.15cm

Volume of wire = Area of cross-section of wire × Length of wire = p (0.15)² × 1256 = 3.14 x 0.0225 x 1256 = 88.736 cm³

Mass = Volume × Density = 88.736 × 8.88 = 787.979 gm

Question 2: A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of p as found appropriate.)

Solution: The double cone so formed by revolving this right-angled triangle ABC about its hypotenuse is shown in the figure.

AC = √ (3² + 4²) = 5 cm

Area of DABC = ½ x AC x r =1/2 x BC x AB

Þ 5 x r = 3 x 4 Þ 12/5=2.4cm

Volume of double cone = Volume of cone 1 + Volume of cone 2

= 1/3 p r²H + /3 p r²h = 1/3 p r²(H + h)

= 1/3 x 3.14 x 2.4 x 2.4 x 5 = 30.14 cm³

Surface area of double cone = Surface area of cone 1 + Surface area of cone 2

= p r L + p r l

= p r ( L + l )

= 3.14 x 2.4 (4+3)

= 3.14 x 2.4 x7

= 52.75 cm2

Question 3: A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm3 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

Solution: Volume of cistern = 150 × 120 × 110 = 1980000 cm3

Volume to be filled in cistern = 1980000 – 129600 = 1850400 cm3

Volume of n bricks = 22.5 × 7.5 × 6.5 = 1096.875

As each brick absorbs one-seventeenth of its volume,

Þ Volume absorbed by 1 bricks = 1/17 x 1096.875 =64.52

Actual volume of bricks without water = 1096.875 - 64.52 =1032.375

Number of bricks = 1850400/1032.375 =1792.37

Therefore, 1792 bricks were placed in the cistern.

Q 4. In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 97280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Solution: Area of the valley, A = 97280 km2

Level in the rise of water in the valley, h = 10 cm = (10/100000) km = (1/10000) km

Thus, amount of rain fall in 14 day = Ah = 97280 km2 × (1/10000) km = 9.828 km3

Amount of rain fall in 1 day = 9.828 /14 = 0.702km3

Volume of water in 3 rivers = length × breadth × height

= 1072 km × 75 m × 3 m

= 1072 km × (75/1000) km × (3/1000) km = 0.2412 x3

= 0.7236 km3

This shows that the amount of rain fall is approximately equal to the amount of water in three rivers.

Question 5: An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see the given figure).

Solution: Radius (R) of upper circular end of frustum

=18/2 = 9 cm

Radius (r) of lower circular end of frustum

= Radius of circular end of cylindrical part

= 8/2 = 4 cm

Height (H) of frustum

= 22 − 10 = 12 cm

Height (h) of cylindrical = 10 cm

Slant height (l) of frustum

= √(R-r)² + H² =√(9-4)² + 12² =13 cm

Area of tin sheet required = CSA of frustum t + CSA of cylindrical

= p (R+r)l + 2prh = p [{(9+4)x13} + {2x4x10}]=22/7{169+80}=782.57 cm2

Question 6: Derive the formula for the volume of the frustum of a cone

Solution: Let ABC be a cone. A frustum DECB is cut by a plane parallel to its base. Let R and r be the radii of the ends of the frustum of the cone and h be the height of the frustum of the cone.

In D ABG and D ADF, DF||BG

<A = <A and <AGB = <AFD
∴ D ABG ∼ D ADF (AA similarity)

DF/BG = AF/AG =AD/AB

Þ r/R = H-h/H=L-l/L

Þif r/R = H-h/HÞ H =(Rh/R-r)

Volume of frustum of cone = Volume of cone ABC − Volume of cone ADE

= 1/3xpR²H - 1/3xpr²(H-h)

= 1/3p [R²H - r²(H-h)]

= 1/3p [R²(Rh/R-r) - r²{(Rh/R-r)-h}]

= 1/3p [(R³h/R-r) - r²{(Rh –Rh+rh) /(R-r)}]

