SSC CGL 19th April 2022 Shift-3

If $$\left(x + y\right)^{3} - \left(x - y \right)^{3} - 3y\left(2x^{2} - 3y^{2}\right) = ky^{3}$$ , then find the value of k.

The bar graph shows the number of people who visited Mall A and Mall B on different days of a week.

What is the ratio of the number of people visiting Mall A on Thursday. Saturday and Sunday together to the number of people visiting Mall B on these three days together?

In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2BD. If AC - AB = 5 cm, then find
the length of AB (in cm).

A shopkeeper bought 60 pencils at a rate of 4 for ₹5 and another 60 pencils at a rate of 2 for ₹3. He mixed all the pencils and sold them at a rate of 3 for ₹4. Find his gain or loss percentage.

In a circle with centre O and of radius 13 cm, two parallel chords are drawn on different sides of the centre. If the length of one chord is 10 cm and the distance between the two chords is 17 cm, then find the difference in lengths of the two chords (in cm).

A and B entered into a partnership with certain investments. At the end of 8 months, A withdrew and collected back his money. A and B received profit in the ratio 5 : 9 at the end of the year. If B bad invested ₹36,000, then how much (in ₹) had A invested?

A fruit seller sells 45% of the oranges that he has along with one more orange to a customer. He then sells 20% of the remaining oranges and 2 more oranges to a second customer. He then sells 90% of the now remaining oranges to a third customer and is still left with 5 oranges. How many oranges did the fruit seller have initially?

Simplify the following expression:
$$\frac{\cos A}{1-\tan A} + \frac{\sin A}{1- \cot A} - \sin A$$

In a right-angled triangle, the lengths of the medians from the vertices of acute angles are 7 cm and $$4\sqrt{6}$$ cm. What is the length of the hypotenuse of the triangle (in cm)?

Find the greatest 3-digit number which , when divided by 3, 4, 5 and 8, leaves remainder 2 in each case.