If a 3 by 3 matrix has rank 2, then its nullity is:

If the sum of the first n terms of a sequence is S_n = 3n^2 + 2n, then the nth term is:

The derivative of x^x for x greater than 0 is:

If n is a positive integer and n^2 is divisible by 72, then the least possible value of n is:

The integral from 0 to pi of sin^2 x dx equals:

The minimum value of x^2 - 6x + 13 for real x is:

If 2^(x+1) = 32^(x-1), then x equals:

The sum of the series 1 + 1/2 + 1/4 + 1/8 + ... is:

The eccentricity of the ellipse x^2/25 + y^2/16 = 1 is:

The remainder when 5^100 is divided by 13 is:

Two cards are drawn without replacement from a standard deck. The probability that both are aces is:

The solution set of |2x - 3| less than or equal to 5 is:

A committee of 5 is selected from 7 men and 6 women. The number of committees containing exactly 3 women is:

If gcd(a,b)=6, lcm(a,b)=180 and a=30, then b equals:

For the matrix A = [[2,1],[1,2]], the determinant of A^5 is:

If y = ln(sin x), then dy/dx is:

The greatest power of 3 that divides 100! is:

The number of onto functions from a 5-element set to a 3-element set is:

If the scalar product of two non-zero vectors is zero, then the vectors are:

The integral from 0 to 1 of x/(1+x^2) dx equals:

If a, b and c are positive numbers such that abc = 8, the minimum value of a + b + c is:

If Var(X) = 16, then Var(3X - 5) is:

For positive x and y satisfying x + y = 10, the maximum value of xy is:

If A is a 3 by 3 matrix and det(A)= -2, then det(3A) is:

If x + 1/x = 4, then x^3 + 1/x^3 equals:

The equation x^4 + 4x^2 + 16 = 0 has how many real solutions?

Four fair dice are thrown simultaneously. The probability that all four show distinct numbers is:

If two events A and B are independent with P(A)=1/3 and P(B)=1/4, then P(A union B) is:

The coefficient of x^4 in the expansion of (1 + x)^6(1 - x)^4 is:

If z is a complex number satisfying |z - 2| = |z + 2|, then z lies on:

If x - 1/x = 3, then x^2 + 1/x^2 is:

If vectors a and b have magnitudes 3 and 4 and the angle between them is 60 degrees, then |a+b| is:

An infinite geometric progression has first term 9 and sum 12. Its common ratio is:

The remainder when 2^50 is divided by 7 is:

The distance between the parallel lines 3x + 4y - 7 = 0 and 3x + 4y + 8 = 0 is:

The value of the limit as x approaches 0 of (tan x - sin x) divided by x^3 is:

If x, y and z are positive numbers satisfying xyz=1, then the minimum value of x^2 + y^2 + z^2 is:

The area enclosed between y=x and y=x^2 is:

The number of ways to arrange the letters of the word LEVEL is:

How many positive integers less than 500 are coprime to 500?

The general solution of d2y/dx2 - 4dy/dx + 4y = 0 is:

The number of real roots of x^4 - 5x^2 + 4 = 0 is:

If the roots of the equation x^2 - 7x + k = 0 differ by 3, then the value of k is:

The solution of the differential equation dy/dx = 3y is:

If alpha and beta are roots of x^2 - 5x + 3 = 0, then alpha^3 + beta^3 is:

The value of the limit as x approaches 0 of (e^x - 1 - x) divided by x^2 is:

A random variable X has mean 8 and variance 9. The value of E(X^2) is:

The maximum value of x(10-x) for real x is:

If log base 3 of x plus log base 3 of (x-2) equals 2, then x is:

The sum of the first 20 terms of the arithmetic progression 7, 11, 15, 19, ... is:

If y = sin(x^2), then the second derivative of y is:

The eigenvalues of the matrix [[4,1],[2,3]] are:

If z = (1 + i)/(1 - i), then z^8 is:

The equation of the circle with centre (2,-3) and radius 5 is:

The number of trailing zeroes in 125! is:

The distance between the points (2,-1,3) and (-1,3,5) is: