Tripura Board Class 10 2026 Mathematics (Basic) Question Paper with Solution PDF : Available Here

In the AP: \( \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \dots \), the common difference is:

• (A) -1
• (B) 2
• (C) 1
• (D) 4

If the radius of a sphere is 3 cm, then its volume is:

• (A) \( 4\pi r^3 \) cm\(^3\)
• (B) \( \frac{4}{3} \pi r^3 \) cm\(^3\)
• (C) \( 4\pi r^2 \) cm\(^3\)
• (D) \( \frac{3}{4} \pi r^3 \) cm\(^3\)

The two roots of the quadratic equation \( x^2 - 4 = 0 \) are:

• (A) 2, 2
• (B) -2, 2
• (C) -2, -2
• (D) 2, 0

In the equation \( 2x - 3y = 5 \), if the value of \( y \) is 3, then the value of \( x \) is:

• (A) -7
• (B) 14
• (C) 7
• (D) -14

The distance of the point \( P(-6, 0) \) from the origin is:

• (A) 36
• (B) 3
• (C) 6
• (D) -6

For what value of k, \(x-3y=7\) and \(kx+6y=5\) will have no solution?

Find the quadratic polynomial whose sum and product of zeros are 6 and -2 respectively.

Find the value of \(p(x) = x^2 + x + 1\) when \(x = -1\).

In the given figure, the angle of elevation of the top of a tower AC from a point B on the ground is \(60^\circ\). If the height of the tower is 20m, find the distance of the point from the foot of the tower.

A die is thrown once. Find the probability of getting (i) a prime number (ii) an odd number.

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Find the area of the triangle whose vertices, taken in order are (-4, -2), (-3, -5) & (3, -2).

The cost of fencing a circular field at the rate of Rs. 24 per meter is Rs. 5280. The field is ploughed at the rate of Rs. 0.50 per m². Find the cost of ploughing the field. (Take \( \pi = \frac{22}{7} \))

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Prove that the lengths of tangents drawn from an external point to a circle are equal and they subtend equal angles at the center.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center.

Evaluate \(-5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan 45^\circ\)

If \(\cot \theta = \frac{7}{8}\), then evaluate \[ \frac{(1 + \sin \theta)(1 - \sin \theta)}{(1 + \cos \theta)(1 - \cos \theta)} \]

Two coins are tossed simultaneously. What is the probability of getting (i) at least one head (ii) no head?

Find the L.C.M of 17, 23, and 29.

If \( \tan A = \cot B \), prove that \( A + B = 90^\circ \).