# Question(s) from Search: IIT

Search Results Difficulty Solution
1

The equation of the common tangent touching the circle
and the parabola , above X–axis is

a)

b)

c)

d)

The equation of the common tangent touching the circle
and the parabola , above X–axis is

a)

b)

c)

d)

IIT 2001
05:54 min
2

Evaluate

a) 0

b)

c) 1

d) 2

Evaluate

a) 0

b)

c) 1

d) 2

IIT 1979
00:54 min
3

The angle between the tangents drawn from the point (1, 4) to the parabola  is

a)

b)

c)

d)

The angle between the tangents drawn from the point (1, 4) to the parabola  is

a)

b)

c)

d)

IIT 2004
02:56 min
4

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
5

If

a)

b) [2, ∞)

c)

d)

If

a)

b) [2, ∞)

c)

d)

IIT 2002
06:15 min
6

A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.

A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.

IIT 1982
06:08 min
7

Show that the locus of a point that divides a chord of slope 2 of the parabola  internally in the ratio 1:2 is a parabola. Find its vertex.

Show that the locus of a point that divides a chord of slope 2 of the parabola  internally in the ratio 1:2 is a parabola. Find its vertex.

IIT 1995
06:25 min
8

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
9

Three normals with slopes  are drawn from a point P not on the axis of the parabola . If  results in the locus of P being a part of the parabola, find the value of α.

Three normals with slopes  are drawn from a point P not on the axis of the parabola . If  results in the locus of P being a part of the parabola, find the value of α.

IIT 2003
05:59 min
10

Find

a) 0

b) e

c) ez

d) e3

Find

a) 0

b) e

c) ez

d) e3

IIT 1993
05:49 min
11

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
12

For a fixed value of n
D =
Then show that  is divisible by n

For a fixed value of n
D =
Then show that  is divisible by n

IIT 1992
07:32 min
13

Let E be the ellipse  and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then

a) Q lies inside C but outside E

b) Q lies outside both C and E

c) P lies inside both C and E

d) P lies inside C but outside E

Let E be the ellipse  and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then

a) Q lies inside C but outside E

b) Q lies outside both C and E

c) P lies inside both C and E

d) P lies inside C but outside E

IIT 1994
04:15 min
14

For any positive integers m, n (with n ≥ m), prove that

For any positive integers m, n (with n ≥ m), prove that

IIT 2000
05:45 min
15

If tangents are drawn to the ellipse  then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is

a)

b)

c)

d)

If tangents are drawn to the ellipse  then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is

a)

b)

c)

d)

IIT 2004
03:11 min
16

A =  is equal to

a) 0

b) 1

c)

d)

A =  is equal to

a) 0

b) 1

c)

d)

IIT 1978
02:30 min
17

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

IIT 1994
02:27 min
18

For the function

The derivative from right  .  .  .  . and the derivative from the left  .  .  .  .

a) 0, 0

b) 0, 1

c) 1, 0

d) 1, 1

For the function

The derivative from right  .  .  .  . and the derivative from the left  .  .  .  .

a) 0, 0

b) 0, 1

c) 1, 0

d) 1, 1

IIT 1983
03:28 min
19

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin then n must be of the form

a) 4k + 1

b) 4k + 2

c) 4k + 3

d) 4k

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin then n must be of the form

a) 4k + 1

b) 4k + 2

c) 4k + 3

d) 4k

IIT 2001
05:59 min
20

The equation  represents

a) An ellipse

b) A hyperbola

c) A circle

d) None of these

The equation  represents

a) An ellipse

b) A hyperbola

c) A circle

d) None of these

IIT 1981
01:03 min
21

a) 0

b) 1

c) e3

d) e5

a) 0

b) 1

c) e3

d) e5

IIT 1990
04:42 min
22

If |z| = 1 and  then Re (w) is

a) 0

b)

c)

d)

If |z| = 1 and  then Re (w) is

a) 0

b)

c)

d)

IIT 2003
02:36 min
23

For the hyperbola  which of the following remains constant with change in α

a) Abscissae of vertices

b) Abscissae of focii

c) Eccentricity

d) Directrix

For the hyperbola  which of the following remains constant with change in α

a) Abscissae of vertices

b) Abscissae of focii

c) Eccentricity

d) Directrix

IIT 2003
01:32 min
24

If w ( ≠1 ) is cube root of unity, then

a) 0

b) 1

c) - 1

d) w

If w ( ≠1 ) is cube root of unity, then

a) 0

b) 1

c) - 1

d) w

IIT 1995
01:46 min
25

India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is

a) 0.8730

b) 0.0875

c) 0.0625

d) 0.0250

India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is

a) 0.8730

b) 0.0875

c) 0.0625

d) 0.0250

IIT 1992
03:03 min

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