All BASICSTANDARDADVANCED

Question(s) from Search: IIT

Search Results Difficulty Solution
326

If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral   is

a)

b)

c)

d)

If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral   is

a)

b)

c)

d)

IIT 1999
07:44 min
327

If  and  then b is equal to

a)

b)

c)

d)

If  and  then b is equal to

a)

b)

c)

d)

IIT 2004
02:35 min
328

A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.

A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.

IIT 1988
06:49 min
329

 and
where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are

a) 0

b) 1

c) 2

d) 4

 and
where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are

a) 0

b) 1

c) 2

d) 4

IIT 2005
04:42 min
330

Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then

a) n = 2r

b) n = 2r + 1

c) n = 3r

d) none of these

Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then

a) n = 2r

b) n = 2r + 1

c) n = 3r

d) none of these

IIT 1980
03:03 min
331

The number of distinct real values of λ for which   are coplanar is

a) Zero

b) One

c) Two

d) three

The number of distinct real values of λ for which   are coplanar is

a) Zero

b) One

c) Two

d) three

IIT 2007
03:01 min
332

If , then  

a) True

b) False

If , then  

a) True

b) False

IIT 1980
04:29 min
333

If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is

a) 6

b) 9

c) 12

d) 24

If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is

a) 6

b) 9

c) 12

d) 24

IIT 1999
04:34 min
334

If  then  at x = e is .  .  .

a) 0

b)

c) e

d) 1

If  then  at x = e is .  .  .

a) 0

b)

c) e

d) 1

IIT 1985
01:35 min
335

If  then the expression for  in terms of  is

a)

b)

c)

d)

If  then the expression for  in terms of  is

a)

b)

c)

d)

IIT 2003
01:32 min
336

Multiple choice

Which of the following expressions are meaningful

a)

b)

c)

d)

Multiple choice

Which of the following expressions are meaningful

a)

b)

c)

d)

IIT 1998
01:15 min
337

If  then at x = 0,  is equal to

a) 0

b) 1

c) 2

d) 4

If  then at x = 0,  is equal to

a) 0

b) 1

c) 2

d) 4

IIT 1996
02:05 min
338

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
339

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
340

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
341

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
342

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
343

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
344

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
345

If a, b, c are coplanar, show that
  

If a, b, c are coplanar, show that
  

IIT 1989
02:38 min
346

 is the reflexion of in the line whose equation is . .

 is the reflexion of in the line whose equation is . .

IIT 1982
00:57 min
347

Use mathematical induction to prove that  is divisible by 24 for all n > 0.

Use mathematical induction to prove that  is divisible by 24 for all n > 0.

IIT 1985
03:43 min
348

If

Where [x] denotes the greatest integer less than or equal to x then  equals

a) 1

b) 0

c) – 1

d) None of these

If

Where [x] denotes the greatest integer less than or equal to x then  equals

a) 1

b) 0

c) – 1

d) None of these

IIT 1985
02:39 min
349

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

IIT 1984
03:38 min
350

Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .

Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .

IIT 1983
05:23 min

Play Selected  Login to save this search...