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Mathematics Delhi Set 2 2016-2017 CBSE Class 10 Question Paper Solution

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Mathematics [Delhi Set 2]
Marks: 90Date: 2017-04-02
Duration: 3h

[1]1

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

Concept: Simple Problems on Single Events
Chapter: [5.01] Probability
[1]2

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[1]3

The ratio of the height of a tower and the length of its shadow on the ground is `sqrt3 : 1`. What is the angle of elevation of the sun?

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

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Concept: Surface Areas and Volumes Examples and Solutions
Chapter: [7.02] Surface Areas and Volumes
[2]5

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[2]6

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[2]7

Find the roots of the following quadratic equations by factorisation

`sqrt2 x^2 +7x+ 5sqrt2 = 0`

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [2.03] Quadratic Equations
[2]8

Find how many integers between 200 and 500 are divisible by 8.

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[2]9

Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.

Concept: Nature of Roots
Chapter: [2.03] Quadratic Equations
[2]10

Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.

Concept: Division of a Line Segment
Chapter: [3.03] Constructions
[3]11

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (`7/2`, y). Find the value of y

Concept: Area of a Triangle
Chapter: [6.01] Lines (In Two-dimensions)
[3]12

Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles

Concept: Similarity of Triangles
Chapter: [3.02] Triangles
[3]13

Two different dice are thrown together. Find the probability that the numbers obtained have a sum less than 7

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

Two different dice are thrown together. Find the probability that the numbers obtained have a product less than 16

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

In a simultaneous throw of a pair of dice, find the probability of getting a doublet of odd numbers

Concept: Probability - A Theoretical Approach
Chapter: [5.01] Probability
[3]14

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[3]15

Find the sum of n terms of the series `(4 - 1/n) + (4 - 2/n) + (4 - 3/n)+ ......`

Concept: nth Term of an AP
Chapter: [2.02] Arithmetic Progressions
[3]16

If the equation (1 + m2) x2 + 2mcx + c2 – a2 = 0 has equal roots then show that c2 = a2 (1 + m2)

Concept: Quadratic Equations
Chapter: [2.03] Quadratic Equations
[3]17

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

Concept: Areas of Sector and Segment of a Circle
Chapter: [7.01] Areas Related to Circles
[3]18

If the mth term of an A.P. be `1/n` and nth term be `1/m`, then show that its (mn)th term is 1.

Concept: Arithmetic Progression
Chapter: [2.02] Arithmetic Progressions
[3]19

A metallic solid sphere of radius 10.5 cm is melted and recasted into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made?

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

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[4]21

In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water.

Concept: Surface Areas and Volumes Examples and Solutions
Chapter: [7.02] Surface Areas and Volumes
[4]22

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.

Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
Chapter: [7.01] Areas Related to Circles
[4]23

Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25

Concept: Concept Or Properties of Probability
Chapter: [5.01] Probability
[4]24

A chord PQ of a circle of radius 10 cm substends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle.

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[4]25

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]26

Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Concept: Pair of Linear Equations in Two Variables
Chapter: [2.01] Pair of Linear Equations in Two Variables
[4]27

If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[4]28

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are `3/5` times the corresponding sides of the given triangle.

Concept: Division of a Line Segment
Chapter: [3.03] Constructions
[4]29

If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[4]30

Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height of the tower is 15 m, then find the distance between the points.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[4]31

The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is `1/27` of the given cone, then at what height it is cut from its base?

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

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