# CBSE Class 10 Questions

• ### Given that √3 is an irrational number, prove that (2 + √3) is an irrational number

Given that √3 is an irrational number, prove that (2 + √3) is an irrational number.

• ### X is a point on the side BC of ΔABC. XM and XN are drawn parallel

X is a point on the side BC of ΔABC. XM and XN are drawn parallel to AB and AC respectively meeting AB in N and AC in M. MN produced meets CB produced at T. Prove that TX2 = TB × TC

• ### In Figure, ABC is a triangle in which ∠B = 90º, BC = 48 cm and AB = 14 cm

In Figure, ABC is a triangle in which ∠B = 90º, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.

• ### Find the linear relation between x and y such that P(x, y) is equidistant

Find the linear relation between x and y such that P(x, y) is equidistant from the points A(1, 4) and B(–1, 2).

• ### A, B, C are interior angles of ΔABC. Prove that cosec (A+B)/2 = sec C/2

A, B, C are interior angles of ΔABC. Prove that cosec (A+B)/2 = sec C/2

• ### A right circular cylinder and a cone have equal bases and equal heights

A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3 : 4.

• ### Seven times a two digit number is equal to four times the number

Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.

• ### Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3

Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3.

• ### If two positive integers p and q are written as p = a^2b^3 and q = a^3b

If two positive integers p and q are written as p = a2b3 and q = a3b; a, b are prime numbers, then verify:
LCM (p, q) × HCF (p, q) = pq

• ### Use Euclid’s algorithm to find the HCF of 4052 and 12576

Use Euclid’s algorithm to find the HCF of 4052 and 12576.

• ### Using Euclid’s division algorithm find the HCF of the numbers 867 and 255

Using Euclid’s division algorithm find the HCF of the numbers 867 and 255.

• ### Divide 27 into two parts such that the sum of their reciprocals is 3/20

Divide 27 into two parts such that the sum of their reciprocals is 3/20.

• ### The sum of first n terms of an AP is given by Sn = 2n^2 + 3n

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

• ### An AP consists of 37 terms. The sum of the three middle most terms is 225

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP.

• ### In an A.P if sum of its first n terms is 3n^2 + 5n and its kth term is 164

In an A.P if sum of its first n terms is 3n2 + 5n and its kth term is 164, find the value of k.

• ### If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0)

If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, –5), find coordinates of the other two vertices.

• ### If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units

If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.

• ### In figure, AB is a chord of length 8 cm of a circle of radius 5 cm

In figure, AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP.

Evaluate:

Prove that

• ### The side of a square is 10 cm. Find the area between inscribed and circumscribed circles

The side of a square is 10 cm. Find the area between inscribed and circumscribed circles of the square.

• ### The short and long hands of a clock are 4 cm and 6 cm long respectively

The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 48 hours.

• ### If sin (A + 2B) = √3/2 and cos (A + 4B) = 0, A > B

If sin (A + 2B) = √3/2 and cos (A + 4B) = 0, A > B, and A + 4B ≤ 90º, then find A and B.

• ### The following frequency distribution shows the distance thrown by 68 students

The following frequency distribution shows the distance (in metres) thrown by 68 students in a Javelin throw competition.

Draw a less than type Ogive for the given data and find the median distance thrown using this curve.

• ### The following distribution shows the daily pocket allowance of children of a locality

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency k.

• ### By changing the following frequency distribution ‘to less than type’

By changing the following frequency distribution ‘to less than type’ distribution, draw its ogive.

• ### Find the value(s) of k for which the pair of linear equations kx + y = k^2 and x + ky = 1

Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions.

