Question(s) from Search: IIT

The equation  has

a) no real solutions

b) one real solution

c) two real solutions

d) infinite real solutions

For positive numbers x, y and z the numerical value of the determinant
 is ………..

a) 1

b) –1

c) ±1

d) 0

If a > 0, b > 0, c > 0, prove that  

The third term of Geometric Progression is 4. The product of the five terms is

a)

b)

c)

d)

Find the set of all x for which

Sum of the first n terms of the series  is

a) 2ⁿ – n – 1

b) 1 – 2^{− n}

c) n + 2^{− n} – 1

d) 2ⁿ + 1

Let  be in Arithmetic Progression and
 be in Harmonic Progression. If  and
 then  is

a) 2

b) 3

c) 5

d) 6

If α, β are roots of  and  are roots of  for some constant δ, then prove that
 

Let the positive numbers a, b, c, d be in Arithmetic Progression. Then
abc, abd, acd, bcd are

a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression

b) In Arithmetic Progression

c) In Geometric Progression

d) In Harmonic Progression

If  is the area of a triangle with sides a, b, c then show that
 .
Also show that equality occurs if a = b = c

An infinite Geometric Progression has first term x and sum 5 then

a)

b)

c)

d)

If a < b < c < d then the roots of the equation
  
are real and distinct.

a) True

b) False

The angles of a triangle are in Arithmetic Progression and let . Find the angle A.

If α, β, γ are the cube roots of P, P < 0, then for any x, y, z,
………..

If n is a natural number such that  and  are distinct primes, then show that
 

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

If  satisfies ,
find the value of

The value of the expression  is equal to

a) 2

b)

c) 4

d)

Let  then  equals

a) tan

b) tan

c) tan

d) tan²

The length of longest interval in which the function  is increasing is

a)

b)

c)

d)

Let p, q be the roots of the equation , and r and s are roots of the equation . If  are in arithmetic progression then A = .  .  .  .  . , B = .  .  .  .  .

a) True

b) False

If tan θ =  then sin θ is

a)  but not  

b)  or

c)  but not −

d) None of these

Find the sum of the series
 

The general solution of
 is

a)

b)

c)

d)