Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of  and 0 < α < β then the equation  has a root γ that always satisfies

a) γ =

b) γ =

c) γ = α

d) α < γ < β

Let α, β be roots of the equation (x – a) (x – b) = c, c ≠ 0. Then the roots of the equation (x – α) (x – β) + c = 0 are

a) a, c

b) b, c

c) a, b

d) a + c, b + c

The expression  is a polynomial of degree

a) 5

b) 6

c) 7

d) 8

The number of points of intersection of the two curves y = 2sinx and y =  is

a) 0

b) 1

c) 2

d)

The equation  has

a) No solution

b) One solution

c) Two solutions

d) More than two solutions

The roots of the equation  are real and less than 3, then

a) a < 2

b) 2 < a < 3

c) 3 ≤ a ≤ 4

d) a > 4

If α and β (α < β) are roots of the equation  where c < 0 < b then

a) 0 < α < β

b) α < 0 < β < | α |

c) α < β < 0

d) α < 0 < | α | < β

If a, b, c, d are positive real numbers such that a + b + c + d = 2 then M = ( a + b ) ( c + d ) satisfies

a) 0 ≤ M ≤ 1

b) 1 ≤ M ≤ 2

c) 2 ≤ M ≤ 3

d) 3 ≤ M ≤ 4

For the equation  if one of the roots is square of the other then p is equal to

a)

b)

c) 3

d)

For all x ε ( 0, 1 )

a)

b) ln (1 + x) < x

c) sinx > x

d) lnx > x

Let α, β be the roots of  and γ, δ roots of . If α, β, γ, δ are in geometric progression then the integral values of p and q respectively are

a) −2, −32

b) −2, 3

c) −6, 3

d) −6, −32

Let f(x) =  and m(b) be the minimum value of f(x). As b varies, range of m(b) is

a)

b) [ 0,

c) [

d)

The number of solutions of  is

a) 3

b) 1

c) 2

d) 0

The number of values of k for which the system of equations

(k + 1) x + 8y = 4k

kx + ( k + 3 ) y = 3k – 1

has infinitely many solutions is

a) 0

b) 1

c) 2

d) Infinity

If  are positive real numbers whose product is a fixed number c then the minimum value of  is

a)

b)

c)

d)

The set of all real numbers x for which  is

a)

b)

c)

d)

If ε then  is always greater than or equal to

a) 2 tan

b) 1

c) 2

d)

For all x,  then the interval in which a lies is

a) a <

b)

c)

d)

If one root is square of the other root of the equation  then the relation between p and q is

a)

b)

c)

d)

The second degree polynomial satisfying f (0) = 0, f (1) = 1,  for all x ε [0, 1] is

a)

b) No such polynomial

c)

d)

Let a, b, c be the sides of a triangle where a ≠ c and λ ε R. If roots of the equation  are real then

a)

b)

c)

d)

Let α, β be roots of the equation are the roots of the equation  then the value of r is equal to

a)

b)

c)

d)

Multiple choices

For real x, the function  will assume all real values provided

a)

b)

c)

d)