• ### For what values of m and n the following system of linear equations

For what values of m and n the following system of linear equations has infinitely many solutions.
3x + 4y = 12
(m + n)x + 2(m – n)y = 5m – 1

• ### Find all the zeroes of the polynomial 3x^4 + 6x^3 - 2x^2 - 10x - 5

Find all the zeroes of the polynomial 3x4 + 6x3 - 2x2 - 10x - 5 if two of its zeroes are √(5/3) and – √(5/3)

• ### Obtain all zeroes of 3x^4 – 15x^3 + 13x^2 + 25x – 30

Obtain all zeroes of 3x4 – 15x3 + 13x2 + 25x – 30, if two of its zeroes are √5/3 and – √5/3

• ### A train travelling at a uniform speed for 360 km would have taken 48 minutes less

A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed were 5 km/hour more. Find the original speed of the train.

• ### Check whether the equation 5x^2 – 6x – 2 = 0 has real roots

Check whether the equation 5x2 – 6x – 2 = 0 has real roots and if it has, find them by the method of completing the square. Also verify that roots obtained satisfy the given equation.

• ### A faster train takes one hour less than a slower train for a journey of 200 km

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of slower train is 10 km/hr less than that of faster train, find the speeds of two trains.

• ### Prove that the ratio of the areas of two similar triangles is equal to

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

• ### Two poles of equal heights are standing opposite to each other

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point in between them on the road, the angles of elevation of the top of poles are 60º and 30º respectively. Find the height of the poles and the distances of the point from the poles.

• ### If sin θ + cos θ = √2, then evaluate: tan θ + cot θ

If sin θ + cos θ = √2, then evaluate: tan θ + cot θ

• ### The angle of elevation of the top of a hill at the foot of a tower is 60º

The angle of elevation of the top of a hill at the foot of a tower is 60º and the angle of depression from the top of tower to the foot of hill is 30º. If tower is 50 metre high, find the height of the hill.

• ### A cone of maximum size is carved out from a cube of edge 14 cm

A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out.

• ### A man donates 10 aluminum buckets to an orphanage. A bucket made of aluminum is of height 20 cm

A man donates 10 aluminum buckets to an orphanage. A bucket made of aluminum is of height 20 cm and has its upper and lowest ends of radius 36 cm and 21 cm respectively. Find the cost of preparing 10 buckets if the cost of aluminum sheet is Rs. 42 per 100 cm2.

• ### Find the mean and mode for the following data

Find the mean and mode for the following data:

• ### A box contains cards numbered from 1 to 20. A card is drawn at random

A box contains cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that number on the drawn card is

1. a prime number
2. a composite number
3. a number divisible by 3
• ### A box contains cards numbered 11 to 123. A card is drawn at random from the box

A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is

1. a square number
2. a multiple of 7
• ### A box contains 12 balls of which some are red in colour

A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

• ### The King, Queen and Jack of clubs are removed from a pack of 52 cards

The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card

2. of black king
3. of club
4. of jacks
• ### Carbon has four electrons in its valence shell

Carbon has four electrons in its valence shell. Which type of compounds can be formed by carbon atom and why ? Give any one example of such compounds.

• ### An object is kept 40 cm in front of a concave mirror of focal length 20 cm

An object is kept 40 cm in front of a concave mirror of focal length 20 cm. Find the position and nature of the image. Draw a ray diagram to show the formation of image in this case.

• ### In the reaction: MnO2 + 4HCl → MnCl2 + 2H2O + Cl2

In the reaction:

MnO2 + 4HCl → MnCl2 + 2H2O + Cl2

1. Name the compound (i) oxidised, (ii) reduced.
2. Define oxidation and reduction on its basis.
• ### For the preparation of cakes, baking powder is used

(a) For the preparation of cakes, baking powder is used. If at home your mother uses baking soda instead of baking powder, how will it affect the taste of the cake and why?

(b) How is baking soda be converted into baking powder?

(c) What makes the cake soft and spongy?

• ### In the electrolysis of water

In the electrolysis of water,

1. Name the gas collected at anode and cathode?
2. Why is the volume of gas collected at one electrode double than the other?
3. What would happen if dil H2SO4 is not added to water?
• ### pH has a great importance in our daily life

"pH has a great importance in our daily life". Explain by giving three examples.