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Mathematics Delhi Set 3 2016-2017 CBSE Class 10 Question Paper Solution

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

[1]1

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]2

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]3

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
[1]4

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
[2]5

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]6

Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5

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

In the figure, AB and CD are common tangents to two circles of unequal radi. Prove that AB = CD

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[3]11

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]12

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]13

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]14

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]15

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]16

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]17

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]18

If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n)

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

A solid metallic sphere of diamter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.

Concept: Surface Areas and Volumes Examples and Solutions
Chapter: [7.02] Surface Areas and Volumes
[3]20

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.

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

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]22

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]23

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]24

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]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

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]29

If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.

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

An observer finds the angle of elevation of the top of the tower from a certain point on the ground as 30°. If the observe moves 20 m towards the base of the tower, the angle of elevation of the top increases by 15°, find the height of the tower.

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

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

Concept: Volume of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes

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