SSC CGL Tier l 2023 Question Paper Shift 3 (July 18th)

If $$a^{2} + b^{2} + c^{2} = ab + bc + ac$$, then the value of $$\frac{11a^{4} + 13b^{4} + 17c^{4}}{17a^{2}b^{2} + 9b^{2}c^{2} + 15c^{2}a^{2}}$$ is:

D and E are points on the sides AB and AC, respectively of $$\triangle ABC$$ such that DE is parallel to BC and AD : DB - 7 : 9. If CD and BE intersect each other at F. then find the ratio of areas of $$\triangle DEF$$ and $$\triangle CBF$$.

A and B are equally efficient, and each could individually complete a piece of work in 30 days, if none took any holiday. A and B started working together on this piece of work, but A took a day off after every four days of work, while B took a day off after every five days of work. If the duo had started work on 01 August 2022, on which date was the work completed?

A conical tent with radius 6 units and height 8 units is to be made by canvas. How much canvas is needed to make the tent? (Rounded off to two places of decimals)

The smallest number added to 888 so that it is exactly divisible by 35 is:

The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.

A alone can finish a work in 15 days. A works only for the first two days and last two days. The rest work is done by B and the work is completed in 20 days. In how many days A and B together can finish the work?

The value of $$51 \div \left\{25 + \left(25 \ of \ 12 \div 30\right) - \left(5^{4} \div 5 \ of \ 125\right)\right\}$$

If $$\sin(5x - 25^{\circ}) - \cos(5y + 25^{\circ})$$, where $$5x - 25^{\circ}$$ and $$5y+ 25^{\circ}$$ are acute angles, then the value of $$(x + y)$$ is:

A and B can finish a work in 10 days, B and C can finish it in 12 days and C and A can finish in 6 days. In how many days A alone can finish the work?