Subject

Mathematics

Class

CBSE Class 10

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

Download the PDF Sample Papers Free for off line practice and view the Solutions online.
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 Multiple Choice QuestionsMultiple Choice Questions

1.

The length of shadow of a tower on the plane ground is 3 times the height of the tower. The angle of elevation of sun is

  • 450

  • 300

  • 600

  • 900


2.

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

  • 34

  • 26

  • 17

  • 14


3.

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


4.

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

  • 12

  • 13

  • 16

  • 112


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5.

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

  • ( 2, 4 )

  • ( 3, 5 )

  • ( 4, 2 )

  • ( 5, 3 )


6.

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

  • 3

  • -72

  • 6

  • -3


7.

In Fig., 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

                        

  • 11

  • 10

  • 14

  • 15


8.

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

                            

  • 18

  • 13.5

  • 12

  • 9


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 Multiple Choice QuestionsShort Answer Type

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9.

If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5) then find the value of p.


It is given that the point  A(0, 2) is equidistant from the points B(3, p) and C(p, 5).

So, AB = AC  AB2 = AC2

Using distance formula, we have

 ( 0 - 3 )2 + (2 - p )2 = ( 0 - p )2 = ( 2 - 5 )2

 9 + 4 + p2 - 4p = p2 + 9

4 - 4p = 0

 p = 1

Hence, the value of p = 1.


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10.

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


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