# Mathematics Delhi Set 1 2014-2015 English Medium Class 10 Question Paper Solution

Mathematics [Delhi Set 1]
Date: March 2015

[1] 1

If x=1/2, is a solution of the quadratic equation 3x2+2kx3=0, find the value of k

Concept: Nature of Roots of a Quadratic Equation
[1] 2

The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x, y.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[1] 3

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is consonant.

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[1] 4

In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Chapter: [3.01] Circles [3.01] Circles
[2] 5

In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If ∠AOQ = 58°, find ∠ATQ.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Chapter: [3.01] Circles [3.01] Circles
[2] 6

Solve the following quadratic equation for x4x2  4a2x + (a4  b4) =0.

Concept: Solutions of Quadratic Equations by Factorization
[2] 7

From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Chapter: [3.01] Circles [3.01] Circles
[2] 8

Find the middle term of the A.P. 6, 13, 20, ... , 216.

Concept: Arithmetic Progression
Chapter: [2.02] Arithmetic Progressions
[2] 9

If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[2] 10

Find the ratio in which the point P(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2,-5)

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

Find the area of the triangle ABC with A(1, −4) and mid-points of sides through A being (2, −1) and (0, −1).

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

Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.

Concept: Nature of Roots of a Quadratic Equation
[3] 13

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m high, find the height of the building.

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

Two different dice are rolled together. Find the probability of getting the sum of numbers on two dice to be 5.

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

Two different dice are rolled together. Find the probability of getting even numbers on both dice.

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[3] 15

If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).

Concept: Sum of First n Terms of an A.P.
Chapter: [2.02] Arithmetic Progressions
[3] 16

In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use pi=22/7]

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

In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use pi=22/7 and sqrt5=2.236)

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[3] 18

A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 5/6  cm3. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2 .[Usepi=22/7]

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

In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use

pi=22/7]

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[3] 20

In Figure, find the area of the shaded region [Use π = 3.14]

Concept: Circumference of a Circle
Chapter: [7.01] Areas Related to Circles [7.01] Areas Related to Circles
[4] 21

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is 29/20. Find the original fraction.

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

Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

What value is generated in the above situation?

Concept: Sum of First n Terms of an A.P.
Chapter: [2.02] Arithmetic Progressions
[4] 23

Solve for x :

2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2

Concept: Solutions of Quadratic Equations by Factorization
[4] 24

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[4] 25

In Fig. 7, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Chapter: [3.01] Circles [3.01] Circles
[4] 26

Construct a triangle ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.

Concept: Division of a Line Segment
Chapter: [3.03] Constructions
[4] 27

From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.

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

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is divisible by 2 or 3.

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

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[4] 29

If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.

Concept: Area of a Triangle
Chapter: [6.01] Lines (In Two-dimensions)
[4] 30

A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.

Concept: Concept of Surface Area, Volume, and Capacity
Chapter: [7.02] Surface Areas and Volumes [7.02] Surface Areas and Volumes
[4] 31

Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter 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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