CBSE Class 10 Maths Previous Year Question Paper

If the quadric equation px² – 2√5px + 15 = 0 has two equal roots, then find the value of p.

In figure 1, a tower AB is 20 m high and BC, its shadow on the ground, is 20√3 m long. Find the Sun’s altitude.

Two different dices are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.

In figure 2, PQ is a chord of a circle with center O and PT is a tangent. If ∠ QPT = 60°, find ∠PRQ.

In figure 3, two tangents RQ and RP are drawn from an external point R to the circle with center O. If ∠PRQ = 120°, then prove that OR = PR + RQ.

In figure 4, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of ∆ABC is 54 cm², then find the lengths of sides AB and AC.

Solve the following quadric equation for x :

4x² + 4bx – (a² – b²) = 0

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

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

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