All BASICSTANDARDADVANCED

Question(s) from Search: IIT

Search Results Difficulty Solution
1

 

a)

b)

c) 1

d) 2

 

a)

b)

c) 1

d) 2

IIT 1994
01:46 min
2

Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If  then the acute angle between a and c is  .  .  .  .  .

Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If  then the acute angle between a and c is  .  .  .  .  .

IIT 1997
04:42 min
3

The equation of the tangents drawn from the origin to the circle  are

a) x= 6

b) y = 0

c)

d)

The equation of the tangents drawn from the origin to the circle  are

a) x= 6

b) y = 0

c)

d)

IIT 1988
04:06 min
4

Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies
f  = f (x) – f (y) for all x and y and f (e) = 1 then

a) f (x) is bounded

b) f  → 0 as x → 0

c) x f  → 0 as x → 0

d) f (x) = lnx

Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies
f  = f (x) – f (y) for all x and y and f (e) = 1 then

a) f (x) is bounded

b) f  → 0 as x → 0

c) x f  → 0 as x → 0

d) f (x) = lnx

IIT 1995
02:06 min
5

The value of  is equal to

a)

b)

c)

d) None of these

The value of  is equal to

a)

b)

c)

d) None of these

IIT 1980
03:48 min
6

The area bounded by the curve y = f(x), the X–axis and the ordinate x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is

a) (x – 1) cos (3x + 4)

b) sin(3x + 4)

c) sin(3x + 4) + 3(x – 1) cos (3x + 4)

d) none of these

 

The area bounded by the curve y = f(x), the X–axis and the ordinate x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is

a) (x – 1) cos (3x + 4)

b) sin(3x + 4)

c) sin(3x + 4) + 3(x – 1) cos (3x + 4)

d) none of these

 

IIT 1983
01:13 min
7

Through a fixed point (h, k) secants are drawn to the circle  . Show that the locus of the mid points of the secant intercepted by the circle is

Through a fixed point (h, k) secants are drawn to the circle  . Show that the locus of the mid points of the secant intercepted by the circle is

IIT 1983
02:28 min
8

There exists a solution of θ between 0 and 2π that satisfies the equation .

a) True

b) False

There exists a solution of θ between 0 and 2π that satisfies the equation .

a) True

b) False

IIT 1980
02:16 min
9

The number of values of x where the function
f (x) = cos x + cos () attains the maximum is

a) 0

b) 1

c) 2

d) Infinite

The number of values of x where the function
f (x) = cos x + cos () attains the maximum is

a) 0

b) 1

c) 2

d) Infinite

IIT 1998
01:38 min
10

Evaluate

a) 0

b)

c) 1

d) 2

Evaluate

a) 0

b)

c) 1

d) 2

IIT 1979
00:54 min
11

The circle  is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circum centre of the triangle is  find k.

The circle  is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circum centre of the triangle is  find k.

IIT 1987
07:11 min
12

The domain of definition of the function f (x) given by the equation

2x + 2y = 2 is

a) 0 < x ≤ 1

b) 0 ≤ x ≤ 1

c)  < x ≤ 0

d)  < x ≤ 1

The domain of definition of the function f (x) given by the equation

2x + 2y = 2 is

a) 0 < x ≤ 1

b) 0 ≤ x ≤ 1

c)  < x ≤ 0

d)  < x ≤ 1

IIT 2000
01:23 min
13

Determine the values of a, b, c for which the function

 

is continuous at x = 0

a)

b)

c)

d)

Determine the values of a, b, c for which the function

 

is continuous at x = 0

a)

b)

c)

d)

IIT 1982
04:00 min
14

If

a)

b) [2, ∞)

c)

d)

If

a)

b) [2, ∞)

c)

d)

IIT 2002
06:15 min
15

The function  is

a) Increasing on (0, ∞)

b) Decreasing on (0, ∞)

c) Increasing on  and decreasing on  

d) Increasing on  and decreasing on

The function  is

a) Increasing on (0, ∞)

b) Decreasing on (0, ∞)

c) Increasing on  and decreasing on  

d) Increasing on  and decreasing on

IIT 1995
02:10 min
16

A point P is given on the circumference of a circle of radius r. Chord QR is parallel to the tangent at P. Determine the maximum possible area of ΔPQR.

A point P is given on the circumference of a circle of radius r. Chord QR is parallel to the tangent at P. Determine the maximum possible area of ΔPQR.

IIT 1990
08:40 min
17

If we consider only the principal values of the inverse trigonometric functions then the value of

 is

a)

b)

c)

d)

If we consider only the principal values of the inverse trigonometric functions then the value of

 is

a)

b)

c)

d)

IIT 1994
02:29 min
18

Let g (x) = 1 + x – [ x ] and f (x) =  then for all x,
f (g (x)) is equal to

a) x

b) 1

c) f ( x )

d) g ( x )

Let g (x) = 1 + x – [ x ] and f (x) =  then for all x,
f (g (x)) is equal to

a) x

b) 1

c) f ( x )

d) g ( x )

IIT 2001
01:01 min
19

Let P(asecθ, btanθ) and Q(asecɸ, btanɸ) where θ + ɸ =  be two points on the hyperbola . If (h, k) be the point of intersection of the normals at P and Q then k is equal to

a)

b)

c)

d)

Let P(asecθ, btanθ) and Q(asecɸ, btanɸ) where θ + ɸ =  be two points on the hyperbola . If (h, k) be the point of intersection of the normals at P and Q then k is equal to

a)

b)

c)

d)

IIT 1999
07:25 min
20

Find the value of  at  where
.

a) 1

b)

c)

d)

Find the value of  at  where
.

a) 1

b)

c)

d)

IIT 1981
03:44 min
21

Let ℝ be the set of real numbers and f : ℝ → ℝ such that for all x and y in ℝ, . Then f (x) is a constant.

a) True

b) False

Let ℝ be the set of real numbers and f : ℝ → ℝ such that for all x and y in ℝ, . Then f (x) is a constant.

a) True

b) False

IIT 1988
01:50 min
22

Let

Then at x = 0, f has

a) A local maximum

b) No local maximum

c) A local minimum

d) No extremum

Let

Then at x = 0, f has

a) A local maximum

b) No local maximum

c) A local minimum

d) No extremum

IIT 2000
01:52 min
23

Let C be any circle with centre (0, . Prove that at the most two rational points can be there on C (A rational point is a point both of whose coordinates are rational numbers).

Let C be any circle with centre (0, . Prove that at the most two rational points can be there on C (A rational point is a point both of whose coordinates are rational numbers).

IIT 1997
01:58 min
24

Find

a) 0

b) e

c) ez

d) e3

Find

a) 0

b) e

c) ez

d) e3

IIT 1993
05:49 min
25

The relatives of a man comprise 4 ladies and 3 gentlemen and his wife has 7 relatives 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that so that three of man’s relatives and three of wife’s relatives are included?

The relatives of a man comprise 4 ladies and 3 gentlemen and his wife has 7 relatives 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that so that three of man’s relatives and three of wife’s relatives are included?

IIT 1985
04:27 min

Play Selected  Login to save this search...