March 2024

Find the maximum possible value of  sec2 θ+cos2 θ a) 17/4 b) 2 c) not defined d) 19/4

As shown in the given figure, inside the large semicircle, three semicircles (with equal radii) are drawn so that their diameters all sit on the large semicircle’s diameter. What is the ratio between the red and blue areas? a) 1:3 b) 1:2 c) 1:4 d) 2:3 Sol: Let the diameter of bigger circle be 6R.

A boat moves downstream at the rate of 1 km in 7.5 minutes and upstream at the rate of 5 km an hour. Find the speed of boat in still water. a)            8.5 km/h b)            6.5 km/h c)            7.00 km/h d)            8.00 km/h Sol: Speed of boat in still water = xkm/h (say) and that

A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could

The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area. a) 3010.5 b) 3391.2 c) 3232.3 d) 3555.4 Sol: Let the height be 7x and radius be 5x  According to the question,  Volume = π (5x)2 × 7x  ⇒ 14836.5

In the given figure, CD is angle bisector and AD = AM then find    = ? , if ∠ABC = 47°. a) 53° b) 143° c) 47° d) None of these Sol:

In the fig. CD = DE, BC = 4 cm, AE = 3 cm, ∠A = 90°. ABCD is a quadrilateral and EFGB is a square. Find the area of the square EFGB? a)            4 cm² b)            16 cm² c)            2 cm² d)            36 cm² Sol: Construction- join BD Let AD = y, EB =

Find the number of zeroes at the end of the product 2 × 4 × 6 × 8 × 10 … × 180 a) 1 b) 0 c) 21 d) 120 Sol: 2 × 4 × 6 × 8 × 10 … × 180  ⇒ 290(1 × 2 × 3 × 4 × 5 ×

If the 6-digit numbers x35624 and 1257y4 are divisible by 11 and 72, respectively, then what is the value of (5x-2y)?  (a) 14 (b) 12 (c) 10 (d) 13 Sol: In such questions directly check divisibility by 11, 9 and 8. For a number to be divisible by 11, the difference of the sum of

The price of tea increases by 32%, therefore the expenditure on tea increase by 10%. If 10 kg tea was bought earlier, then what is the quantity can buy now? a) 12 kg b) 8 1/3kg c) 6 2/3kg d) 9kg Sol: Let original price of the tea is and consumption after increase in price