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

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 Multiple Choice QuestionsShort Answer Type

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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.


The given quadratic equation haspx squared minus 2 square root of 5px plus 15 equals 0 two equal roots.
therefore,

by using the discriminant method

straight b squared space minus space 4 ac space equals space 0 space.. left parenthesis straight i right parenthesis

straight b space equals space minus 2 square root of 5 straight p

straight a space space equals space straight p

straight c space equals space 15

thus comma space putting space the space value space in space equation space left parenthesis straight i right parenthesis
left parenthesis negative 2 square root of 5 straight p end root right parenthesis squared minus 4 space straight x space straight p space straight x 15 space equals 0

rightwards double arrow space left parenthesis negative 2 square root of 5 straight p right parenthesis squared minus 4 space straight x space straight p space straight x 15 space equals 0


⇒  20p2 - 60p = 0

⇒  20p (p - 3) = 0

⇒  p = 0 or p - 3 = 0

⇒  p = 0 or p = 3

p cannot be zero.

Hence, the value of p  is 3. 

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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.

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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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