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Question(s) from Search: IIT

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601

is equal to

a) 0

b) 4

c) 6

d) −4

is equal to

a) 0

b) 4

c) 6

d) −4

IIT 2004
03:15 min
602

Find all values of λ such that  and

 where  are unit vectors along the coordinate vectors.

Find all values of λ such that  and

 where  are unit vectors along the coordinate vectors.

IIT 1982
04:48 min
603

The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for

a) a = nπ

b) x = 0

c) x =  

d) None of these

The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for

a) a = nπ

b) x = 0

c) x =  

d) None of these

IIT 1988
02:59 min
604

Suppose  is an identity in x where  are constants and . Then the value of n = ……….

a) 4

b) 5

c) 6

d) 7

Suppose  is an identity in x where  are constants and . Then the value of n = ……….

a) 4

b) 5

c) 6

d) 7

IIT 1981
02:56 min
605

Prove that  is divisible by 25 for any natural number n.

Prove that  is divisible by 25 for any natural number n.

IIT 1982
03:55 min
606

Evaluate   where n is a positive integer and t is a parameter independent of x.

a)

b)

c)

d)

Evaluate   where n is a positive integer and t is a parameter independent of x.

a)

b)

c)

d)

IIT 1981
05:47 min
607

Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.

Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.

IIT 1988
04:37 min
608

For positive integers n1 and n2 the value of the expression  where  is real if and only if

a)

b)

c)

d)

For positive integers n1 and n2 the value of the expression  where  is real if and only if

a)

b)

c)

d)

IIT 1995
04:45 min
609

 is equal to

a) 0

b)

c)

d) None of these

 is equal to

a) 0

b)

c)

d) None of these

IIT 1984
01:15 min
610

Find the area bounded by the X - axis, part of the curve  and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a,

a)

b)

c)

d)

Find the area bounded by the X - axis, part of the curve  and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a,

a)

b)

c)

d)

IIT 1983
06:17 min
611

Determine the value of c so that for all real x the vector cx and  make an obtuse angle with each other.

Determine the value of c so that for all real x the vector cx and  make an obtuse angle with each other.

IIT 1991
03:25 min
612

The equation  has

a) No solution

b) One solution

c) More than one real solution

d) Cannot be said

The equation  has

a) No solution

b) One solution

c) More than one real solution

d) Cannot be said

IIT 1980
01:57 min
613

The value of  is   

a) 1

b) – 1

c) 0

d) None of these

The value of  is   

a) 1

b) – 1

c) 0

d) None of these

IIT 1991
02:34 min
614

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1986
05:55 min
615

The number of solutions of the equation

a) 0

b) 1

c) 2

d) Infinitely many

The number of solutions of the equation

a) 0

b) 1

c) 2

d) Infinitely many

IIT 1990
01:46 min
616

 

a) exists and equals

b) exists and equals

c) does not exist because x – 1 → 0

d) does not exist because the left hand limit is not equal to the right hand limit.

 

a) exists and equals

b) exists and equals

c) does not exist because x – 1 → 0

d) does not exist because the left hand limit is not equal to the right hand limit.

IIT 1998
03:32 min
617

The number of values of x in the interval (0, 5π) satisfying the equation  is

a) 0

b) 5

c) 6

d) 10

The number of values of x in the interval (0, 5π) satisfying the equation  is

a) 0

b) 5

c) 6

d) 10

IIT 1998
03:17 min
618

Find the natural number a for which
 
where the function f satisfies the relation f (x + y) = f (x).f(y)for all natural numbers x and y and further f (1) = 2

Find the natural number a for which
 
where the function f satisfies the relation f (x + y) = f (x).f(y)for all natural numbers x and y and further f (1) = 2

IIT 1992
06:01 min
619

The lines  and  are diameters of a circle of area 154 square units. Then the equation of the circle is

a)

b)

c)

d)

The lines  and  are diameters of a circle of area 154 square units. Then the equation of the circle is

a)

b)

c)

d)

IIT 1989
03:02 min
620

If α + β =  and β + γ = α, then tanα equals

a) 2(tanβ + tanγ)

b) tanβ + tanγ

c) tanβ + 2tanγ

d) 2tanβ + tanγ

If α + β =  and β + γ = α, then tanα equals

a) 2(tanβ + tanγ)

b) tanβ + tanγ

c) tanβ + 2tanγ

d) 2tanβ + tanγ

IIT 2001
02:03 min
621

Let n be a positive integer and
(1 + x + x2)n = a0 + a1x + a2x + a2x2 +  .  .  . + a2nx2n then prove that
 

Let n be a positive integer and
(1 + x + x2)n = a0 + a1x + a2x + a2x2 +  .  .  . + a2nx2n then prove that
 

IIT 1994
06:48 min
622

Evaluate

a) πln2

b)

c)

d)

Evaluate

a) πln2

b)

c)

d)

IIT 1997
02:50 min
623

The angle between a pair of tangents drawn from a point P to the circle  is 2α. Then the locus of P is

a)

b)

c)

d)

The angle between a pair of tangents drawn from a point P to the circle  is 2α. Then the locus of P is

a)

b)

c)

d)

IIT 1996
05:15 min
624

If  where n is a non–zero real number, then a is equal to

a) 0

b)

c) n

d)

If  where n is a non–zero real number, then a is equal to

a) 0

b)

c) n

d)

IIT 2003
02:22 min
625

If f (x) is an even function then prove that
 .

If f (x) is an even function then prove that
 .

IIT 2003
07:55 min

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