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Question(s) from Search: IIT

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1

Fill in the blank
If f (x) = sin ln  then the domain of f (x) is ………….

a) (−2, −1)

b) (−2, 1)

c) (0, 1)

d) (1, ∞)

Fill in the blank
If f (x) = sin ln  then the domain of f (x) is ………….

a) (−2, −1)

b) (−2, 1)

c) (0, 1)

d) (1, ∞)

IIT 1985
01:25 min
2

If x, y, z are real and distinct then
8u =
is always

a) Non–negative

b) Non–positive

c) Zero

d) None of these

If x, y, z are real and distinct then
8u =
is always

a) Non–negative

b) Non–positive

c) Zero

d) None of these

IIT 1979
02:14 min
3

If  are any real numbers and n is any positive integer then

a)

b)

c)

d) none of these

If  are any real numbers and n is any positive integer then

a)

b)

c)

d) none of these

IIT 1982
01:04 min
4

Let a + b + c = 0, then the quadratic equation  has

a) at least one root in (0, 1)

b) one root in (2, 3) and the other in

c) imaginary roots

d) none of these

Let a + b + c = 0, then the quadratic equation  has

a) at least one root in (0, 1)

b) one root in (2, 3) and the other in

c) imaginary roots

d) none of these

IIT 1983
02:32 min
5

If α and β are roots of  and  are roots of  then the equation  has always

a) Two real roots

b) Two positive roots

c) Two negative roots

d) One positive and one negative root

If α and β are roots of  and  are roots of  then the equation  has always

a) Two real roots

b) Two positive roots

c) Two negative roots

d) One positive and one negative root

IIT 1989
04:41 min
6

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

a) 0

b) 1

c) 2

d)

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

a) 0

b) 1

c) 2

d)

IIT 1994
01:51 min
7

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

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

IIT 1999
02:39 min
8

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)

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)

IIT 2001
03:22 min
9

The set of all real numbers x for which  is

a)

b)

c)

d)

The set of all real numbers x for which  is

a)

b)

c)

d)

IIT 2002
03:01 min
10

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

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)

IIT 2004
03:14 min
11

If a ≠ p, b ≠ q, c ≠ r and
 = 0

Then find the value of
  +  +

a) 0

b) 1

c) 2

d) 3

If a ≠ p, b ≠ q, c ≠ r and
 = 0

Then find the value of
  +  +

a) 0

b) 1

c) 2

d) 3

IIT 1991
03:41 min
12

The number of solutions of the pair of equations


in the interval [ 0, 2π ] is

a) 0

b) 1

c) 2

d) 4

The number of solutions of the pair of equations


in the interval [ 0, 2π ] is

a) 0

b) 1

c) 2

d) 4

IIT 2007
07:12 min
13

The equation  has

a) At least one real solution

b) Exactly three real solutions

c) Has exactly one irrational solution

d) Complex roots

The equation  has

a) At least one real solution

b) Exactly three real solutions

c) Has exactly one irrational solution

d) Complex roots

IIT 1989
03:53 min
14

Show that for for any triangle with sides a, b, c
3 (ab + bc + ac) ≤ (a + b + c)2 < 4 (ab + bc + ca)

Show that for for any triangle with sides a, b, c
3 (ab + bc + ac) ≤ (a + b + c)2 < 4 (ab + bc + ca)

IIT 1979
03:38 min
15

The solution set of equation  = 0 is ……….

a) {0}

b) {1, 2}

c) {−1, 2}

d) {−1, −2}

The solution set of equation  = 0 is ……….

a) {0}

b) {1, 2}

c) {−1, 2}

d) {−1, −2}

IIT 1981
02:12 min
16

The equation  has

a) no real solutions

b) one real solution

c) two real solutions

d) infinite real solutions

The equation  has

a) no real solutions

b) one real solution

c) two real solutions

d) infinite real solutions

IIT 1982
03:09 min
17

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

a) 1

b) –1

c) ±1

d) 0

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

a) 1

b) –1

c) ±1

d) 0

IIT 1993
02:04 min
18

If a > 0, b > 0, c > 0, prove that  

If a > 0, b > 0, c > 0, prove that  

IIT 1984
02:45 min
19

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

a)

b)

c)

d)

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

a)

b)

c)

d)

IIT 1982
01:07 min
20

Find the set of all x for which

Find the set of all x for which

IIT 1987
05:05 min
21

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

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

IIT 1988
03:20 min
22

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

a) 2

b) 3

c) 5

d) 6

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

a) 2

b) 3

c) 5

d) 6

IIT 1999
04:53 min
23

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

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

IIT 2000
03:16 min
24

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

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

IIT 2001
01:12 min
25

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

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

IIT 2001
05:12 min

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