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
|
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
|