A to Z Exams

A singles tennis tournament is held, in which 30 men participated. If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner

If x + y > 4 and x < 3, then y > 1 is true.  Is this statement true?

If a2 = b4 = c8 = d16, then logd2 (abc)1/3

Which family has the lowest average savings?

If x2 + 1/x2 = 51 , then the value of x-1/x is

The number of positive integers n in the range 12  ? n? 40 such that the product (n – 1) (n –2)…3.2.1 is not divisible by n is 

The factors of x2 + xy − 2 xyz −2z are:

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

a, b, c, d be real numbers in G.P. If u, v,w satisfy the equations u + 2v + 3w = 6; 4u + 5v + 6w = 12; 6u + 9v = 4 then roots of the equations (1/u + 1/v + 1/w)x2 + [(b − c)2 + (c − a)2 + (d − b)2]x + u + v + w = 0 and 20x2 + [10(a − d)2]x − 9 = 0 are

If 8a + 4b = 11 and 2a + 4g = 5. The value of b = 2. You need to find the value of a and g.

If a - 4 = 4 (2- a), then what is the value of a?

P lent Rs.600 to Q for 2 years and Rs.150 to R for 4 years and received altogether from both Rs.90 as interest. Find the rate of interest, simple interest being calculated

If a1=1 and an+1-3an+2 = 4n for every positive integer n, then a100 equals

if (64)2 - (36)2 = 10x, then x = ?

If 1 + 2 + 22 + 23 +.......+ 250 is divided by 7, what will be the remainder?

Find tan 9 − tan 27 − tan 63 + tan 81 ( all angles in degrees)

If a1 = 1 and an+1 = 2an + 5, n = 1, 2 ...., then a100 is equal to :

What is the minimum value of x for which the expression x3 – 7x2 + 11x – 5 gives positive values

Find the number of pairs of real numbers x, y such that (x2 + 8x +17)(y2 − 2y + 6) = 5

If one root of ax2 + bx + c = 0 is double the other, then a, b, c are related as

A ship 55 kms. From the shore springs a leak which admits 2 tones of water in 6 min; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.

If x + y = 2, then the value of x4 + y4 – x3 y2 – x2 y3+16xy is equal to

If 2x – ky + z = 0 is a factor of 9y2– z2 – 2xz + 6xy, then the value of k is equal to

If l + m + n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x + 3y -4z = l, 2x - y - z = m, x + y - 2z = n has at least one ?

If p and q are real numbers; p ≠  0, then the equation 3x – 5 + q = px + 1 has no solution, if

Solve for real x: 6x2 + 5x - 6 ≥ 0

n4 − 20n2 + 4 = k where k is a prime number and n is an integer. How many such k exist?

If 3x – 4y + z = 7; 2x – z + 3y = 19; x + 2y + 2z = 24, then what is the value of z ?

Simplify the expression (1+i)6+(1+i)4 .

If the interest on Rs. 800 exceeds that on Rs. 600 by Rs. 15.50 in 6 months, find the rate percent p.a