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Mathematics All india set 1 2010-2011 CBSE Class 10 Question Paper Solution

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Mathematics
All india set 1
2010-2011 March
Marks: 80

[1]1

The roots of the equation x2 − 3x − m (m + 3) = 0, where m is a constant, are 

A. mm + 3 

B. − mm + 3 

C. m, − (m + 3) 

D. m, − (m + 3) 

Concept: Quadratic Equations
Chapter: [2.03] Quadratic Equations
[1]2

If the common differences of an A.P. is 3, then a20 − a15 is 

A. 5

B. 3

C. 15

D. 20

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[1]3

In figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P.

If ∠POQ = 70°, then ∠TPQ is equal to

A. 55°

B. 70°

C. 45°

D. 35°

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[1]4

In Figure 2, AB and AC are tangents to the circle with centre O such that

∠BAC = 40°. Then ∠BOC is equal to

A. 40°

B. 50°

C. 140°

D. 150°

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[1]5

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

A. a

B. a

C. a

D. 16 a

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[1]6

The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

A. 4.2

B. 2.1

C. 8.4

D. 1.05

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[1]7

A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45°. Then the height (in meters) of the tower is

A. `25sqrt2`

B. `25sqrt3`

C. 25

D. 12.5

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

If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is

A. −8

B. 3

C. −4

D. 4

Concept: Coordinate Geometry Examples and Solutions
Chapter: [6.01] Lines (In Two-dimensions)
[1]9

If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance

2AB is equal to

A. 13

B. 26

C. 169

D. 238

Concept: Distance Formula
Chapter: [6.01] Lines (In Two-dimensions)
[1]10

A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will not be an ace is 

A. `1/13`

B. `1/4`

C. `12/13`

D.`3/4`

Concept: Probability Examples and Solutions
Chapter: [5.01] Probability
[2]11

Find the value of m so that the quadratic equation mx (x − 7) + 49 = 0 has two equal roots.

Concept: Quadratic Equations Examples and Solutions
Chapter: [2.03] Quadratic Equations
[2]12

How many two-digit number are divisible by 6?

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[2]13

In Figure 3, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of the side AD.

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[2]14

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB)=3/5`.

 

 
Concept: Division of a Line Segment
Chapter: [3.03] Constructions
[2]15

Find the perimeter of the shaded region in Figure 4, if ABCD is a square of side 14 cm and APB and CPD are semicircles. Use `pi22/7`

Concept: Areas of Combinations of Plane Figures
Chapter: [7.01] Areas Related to Circles
[2]16 | attempt any one of the following
[2]16.1

Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid. 

Concept: Surface Area of a Combination of Solids
Chapter: [7.02] Surface Areas and Volumes
[2]16.2

A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

Concept: Frustum of a Cone
Chapter: [7.02] Surface Areas and Volumes
[2]17

Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.

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

A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. Find the probability that the selected ticket has a number which is a multiple of 5.

Concept: Simple Problems on Single Events
Chapter: [5.01] Probability
[3]19

Find the roots of the following quadratic equation: 

`x^2-3sqrt5x+10=0`

Concept: Quadratic Equations
Chapter: [2.03] Quadratic Equations
[3]20

Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[3]21

In Figure 5, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of ΔPQR = 189 cm2, then find the lengths of sides PQ and PR.

Concept: Tangent to a Circle
Chapter: [3.01] Circles
[2]22 | attempt any one of the following
[2]22.1

Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°. 

Concept: Construction of Tangents to a Circle
Chapter: [3.03] Constructions
[2]22.2

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
[3]23

A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. `[User pi22/7 and sqrt3=1.73]`

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[3]24

An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 30 per litre. `[User pi22/7]`

Concept: Frustum of a Cone
Chapter: [7.02] Surface Areas and Volumes
[3]25

Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

Concept: Concepts of Coordinate Geometry
Chapter: [6.01] Lines (In Two-dimensions)
[3]26 | attempt any one of the following
[3]26.1

Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).

Concept: Coordinate Geometry Examples and Solutions
Chapter: [6.01] Lines (In Two-dimensions)
[3]26.2

Find the area of triangle formed by joining the mid-points of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).

Concept: Areas of Combinations of Plane Figures
Chapter: [7.01] Areas Related to Circles
[3]27

From the top of a vertical tower, the angles depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45°  and 60° . If the cars are 100 m apart and are on the same side of the tower, find the height of the tower.

Concept: Heights and Distances
Chapter: [4.01] Heights and Distances
[3]28 | attempt any one of the following
[3]28.1

Two dice are rolled once. Find the probability of getting such numbers on the two dice, whose product is 12. 

Concept: Probability Examples and Solutions
Chapter: [5.01] Probability
[3]28.2

A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

Concept: Probability Examples and Solutions
Chapter: [5.01] Probability
[4]29

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]30 | attempt any one of the following
[4]30.1

The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

Concept: Sum of First n Terms of an AP
Chapter: [2.02] Arithmetic Progressions
[4]30.2

How many multiples of 4 lie between 10 and 250?

Concept: nth Term of an AP
Chapter: [2.02] Arithmetic Progressions
[4]31 | attempt any one of the following
[4]31.1

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
Chapter: [2.03] Quadratic Equations
[4]31.2

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

Concept: Nature of Roots
Chapter: [2.03] Quadratic Equations
[4]32

In Figure 6, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). `[Use pi=22/7]`

Concept: Circles Examples and Solutions
Chapter: [3.01] Circles
[4]33

Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Concept: Surface Areas and Volumes Examples and Solutions
Chapter: [7.02] Surface Areas and Volumes
[4]34

The angle of elevation of the top of a vertical tower from a point on the ground is 60° . From another point 10 m vertically above the first, its angle of elevation is 30° .Find the height of the tower.

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

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CBSE previous year question papers Class 10 Mathematics with solutions 2010 - 2011

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