Practice SSC CGL 2025 Tier 2 Maths PYQ – 19 Jan 2026 (29 Questions with Solutions)

The diagonals of three faces of a rectangular parallelepiped that meet at a single corner measure \(\sqrt{5}\) cm, \(\sqrt{10}\) cm, and \(\sqrt{13}\) cm. What is the volume of this parallelepiped?

In a triangle \(\Delta PQR,\) \(\angle R = 62^{\circ}.\) The perpendicular bisector of PQ at S meets QR at T. If \(\angle TPR = 38^{\circ},\) what is the measure of \(\angle PQR?\)

In an equilateral triangle, the circumcenter coincides with which of the following?

What is the value of \(\frac{3}{2}\left(\frac{\cos 39^\circ}{\sin 51^\circ}\right)\) \({}-\sqrt{\sin^2 39^\circ+\sin^2 51^\circ}\)?

A set of \(n\) values \(X_1, X_2, \ldots, X_n\) has a standard deviation of 5. The standard deviation of \(n\) values \(X_1-7, X_2-7, \ldots,\) \(X_n-7\) will be:

The given table shows the number of people in different age groups. Find the mean age of the given number of people.

A rectangle is such that its area is \(48\text{ cm}^{2}\) and its perimeter is 28 cm. If a rhombus is formed by joining the midpoints of the sides of this rectangle, what is the area of the rhombus?

If a chord of a circle subtends an angle of 60° at the circumference of the circle, then what is the ratio of the radius of the circle and the length of the chord respectively?

A hemispherical tank is full of water. It is connected to a pipe that empties it at a rate of 7 litres per second. How much approximate time (in minutes) will it take to empty half the tank if the internal radius of the tank is 2.1 meters? (Use \(\pi=\frac{22}{7}\) and \(1\text{ m}^{3} = 1000\text{ liters}\))

In a right-angled triangle ABC, the angle at B is 90°. If \(AB = 6\text{ cm}\) and \(BC = 8\text{ cm},\) what is the distance between the centroid G and the orthocenter H?