Find the value of  cot3A-3cotA/3 cot2A-1 (a)          cot²2A + tan²A (b)          tan²2A + cot²A (c)           tan3A ...

Ram travels a certain distance from his room at a constant speed. If his speed was 6km faster than he would take 18 hours less than the scheduled time. If he was 4km/hr. slow, he would take 14 hours more than the scheduled time. Find the distance covered by Ram? (a) 13530km (b) 13440km ...

In the figure, PQR is a right angle triangle with angle Q = 90, QR = 17.5 cm and PQ = 42 cm, with PR as a diameter of a semicircle and with QR as radius, a quarter circle is drawn. Find th e area of the shaded portion correct to two decimal places (a) 3380.125 cm² (b) 3540.251 (c) ...

Two solid hemisphere of radius 9 cm and 7 cm respectively are melted to form a metallic cone of radius 15 cm, what is the height of the cone (in cm) (a)          9.52 cm (b)          8.76 cm ...

A certain bank offers 7% rate of interest on the 1st year and 8% on the 2nd year in a certain fixed deposit scheme (compounded annua). If 17,334are received after investing for 2 years in this scheme, then what was the amount invested? (a) 15500 (b) 16000 (c) 15000 (d) 16500 Sol: ...

Two company invest Rs. 125000 and Rs. 85000 respectively in education industry and agree that 60% of the profit should be divided equally between them and the remaining profit is divided in the ratio of their capital invested. If one company gets Rs.300 more than the other, then find total profit ...

In a class of 78 students, 33.33% are girls and the remaining are boys. The average of the boys’ marks is 77 and that of average of whole class is 65. What are the average marks of the girls? (a) 51.5 (b) 41 (c) 43.25 (d) 53 Sol: Boys: Girls  52 : 26  2 : 1 Avg ...

A man alternatively tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is? (a)  3/4 (b)  1/2 (c)  1/3 (d)  1/7 Sol:

The top of two trees of height 75 metres and 45 metres are connected by a wire. If the rope makes an angle with the horizontal whose tangent is 6/13 metres, then what is the distance (in metres) between the two trees? (a)          60 ...

A polygon has 77 diagonals. Then what is the number of sides of the same polygon? (a)          11 (b)          15 (c)           14 ...

A cylindrical vessel of radius 20.3 m is full of water. If 10749662 liters of water is taken out from it, then find the drop in the water level in the vessel. (a) 9.2 (b) 9.4 (c) 8.3 (d) 6.8 Sol: Volume of cylindrical vessel = πr²h ATQ, ∵ Drop in water level is equal to ...

In a mixture, milk and water are in ratio of 2:3. Some milk is added to the mixture because of which ratio of milk and water becomes 2:1. How much milk was added as a percentage of initial mixture? (a) 75% (b) 60% (c) 80% (d) 50% Sol: