A to Z Exams

If X and Y are positive integers and X + Y = 1, what is the least value of (X+1/X)2 + (Y+1/Y)2 ?

If (c – 5) = 4c – 7, then which of the following could be the value of c?

(3080 + 6160) +28 = ?

If k – 7 = 7 (1 – k), then what is the value of k?

. If the roots, x1,and x2, of the quadratic equation x2 - 2x + c = 0 also satisfy the equation 7x2 - 4x1 = 47, then which of the following is true?

Ujakar and Keshab atternplted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

If x=2+22/3+21/3, then which of the following is true?

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 

If l(s) = 3s2 + 3s + 3, which of the following is equal to l(-3.5)?

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

Evaluation of 83 × 82 × 8-5    is:

Let tan θ = tan 10 − tan 50 + tan 70 then θis ?( all angles in degress)

If x varies as y2 + 2 and is equal to 36 when y = 4, find x when y = 12.

If a = log2, b = log 3 and c = log 7 then find the value of log67 in terms of a, b and c.

If xy = 96 and 3y = 2x, then what is the value of x

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

If x=1+2a+3a2+4a2+……( -1 < a < 1 ) and y=1+3b+6b2+10b3+……( -1 < b < 1 )then find 1+ab+(ab)2+(ab)3+….. in terms of x and y.

If logx/(a2+b2+ab) = logy/(b2+c2+bc) = logz/(c2+a2+ac) then, the value of x(a-b).y(b-c).z(c-a) is

If x = 1 – q and y = 2q + 1, then for what value of q, x is  equal to y?

If ( p - q) 2 = ( x – y ) 2, then x =

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

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

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

What is the minimum value of the expression 2x2+3y2-4x-12y+18?

If a, b and c are the sides of a triangle and a4 + b4 + 2a2b2 = c4, then the triangle is

If n(x) = x2 - 10x, then n(-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

The sum of X and Y's age is 105. When X was Y's age, she was 1.5 times Y's age then what are their present ages?

Solve the following equation 3s + 5 = s – 1

If x3+ ax2+bx +6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), the value of a and b respectively are