SSC CGL 4th March 2020 Shift-1

In $$\triangle ABC, \angle A = 90^\circ$$, M is the midpoint of $$BC$$ and $$D$$ is a point on $$BC$$ such that $$AD \perp BC$$. If $$AB = 7$$ cm and $$AC = 24$$ cm, then $$AD : AM$$ is equal to:

On simplification, $$\frac{x^3 - y^3}{x[(x + y)^2 - 3xy]} \div \frac{y[(x - y)^2 + 3xy]}{x^3 + y^3} \times \frac{(x + y)^2 - (x - y)^2}{x^2 - y^2}$$ is equal to:

If $$5x + \frac{1}{3x} = 4$$, then whatis the value of $$9x^2 + \frac{1}{25x^2}$$?

The given table represents the number of computers sold by four dealers A, B, C and D during the first six months of 2016. Study the table carefully and answer the question that follows.

The total number of computers sold by dealer A during February to June is what percentage more than the total number of computers sold byall the dealers in June? (Correct to one decimal place)

The average of twelve numbers is 45.5. The averageof the first four numbers is 41.5 and that of the next five numbers is 48. The $$10^{th}$$ numberis 4 more than the $$11^{th}$$ number and 9 more than the $$12^{th}$$ number. Whatis the average of the $$10^{th}$$ and $$12^{th}$$ numbers?

The value of $$\frac{\tan 30^\circ \cosec 60^\circ + \tan 60^\circ \sec 30^\circ}{\sin^2 30^\circ + 4 \cot^2 45^\circ - \sec^2 60^\circ}$$ is:

Sonu saves 15% of her income. If her income increases by 20% and she still saves the same amount as before, then what is the percentage increase in her expenditure? (correct to one decimal place)

When 732 is divided by a positive integer x, the remainder is 12. How many values of x are there?

The circumference of the base of a conical tent is 66 m.If the height of the tent is 36 m, what is the area (in m$$^2$$) of the canvas used in making the tent?(Take $$\pi = \frac{22}{7}$$)

If a + b + c = 11, ab + bc + ca = 3 and abc = —135, then what is the value of $$a^3 + b^3 + c^3$$?