CBSE Sample Papers for Class 10 Maths Paper 5 is part of CBSE Sample Papers for Class 10 Maths . Here we have given CBSE Sample Papers for Class 10 Maths Paper 5

## CBSE Sample Papers for Class 10 Maths Paper 5

Board |
CBSE |

Class |
X |

Subject |
Maths |

Sample Paper Set |
Paper 5 |

Category |
CBSE Sample Papers |

Students who are going to appear for CBSE Class 10 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 5 of Solved CBSE Sample Papers for Class 10 Maths is given below with free PDF download solutions.

**Time: 3 Hours**

**Maximum Marks: 80**

**GENERAL INSTRUCTIONS:**

- All questions are compulsory.
- This question paper consists of 30 questions divided into four sections A, B, C and D.
- Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions 1 of 4 marks each.
- There is no overall choice. However, internal choice has been provided in one question of 2 marks, 1 three questions of 3 marks each and two questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
- In question of construction, drawings shall be neat and exactly as per the given measurements.
- Use of calculators is not permitted. However, you may ask for mathematical tables.

**SECTION A**

**Question numbers 1 to 6 carry 1 mark each.**

Question 1.

Which term of the sequence 114, 109, 104,…… is the first negative term?

Question 2.

Find the value of k for which the following are the consecutive terms of an AP: k, 2k – 1, 2k + 1.

Question 3.

Find the distance between the points [,2] and [,2]

Question 4.

Which measure of central tendency is given by the x-coordinate of the point the of intersection of “more than ogive” and “less than ogive”?

Question 5.

What is the distance between two parallel tangents of a circle of radius 4 cm?

Question 6.

In the adjoining figure, O is the centre of a circle. The area of sector OAPB is of the area of the circle. Find x.

**SECTION B**

**Question numbers 7 to 12 carry 2 marks each.**

Question 7.

Using Euclid’s algorithm, find the HCF of 1656 and 4025.

Question 8.

Find the two numbers whose sum is 75 and difference is 15.

Question 9.

If m and n are the zeroes of the polynomial 3x² + 11x – 4, find the value of .

Question 10.

If the distances of P(x, y) from the points A(3, 6) and B(-3, 4) are equal, prove that 3x + y = 5.

Question 11.

Question 12.

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a jingle cube. Find the edge of the cube so formed

**SECTION C**

**Question numbers 13 to 22 carry 3 marks each.**

Question 13.

In the adjoining figure, = 3. If the area of ∆XYZ is 32 cm², then find the area of the quadrilateral PYZQ.

Question 14.

In an equilateral triangle ABC, a point D is taken on base BC such that BD : DC = 2:1. Prove that 9 AD² = 7AB².

Question 15.

Find the values of a and b so that 8x^{4} + 14x^{3} – 2x^{2} + ax + b is exactly divisible by 4x^{2} + 3x – 2.

OR

If one zero of the polynomial 3x^{2} – 8x – (2k + 1) is seven times the other, find both zeroes of the polynomial and the value of k.

Question 16.

Solve for x and y:

(a – b)x + (a + b)y = a² – 2ab – b²

(a + b) (x + y) = a² + b².

Question 17.

Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are A(2, 1), B (4, 3) and C(2, 5).

OR

Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.

Question 18.

There are 100 cards in a box on which numbers from 1 to 100 are written. A card is taken out from the box at random. Find the probability that the number on the selected card is

(i) divisible by 9 and is a perfect square

(ii) a prime number greater than 80.

Question 19.

In a single throw of a pair of different dice, what is the probability of getting

(i) a prime number of each dice?

(ii) a total of 9 or 11?

Question 20.

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.

OR

A solid right-circular cone of height 60 cm and radius 30 cm is dropped in a right-circular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder in cubic metre.

Question 21.

Prove the following: sin^{6} θ + cos^{6} θ + 3 sin^{2} θ cos^{2} θ = 1.

OR

Prove that

Question 22.

If cos θ + sin θ = √2 cos θ, show that cos θ – sin θ = √2 .

**SECTION D**

**Question numbers 23 to 30 carry 4 marks each.**

Question 23.

If the roots of the quadratic equation x² + 2px + mn = 0 are real and equal, show that the roots of the quadratic equation x² – 2(m + n) x + (m² + n² + 2p²) = 0 are also real and equal.

Question 24.

The sum of three numbers in AP is 12 and sum of their cubes is 288. Find the numbers.

OR

The sums of first n terms of three arithmetic progressions are S_{1}, S_{2} and S_{3} respectively. The first term of each AP is 1 and their common differences are 1, 2 and 3 respectively. Prove that S_{1} + S_{3} = 2S_{2}.

Question 25.

Dudhnath has two vessels containing 720 mL and 405 mL of milk. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled.

OR

Show that the cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3 for some integer m.

Question 26.

The following table gives production yield per hectare of wheat of 100 farms of a village.

Change the distribution to more than type, and draw its ogive. Using the ogive, find the median of the given data.

What is the value of proper knowledge of farming?

Question 27.

In the adjoining figure, AB is a chord of length 16 cm of a circle with centre O and of radius 10 cm. The tangents at A and B intersect at the point P. Find the length of PA.

OR

Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Question 28.

The angle of elevation of a cloud from a point h metres above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ. Prove that the height of the cloud above the

Question 29.

Draw a circle of radius 3.5 cm. From a point P Outside the circle at a distance of 6 cm from the centre of the circle, draw two tangents to the circle. Also measure their lengths.

Question 30.

In the adjoining figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If the arcs of equal radii 7 cm with centres A, B, C and D have drawn, then find the area of the shaded region.