# Mathematics All India Set 1 2016-2017 CBSE (English Medium) Class 10 Question Paper Solution

Mathematics [All India Set 1]
Date & Time: 2nd April 2017, 12:30 pm
Duration: 3h

[1] 1

What is the common difference of an A.P. in which a21 – a7 = 84?

Concept: Arithmetic Progression
Chapter: [2.02] Arithmetic Progressions
[1] 2

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[1] 3

If a tower 30 m high, casts a shadow 10sqrt3 m long on the ground, then what is the angle of elevation of the sun?

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[1] 4

The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[2] 5

Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.

Concept: Nature of Roots
[2] 6

Which term of the progression 20, 191/4,181/2,173/4, ... is the first negative term?

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[2] 7

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[2] 8

A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[2] 9

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.

Concept: Coordinate Geometry
Chapter: [6.01] Lines (In Two-dimensions) [6.01] Lines (In Two-dimensions)
[2] 10

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[3] 11

If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots.

Concept: Nature of Roots
[3] 12

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[3] 13

On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[3] 14

A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

Concept: Simple Problems on Single Events
Chapter: [5.01] Probability
[3] 15

In what ratio does the point (24/11, y) divide the line segment joining the points P(2, –2) and Q(3, 7)? Also find the value of y.

Concept: Section Formula
Chapter: [6.01] Lines (In Two-dimensions)
[3] 16

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region

Concept: Circumference of a Circle
Chapter: [7.01] Areas Related to Circles [7.01] Areas Related to Circles
[3] 17

In Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]

Concept: Circumference of a Circle
Chapter: [7.01] Areas Related to Circles [7.01] Areas Related to Circles
[3] 18

Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[3] 19

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.

Concept: Frustum of a Cone
Chapter: [7.02] Surface Areas and Volumes
[3] 20

The dimensions of a solid iron cuboid are 4·4 m × 2·6 m × 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe

Concept: Concept of Surface Area, Volume, and Capacity
Chapter: [7.02] Surface Areas and Volumes [7.02] Surface Areas and Volumes
[4] 21

Solve for x :

1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4

Concept: Solutions of Quadratic Equations by Factorization
[4] 22

Two taps running together can fill a tank in 3 1/13 hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?

Concept: Solutions of Quadratic Equations by Completing the Square
[4] 23

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[4] 24

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[4] 25

In the given figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB=90°

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[4] 26

Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are 3/4 times the corresponding sides of ∆ABC.

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
Chapter: [3.02] Triangles
[4] 27

An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use sqrt3 = 1⋅732]

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[4] 28

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k

Concept: Coordinate Geometry
Chapter: [6.01] Lines (In Two-dimensions) [6.01] Lines (In Two-dimensions)
[4] 29

Two different dice are thrown together. Find the probability that the numbers obtained have

1) even sum, and

2) even product.

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[4] 30

In the given figure, ABCD is  rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Concept: Area of Circle
Chapter: [7.01] Areas Related to Circles
[4] 31

In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

Concept: Concept of Surface Area, Volume, and Capacity
Chapter: [7.02] Surface Areas and Volumes [7.02] Surface Areas and Volumes

#### Request Question Paper

If you dont find a question paper, kindly write to us

View All Requests

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students

only jpg, png and pdf files

## CBSE previous year question papers Class 10 Mathematics with solutions 2016 - 2017

CBSE Class 10 Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our CBSE Class 10 Maths question paper 2017 serve as a catalyst to prepare for your Mathematics board examination.
Previous year Question paper for CBSE Class 10 Maths-2017 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 10.

How CBSE Class 10 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.