SSC CGL 5th Dec 2022 Shift-3

Simplify the following. $$25^{3} - 75^{3} + 50^{3}$$

Find the greatest 5-digit number which is divisible by 11, 33, 99 and 121.

If $$\tan A = \frac{2}{3}$$, then ,what is the value of the following?
$$(5 \sin^{2}A - 2 \cos^{2}A) + (15 \sin^{2}A + 3 \cos^{2}A)$$

The given bar graph shows the data of production of pulses (in lakh tonnes) by three different countries X, Y and Z over the years. Study the bar graph and answer the question that follows.

For which country is the average production (in lakh tonnes) for five years the maximum?

The fourth proportion to 12, 24 and 27 is the same as the third proportion to A and 36.
What is the value of A?

If $$\theta$$ is an acute angle and $$\tan\theta + \cot\theta = 2$$, then the value of $$\tan^{2}\theta + \cot^{2} \theta + 2 \tan^{5}\theta \cot^{4}\theta$$ is:

A shopkeeper offers three types of discount schemes for buyers. Which of them has the maximum discount percentage?
I. Two successive discounts of 10% each.
II. Successive discounts of 15% and 5%.
III. 20% discount.

The lengths (in cm) of three sides of a triangle are, respectively, 48, 55 and 73. What is the length (in cm) of the median joining the mid-point of the longest side to its opposite vertex?

What is the smallest number that should be added to 4567 so that the sum is divisible by 7?

A businessman cheats by using faulty weights, to the tune of 12% each time, when buying and selling material. What is the rise in his profit percentage using faulty weights only?