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 QuestionsShort Answer Type

1.

If the quadratic equation haspx squared minus 2 square root of 5px plus 15 equals 0 two roots, then find the value of p.

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2.

In Given figure, a tower AB is 20 m high and BC, its shadow on the ground, is m20 square root of 3 long. Find the sun's altitude.

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3.

The different dice are tossed together. Find the probability that the product of the two number on the top of the dice is 6.


When two dice are thrown simultaneously, the possible outcomes can be listed as:


 

1

2

3

4

5

6

1

(1, 1)

(1, 2)

(1, 3)

(1, 4)

( 1, 5)

(1, 6)

2

(2, 1)

(2, 2)

(2, 3)

(2, 4)

(2, 5)

(2, 6)

3

(3, 1)

(3, 2)

(3, 3)

(3, 4)

(3, 5)

(3, 6)

4

(4, 1)

(4, 2)

(4, 3)

(4, 4)

(4, 5)

(4, 6)

5

(5, 1)

(5, 2)

(5, 3)

(5, 4)

(5, 5)

(5, 6)

6

(6, 1)

(6, 2)

(6, 3)

(6, 4)

(6, 5)

(6, 6)


∴ Total number of possible outcomes = 36

The outcomes favourable to the event the product of the two number of the top of the dice is 6 denoted by E are (1, 6), (2, 3), (3, 2) and (6, 1)

∴ Number of favourable outcomes = 4

straight P space left parenthesis space straight E right parenthesis space equals space fraction numerator Favourable space number space of space outcomes over denominator Total space number space of space outcomes end fraction
equals space 4 over 36

space equals space 1 over 9

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4.

In the given figure, PQ is a chord of a circle with centre O and PT is tangent. If ∠QPT = 60o, find ∠ PRQ.

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5.

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120o, then prove that OR = PR + RQ.

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6.

In the given figure, a triangle ABC is drawn to circumscribe of radius 3 cm, such that the segments RD and DC are respectively of length 6 cm and 9 cm. If the area of ΔABC is 54 cm2, then find lengths of sides AB and AC.

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7.

Solve the following quadratic equation for x,

4x2 + 4bx - (a2 - b2) = 0

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8.

In an AP, if S5 + S7 = 167 and S10 = 235, then find the AP,  Where Sn denotes the sum of its first n terms.

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9.

The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p.

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10.

Find the relation between x and y if the points A (x, y), B (-5, 7) and C (-4, 5) are collinear.

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