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# Mathematics All India Set 1 2016-2017 CBSE Class 10 Question Paper Solution

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Mathematics [All India Set 1]
Marks: 90Academic Year: 2016-2017
Date & Time: 2nd April 2017, 12:30 pm
Duration: 3h

1

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

Concept: Arithmetic Progression
Chapter: [2.02] Arithmetic Progressions
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
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
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
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
Chapter: [2.03] Quadratic Equations
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
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
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
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)
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)
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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
Chapter: [2.03] Quadratic Equations
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
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
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
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)
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
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
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
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
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
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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
Chapter: [2.03] Quadratic Equations
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
Chapter: [2.03] Quadratic Equations
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
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
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
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
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
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)
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
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
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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

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

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