List of practice Questions

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?

Let f(x) = 2x-5and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

An infinite geometric progression a1 , a2 , a3 ,... has the property that an = 3(an+ l + an+2 +….) for every n ≥ 1. If the sum a1 + a2 + a3 +….... = 32, then a5 is

If a1=1/2×5, a2=1/5×8, a3=1/8×11,...,then a1, +a2, +a3, +....a100 is

If \(9^{2x – 1} – 81^{x-1} = 1944\), then x is

If tan (A + B) = m and tan (A - B) = n then value of tan 2A is

The value of \(\text {log}_{0.008}\sqrt{5}+\text{log}_{\sqrt{3}}81-7\) is equal to

The number of solutions \((x, y, z)\) to the equation \(x\ –\  y \ –\ z = 25\), where x, y, and z are positive integers such that \(x ≤ 40, y ≤ 12\), and \(z ≤ 12\) is

For how many integers n, will the inequality \((n – 5) (n – 10) – 3(n – 2) ≤ 0\) be satisfied?

If \(f_1 (x) = x^2 + 11x + n\) and \(f_2 (x) = x,\) then the largest positive integer n for which the equation \(f_1 (x) = f_2 (x)\) has two distinct real roots, is

If a, b, c, and d are integers such that \(a + b + c + d = 30\), then the minimum possible value of \((a - b)^2 + (a - c)^2 + (a - d)^2\) is

Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A,B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

The shortest distance of the point \((\frac{1}{2},1)\) from the curve \(y = |x -1| + |x + 1|\) is

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

If \(f(x)=\frac{5x+2 }{3x-5}\) and \(g(x)=x^2-2x-1\),then the value of \(g(f(f(3)))\) is 

Let \(a_1 , a_2 ,……..a_{3n}\) be an arithmetic progression with \(a_1 = 3\) and \(a_2 = 7.\) If \(a_1 + a_2 + ….+a_{3n} = 1830\), then what is the smallest positive integer m such that m \((a_1 + a_2 + …. + a_n ) > 1830?\)

The degree and order of the differential equation \((\frac{d^3y}{dx^2})^2 +(\frac{dy}{dx})^4+y^3=0\) is