SSC CHSL 3 July 2019 Shift-3

Let $$\triangle ABC \sim \triangle QPR  and  \frac{ar(\triangle ABC)}{ar(\triangle PQR)} = \frac{9}{4}$$. If AB = 12 cm, BC = 6 cm and AC = 9 cm,then QR is equal to: 

In $$\triangle$$ABC, AD is the bisector of $$\angle$$BAC, meeting BC at D. If AC = 21 cm, BC = 12 cm and the length of BD is 2 cm less than DC, then the length of side AB is: 

If $$8(x + y)^3 - (x - y)^3 = (x + 3y)(Ax^2 + Bxy + Cy^2)$$, then the value of (A - B - C) is:

An article is sold for ₹360 after allowing discount of 20% on its marked price. Had the discount not been allowed, the profit would have been 50%. The cost price of the article is:

If $$9a^2 + 16b^2 + c^2 + 25 = 24 (a + b)$$, then the value of (3a + 4b + 5c) is:

Two trains of equal length travelling in opposite directions at 72 km/h and 108 km/h crosseach otherin 10 seconds. In how much time(in seconds) doesthefirst train cross a platform of length 350 m?

An article is sold for ₹x. If it is sold at $$33\frac{1}{3}$$% of this price, there is a loss of 20%. What is the percentage profit when it is sold for ₹x ?

If $$\tan x = \cot(60^\circ + 6x)$$,then what is the value of x ?

If $$\left(\frac{1}{1 + \cosec \theta} - \frac{1}{1 - \cosec \theta}\right) \cos \theta = 2, 0^\circ < \theta < 90^\circ$$, then the value of $$\sin^2 \theta + \cot^2 \theta + \sec^2 \theta$$ is:

What is the simplified value of $$5 \div 10  of  10 \times 4 + 4 \div 4  of  4 \times 10 - (10 - 4) \div 16 \times 4 =  ?$$