SSC CGL Tier-2 29th January 2022 Maths

Three fractions x, y and z are such rhat x > y > z. When the smallest of them is divided by the greatest, the result is $$\frac{9}{16}$$, which exceeds y by 0.0625 . If  x+y+z=$$2\frac{3}{12}$$, then what is the value of x+z?

If $$x^{2}-\sqrt{7}x+1=0$$, then what is the value of $$x^{5}+\frac{1}{x^{5}}$$?

The total surface area of a cylinder is 4092 $$cm^{2}$$ and the diameter of its base is 21 cm. What is 50% volume (in $$cm^{3}$$) of the cylinder ( nearest to an integer)

The value of $$\frac{4 \tan^{2}30^{\circ}+\sin^{2}30^{\circ}\cos^{2}45^{\circ}+\sec^{2}48^{\circ}-\cot^{2}42^{\circ}}{\cos37^{\circ}\sin53^{\circ}+\sin37^{\circ}\cos53^{\circ}+\tan18^{\circ}\tan72^{\circ}}$$ is?

The radius of the base of a cylindrical tank is 4 m. If three times the sum of the areas of its two circular faces is twice the area of its curved surface, then the capacity (in kilolitres) of the tank is:

If $$\frac{22\sqrt{2}}{4\sqrt{2} - \sqrt{3 + \sqrt{5}}} = a + \sqrt{5}b$$, with a, b > 0, then what is the value of $$(ab):(a + b)?$$

Two pipes A and B can fill a cistern in $$12\frac{1}{2}$$ hours and 25 hours, respectively. The pipes were opened simultaneously, and it was found that, due to leakage in the bottom, it took one hour 40 minutes more to fill the cistern. If the cistern is full, in how much time (in hours) will the leak alone empty 70% of the cistern?

In $$\triangle ABC, \angle A = 66^\circ$$ and $$\angle B = 50^\circ$$. If the bisectors of $$\angle B$$ and $$\angle C$$ meet at P, then $$\angle BPC - \angle PCA = ?$$

A tap can fill a tank in $$5\frac{1}{2}$$ hours. Because of a leak, it took $$8\frac{1}{4}$$ hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?

The monthly expenses of a person are $$66\frac{2}{3}\%$$ more than her monthly savings. If her monthly income increases by 44% and her monthly expenses increase by 60%, then there is an increase of ₹1,040 in her monthly savings. What is the initial expendirure (in ₹)?