# Mathematics Delhi Set 1 2011-2012 English Medium Class 10 Question Paper Solution

Mathematics [Delhi Set 1]
Date: March 2012

[1] 1

If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals: ?

A. 3

B. -7/2

C. 6

D. −3

[1] 2

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

A. 11

B. 10

C. 14

D. 15

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
[1] 3

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

A. 11

B. 10

C. 14

D. 15

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
[1] 4

In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:

A. 18

B. 13.5

C. 12

D. 9

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
[1] 5

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

1 : 2

2 : 1

1 : 4

4 : 1

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[1] 6

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:

A. 34

B. 26

C. 17

D. 14

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
[1] 7

The length of shadow of a tower on the plane ground is sqrt3 times the height of the tower.

The angle of elevation of sun is:

A. 45°

B. 30°

C. 60°

D. 90°

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[1] 8

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:

A. (−6, 7)

B. (6, −7)

C. (6, 7)

D. (−6, −7)

Concept: Section Formula
Chapter: [6.01] Lines (In Two-dimensions)
[1] 9

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:

A. (2, 4)

B. (3, 5)

C. (4, 2)

D. (5, 3)

Concept: Area of a Triangle
Chapter: [6.01] Lines (In Two-dimensions)
[1] 10

Two dice are thrown together. The probability of getting the same number on both dice is.

A1/2

B1/3

C1/6

D1/12

Concept: Basic Ideas of Probability
Chapter: [5.01] Probability [5.01] Probability
[2] 11

Find the value(s) of k so that the quadratic equation x2 − 4kx + k = 0 has equal roots.

Concept: Area of a Triangle
Chapter: [6.01] Lines (In Two-dimensions)
[1] 12

Find the sum of all three digit natural numbers, which are multiples of 11.

Concept: Arithmetic Progressions Examples and Solutions
Chapter: [2.02] Arithmetic Progressions
[2] 13

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.

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] 14 | attempt any one of the following
[1] 14.1

In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

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
[1] 14.2

In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

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] 15

The volume of a hemisphere is 24251/2cm^3cm. Find its curved surface area?

Concept: Volume of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[2] 16

In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. [\text\ User=22/7]

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[2] 17

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[2] 18

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

Concept: Probability - A Theoretical Approach
Chapter: [5.01] Probability
[3] 19
[2] 19.1

Solve for x:

4x2 + 4bx − (a2 − b2) = 0

Concept: Solutions of Quadratic Equations by Factorization
[1] 19.2

Solve for x: 3x^2-2sqrt6x+2=0

[3] 20
[1] 20.1

Prove that a parallelogram circumscribing a circle is a rhombus.

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[2] 20.2

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Concept: Number of Tangents from a Point on a Circle
Chapter: [3.01] Circles
[3] 21

Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then 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
[3] 22

In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and

3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. [User22/7]

Concept: Areas of Combinations of Plane Figures
Chapter: [7.01] Areas Related to Circles
[3] 23
[2] 23.1

From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User pi22/7]

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[1] 23.2

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm. Find the radius and slant height of the heap.

Concept: Conversion of Solid from One Shape to Another
Chapter: [7.02] Surface Areas and Volumes
[3] 24

The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the lighthouse.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[3] 25

A point P divides the line segment joining the points A(3, -5) and B(-4, 8) such that (AP)/(PB) = k/1. If P lies on the line x + y = 0, then find the value of k.

Concept: Section Formula
Chapter: [6.01] Lines (In Two-dimensions)
[3] 26

If the vertices of ΔABC  be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p

Concept: Coordinate Geometry
Chapter: [6.01] Lines (In Two-dimensions) [6.01] Lines (In Two-dimensions)
[3] 27

A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.

Concept: Probability - A Theoretical Approach
Chapter: [5.01] Probability
[3] 28

The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find  its nth term.

Concept: nth Term of an AP
Chapter: [2.02] Arithmetic Progressions
[4] 29 | attempt any one of the following
[2] 29.1

A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.

Concept: Real Numbers Examples and Solutions
Chapter: [1.01] Real Numbers
[2] 29.2

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

Concept: Solutions of Quadratic Equations by Factorization
[4] 30

Sum of the first 14 terms of and AP is 1505 and its first term is 10. Find its 25th term.

Concept: Arithmetic Progressions Examples and Solutions
Chapter: [2.02] Arithmetic Progressions
[4] 31 | attempt any one of the following
[2] 31.1

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
[2] 31.2

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC ?

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] 32

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. (Use π = 22/7).

Concept: Volume of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[4] 33

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Usepi22/7 ]

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[4] 34

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

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

#### 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 2011 - 2012

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 2012 serve as a catalyst to prepare for your Mathematics board examination.
Previous year Question paper for CBSE Class 10 Maths-2012 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.