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Question(s) from Search: IIT

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1

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
2

The equation of the common tangent to the curves  and  is

a)

b)

c)

d)

The equation of the common tangent to the curves  and  is

a)

b)

c)

d)

IIT 2002
03:51 min
3

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
4

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
5

(Multiple choice)

The equation of common tangent to the parabolas  and  is/are

a)

b)

c)

d)

(Multiple choice)

The equation of common tangent to the parabolas  and  is/are

a)

b)

c)

d)

IIT 2006
04:15 min
6

If a > 0, b > 0, c > 0, prove that  

If a > 0, b > 0, c > 0, prove that  

IIT 1984
02:45 min
7

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
8

Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than. One normal is always the X-axis. Find c for which the other two normals are perpendicular.

Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than. One normal is always the X-axis. Find c for which the other two normals are perpendicular.

IIT 1991
05:44 min
9

Find the set of all x for which

Find the set of all x for which

IIT 1987
05:05 min
10

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
11

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
12

Match the following

Normals are drawn at the points P, Q and R lying on the parabola  which intersect at (3, 0) then

Column 1

Column 2

i) Area of ΔPQR

A. 2

ii) Radius of circumcircle of ΔPQR

B.

iii) Centroid of ΔPQR

C.

iv) Circumcentre of ΔPQR

D.

Match the following

Normals are drawn at the points P, Q and R lying on the parabola  which intersect at (3, 0) then

Column 1

Column 2

i) Area of ΔPQR

A. 2

ii) Radius of circumcircle of ΔPQR

B.

iii) Centroid of ΔPQR

C.

iv) Circumcentre of ΔPQR

D.

IIT 2006
07:33 min
13

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
14

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
15

(Assertion and reason)

The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if

a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1.

b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true

Statement 1 – The curve  is symmetric with respect to the line x = 1

Statement 2 – The parabola is symmetric about its axis.

(Assertion and reason)

The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if

a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1.

b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true

Statement 1 – The curve  is symmetric with respect to the line x = 1

Statement 2 – The parabola is symmetric about its axis.

IIT 2007
01:47 min
16

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
17

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

a)

b)

c)

d)

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

a)

b)

c)

d)

IIT 2004
01:34 min
18

Let P = (x, y) be any point on  with focii  and  equals

a) 8

b) 6

c) 10

d) 12

Let P = (x, y) be any point on  with focii  and  equals

a) 8

b) 6

c) 10

d) 12

IIT 1998
01:38 min
19

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

a) True

b) False

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

a) True

b) False

IIT 1984
03:45 min
20

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

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

IIT 1981
03:20 min
21

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

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

IIT 1989
07:21 min
22

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

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

IIT 1983
03:00 min
23

An ellipse has OB as a semi-minor axis. F, F’ are its focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is . . . . .

An ellipse has OB as a semi-minor axis. F, F’ are its focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is . . . . .

IIT 1997
02:22 min
24

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

IIT 1980
02:59 min
25

If x = 9 is the chord of contact of the hyperbola  then the equation of the corresponding pair of tangents is

a)

b)

c)

d)

If x = 9 is the chord of contact of the hyperbola  then the equation of the corresponding pair of tangents is

a)

b)

c)

d)

IIT 1999
03:20 min

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