Mathematics

CBSE Class 10

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If the quadratic equation has two roots, then find the value of p.

The given quadratic equation has two equal roots.

therefore,

by using the discriminant method

⇒ 20p^{2} - 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 m 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 = 60^{o}, 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 = 120^{o}, 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 cm^{2}, then find lengths of sides AB and AC.

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8.

In an AP, if S_{5} + S_{7} = 167 and S_{10} = 235, then find the AP, Where S_{n} 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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