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For how many integers, n, the expression n2 + n + 4 is a perfect square?

A cube is divided into two parts by a plane passing through three non-adjacent vertices. Find the ratio of volume of the smaller part to that of large...

100 liters of milk solution with concentration of 40% is heated so as to evaporate the water. After the heating process is over, concentration of milk...

If it is known that B is a multiple of 5 and C an odd number, then which of the following is possibly A’s unit digit, given that 3A2 + 2B2 = C2 An...

Find the total number of even factors of the L.C.M. of first 25 natural numbers.

ABCD is a square. P and Q are points on the sides, as shown, such that BP: PC = 3: 1 and BQ: AQ = 2: 1. Find the ratio of the area of the shaded re...

The parallel sides of a trapezium are of 6 units and 8 units respectively. Find the length of the line segment parallel to these sides and which divid...

In a circle of radius r units, six points equally spaced are placed on the circumference. ΔABC is formed by joining three points such that ΔABC is nei...

(3,-2), (12,4) and (-3,7) are the three vertices of a triangle. Then the distance between the orthocenter and circumcenter of this triangle is-

What's the length of largest equilateral triangle that can be inscribed in an equilateral triangle of side length 1?

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0.01 1 10 100

The coefficient of x6 in the expansion of (x2-6x+3).(1+x)7 is: 49 70 -63 -70

Two kayak racing champions Santa and Banta challenge each other to a 12 km downstream kayak race. Santa rows downstream at 6kmph whereas Banta rows th...