Practice SSC CGL 2024 Tier 2 Paper 1 Question Paper – 20 Jan 2025 (with Solutions)

In the given figure, ABCD is a quadrilateral in which diagonal \(BD = 70\text{ cm},\) AL is perpendicular to BD and CM is perpendicular to BD such that \(AL = 17\text{ cm}\) and \(CM = 21\text{ cm}.\) Calculate the area of the quadrilateral ABCD.

A tank when full can be emptied by an outlet pipe A in 5.6 hours, while an inlet pipe B can fill the same empty tank in 7 hours. If pipes A and B are turned on alternatively for 1 hour each starting with pipe A when the tank is full, how long will it take to empty the tank?

If a: \(b = 2 : 3,\) \(b : c = 5\): 7, then find the ratio \(c\): a.

In a circle centered at O, a diameter AB is extended to a point C outside the circle. CD is a tangent at point D on the circle. If \(CD = 7\sqrt{3}\text{ cm}\) and \(\angle DBC = 120^{\circ},\) then the length of the diameter of the circle is equal to:

If \(x = 4 + \sqrt{6}\) and \(y = 4 - \sqrt{6}\) then the value of \(x^{2} + y^{2}\) is:

If cos27° = \(\frac{p}{q}\), then find the value of \(\operatorname{cosec} 27^{\circ} - \cos 63^{\circ}.\)

The average of first 92 even numbers is

Simplify \((5z - 7y)^{2}\) \({}+ (7z + 5y)^{2}\) \({}- 49z^{2}\)

Let PQR be a right angled triangle, right-angled at R. Let \(PQ = 29\text{ cm},\) \(QR = 21\text{ cm}\) and \(\angle Q = \theta.\) Find the value of cos²θ – sin²θ.

Simplify the following expression: \(\dfrac{a^{5} \times b^{3} \times c^{7}}{a^{4} \times b^{8} \times c^{9}}\)