SSC CGL 5th March 2020 Shift-2

In $$\triangle ABC, \angle B = 90^\circ$$, If the points D and E are on the side BC such that BD = DE = EC then which of the following is true?

When a positive integer is divided by d, the remainder is 15. When ten times of the same number is divided by d. the remainder is 6. The least possible value of d is:

Reema sold 48 articles for ₹ 2,160 and suffered a loss of 10%. How many articles should she sell for ₹2,016 to earn a profit of 12%?

A and B together borrowed a sum of ₹51,750 at an interest rate of 7%p.a. compound interest in such a way that to settle the loan, A paid as much amount after three years as paid by B after 4 years from the day of borrowing. The sum (in ₹) borrowed by B was:

$$\frac{x^2(x - 4)^2}{(x + 4)^2 - 4x} \div \frac{(x^2 - 4x)^3}{(x + 4)^2} \times \frac{64 - x^3}{16 - x^2}$$ is equal to

The marked price of an item is 25% above its cost price. A shopkeeper sells it, allowing a discount of x % on the marked price. If he incurs a loss of 8%, then the value of x is

What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?

Whatis the value of $$\frac{\cosec(78^\circ + \theta) - \sec(12^\circ - \theta) - \tan(67^\circ + \theta) + \cot(23^\circ - \theta)}{\tan 13^\circ \tan37^\circ \tan45^\circ \tan53^\circ \tan77^\circ}$$

The average of some numbers is 54.6. If 75% of the numbers are increased by 5.6 each, and the rest are decreased by 8.4 each, then what is the average of the numbers so obtained?

Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant which intersects the circle at Q and R such that PQ = 12 cm and PR = 19.2 cm.The length of AB (in cm) is :