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Question(s) from Search: IIT

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326

The number of common tangents to the circles  and  is

a) 0

b) 1

c) 3

d) 4

The number of common tangents to the circles  and  is

a) 0

b) 1

c) 3

d) 4

IIT 1998
04:08 min
327

Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, .  .  .

Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, .  .  .

IIT 2002
10:18 min
328

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

IIT 2003
02:46 min
329

If  are given vectors then the vector B satisfying the equation  and  is . . . . .

If  are given vectors then the vector B satisfying the equation  and  is . . . . .

IIT 1985
03:28 min
330

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

IIT 2000
02:40 min
331

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

IIT 1978
03:06 min
332

(1 + ax)n = 1 + 8x + 24x2 + .  .  . then a = .  . ., n = .  .  .

(1 + ax)n = 1 + 8x + 24x2 + .  .  . then a = .  . ., n = .  .  .

IIT 1983
02:24 min
333

Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3,  then b is equal to

Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3,  then b is equal to

IIT 1991
02:22 min
334

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

IIT 2002
05:23 min
335

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

IIT 1982
03:54 min
336

If f (x) = cos (lnx) then f (x) f (y) −   has the value of

a) −1

b)

c) −2

d) None of these

If f (x) = cos (lnx) then f (x) f (y) −   has the value of

a) −1

b)

c) −2

d) None of these

IIT 1983
02:43 min
337

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

IIT 1988
04:52 min
338

The value of  is

a) 0

b) 1

c) 2

d) 4

The value of  is

a) 0

b) 1

c) 2

d) 4

IIT 1989
03:14 min
339

If b and c are any two non-collinear unit vectors and a is any vector then    .  .  .  .  .

If b and c are any two non-collinear unit vectors and a is any vector then    .  .  .  .  .

IIT 1996
03:25 min
340

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

IIT 2005
05:15 min
341

For n > 0,  is

a)

b) π

c)

d)

For n > 0,  is

a)

b) π

c)

d)

IIT 1996
08:23 min
342

The value of the definite integral  is

a) – 1

b) 2

c)

d)

The value of the definite integral  is

a) – 1

b) 2

c)

d)

IIT 1981
02:44 min
343

Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.

Let A be the centre of the circle . Suppose the tangents at the points B (1, 7) and D (4, 2) on the circle meet at the point C, find the area of the quadrilateral ABCD.

IIT 1981
06:52 min
344

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

IIT 1996
01:41 min
345

If f (x) = 3x – 5 then f -1 (x)

a) is given by

b) is given by

c)

d)

If f (x) = 3x – 5 then f -1 (x)

a) is given by

b) is given by

c)

d)

IIT 1998
01:38 min
346

Evaluate

a) 0

b)

c)

d) 1

Evaluate

a) 0

b)

c)

d) 1

IIT 1978
01:06 min
347

If  has its extremum value at x = 1 and x = 2, then

a) a = 2, b = 1

b) a = 2,

c) a =  2,

d) None of these

If  has its extremum value at x = 1 and x = 2, then

a) a = 2, b = 1

b) a = 2,

c) a =  2,

d) None of these

IIT 1983
02:13 min
348

Let  be a polynomial in a real variable x with 0< then the function p(x) has

a) neither maximum nor minimum

b) only one maximum

c) only one minimum

d) only one maximum and only one minimum

e) none of these

Let  be a polynomial in a real variable x with 0< then the function p(x) has

a) neither maximum nor minimum

b) only one maximum

c) only one minimum

d) only one maximum and only one minimum

e) none of these

IIT 1986
02:37 min
349

Let a given line L1 intersect the X-axis and Y-axis at P and Q respectively. Let another line L2 perpendicular to L1 cut the X and Y axis at R and S respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.

Let a given line L1 intersect the X-axis and Y-axis at P and Q respectively. Let another line L2 perpendicular to L1 cut the X and Y axis at R and S respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.

IIT 1987
07:55 min
350

Fill in the blank
General values of θ satisfying the equation  are

a) θ = nπ

b)

c)

d) θ = nπ or θ =

Fill in the blank
General values of θ satisfying the equation  are

a) θ = nπ

b)

c)

d) θ = nπ or θ =

IIT 1996
02:28 min

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