= 1/3p [(R³h - r³h) /(R-r)]

= 1/3ph [(R³ - r³) /(R-r)]

= 1/3ph [{(R - r)( R² + r²-Rr)} /(R-r)]

= 1/3ph ( R² + r²-R r)

Further Study links

X Maths Surface Areas and Volumes Test paper-1

Download File

X Maths Surface Areas and Volumes Test paper-2

Download File

Mensuration Surface area and volume solved test paper-3

X Maths Surface Areas and Volumes Concepts for class 10 th

10th surface area and volume Cuboid and a Cube Cylinder Cone

CBSE MATHEMATICS (Class-9,10) ch-Surface Area and Volumes

9th Chapter: Probability based on Deck (Card): Question with Solution

2013-01-15T08:06:00.005-08:00

1. Find the probability of drawing a black card.

Answer: 1/2

2. Find the probability of drawing a red card.

Answer: 1/2

3. Find the probability of drawing either a red or black.

Answer: 1

4. Find the probability of drawing an ace.

Answer: 1/13

5. Find the probability of drawing either a jack or queen or king.

Answer: 3/13

6.Find the probability of drawing a black king.

Answer: 1/26

7. Find the probability of drawing a white queen.

Answer: 0

8. Find the probability of drawing a club.

Answer: 1/4

9. Find the probability of drawing a heart.

Answer: 1/4

10. Find the probability of drawing either a spade or diamond.

Answer: ½

11.Find the probability of drawing a club and heart.

Answer: 1/52

12.Find the probability of drawing either a black card or number 10.

Answer:7/13

13.Find the probability of drawing a number more than 5.

Answer: 5/13

14.Find the probability of drawing a picture card. (includes jack, queen or king)

Answer: 3/13

15. Find the probability of drawing a red ace.

Answer: 1/26

16. The probability of selecting neither a jack nor an ace from a well-shuffled pack of 52 playing cards is :

Ans: 11/13

17. From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.

Answer: 1/26

18. A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is an Ace.

Answer: 1/13

19. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting a red face card.

Answer: 3/26

20. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (i) heart (ii) queen (iii) clubs

Ans: (i) 3/49 (ii) 3/49 (iii) 10/49

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Test before Exam:IX Chapter Probability

For more Downloads Visit Page: Link For Pdf Download

CBSE I NCERT Arithmetic Progression-X Solved Problems

2012-12-26T07:19:00.001-08:00

1. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top .If the top and the bottom rungs are two and a half meter apart, what is the length of the wood required for the rungs?

2. The sum of first n terms of an AP is given by Sn = 3n2 + 5n find the nth term of the AP.

3. How many terms of the ap -6,-11/2 , -5,...... are needed to give the sum -25

4. Find a, b such that 27, a, b - 6 are in A.P.

5. Find the sum of all the odd numbers between 50 and 150 divisible by 7

6. The sum of third and seventh term of an AP is 6 and their product is 8.

7. If Sn = n2p and Sm = m2p, (m not equal ton), is an A.P. prove that Sp = p3.

8.Show that the sum of (m+n)th term and (m-n)thterm of an A.Pis equal to twice the mth term.

9. If the ratio of the sums of n terms of 2 APs is n+1:3n+1, then find the ratio of the 7th terms of the AP.

10. Determine the sum of the first 30 terms of the sequence whose nth term is given by tn=2n+9/3

11. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

12.The sum of the first and the last terms of an AP is 60,the sum of n terms of the AP is720.what is n?

13. If pth , qth and rth term of an AP are a,b,c respectively , then show that (a-b)r +(b-c)p + (c-a)q = 0

14. if (b+c)/a, (c+a)/b, (a+b)/c are in A.P. show that bc,ca,ab re in A.P.

15. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms

Class X ARITHMETIC PROGRESSIONS (8) Periods

Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms and their application in solving daily life problems.