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Question(s) from Search: IIT

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326

Find the area bounded by the X–axis, part of the curve  and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a.

a)

b)

c)

d)

Find the area bounded by the X–axis, part of the curve  and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a.

a)

b)

c)

d)

IIT 1983
04:06 min
327

The chord of contact of the pair of tangents drawn from each point on the line  to the circle  passes through the point . . . . .

The chord of contact of the pair of tangents drawn from each point on the line  to the circle  passes through the point . . . . .

IIT 1997
02:57 min
328

The largest interval for which  is

a)

b)

c)

d)

The largest interval for which  is

a)

b)

c)

d)

IIT 1982
04:35 min
329

Find the tangents to the curve
y = cos(x + y), − 2π ≤ x ≤ 2π
that are parallel to the line x + 2y = 0

Find the tangents to the curve
y = cos(x + y), − 2π ≤ x ≤ 2π
that are parallel to the line x + 2y = 0

IIT 1985
07:32 min
330

The equation  has

a) No root

b) One root

c) Two equal roots

d) Infinitely many roots

The equation  has

a) No root

b) One root

c) Two equal roots

d) Infinitely many roots

IIT 1984
01:04 min
331

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
332

Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of  and 0 < α < β then the equation  has a root γ that always satisfies

a) γ =

b) γ =

c) γ = α

d) α < γ < β

Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of  and 0 < α < β then the equation  has a root γ that always satisfies

a) γ =

b) γ =

c) γ = α

d) α < γ < β

IIT 1989
03:43 min
333

The determinant
 = 0 if

a) x, y, z are in arithmetic progression

b) x, y, z are in geometric progression

c) x, y, z are in harmonic progression

d) xy, yz, zx are in arithmetic progression

The determinant
 = 0 if

a) x, y, z are in arithmetic progression

b) x, y, z are in geometric progression

c) x, y, z are in harmonic progression

d) xy, yz, zx are in arithmetic progression

IIT 1997
02:44 min
334

If  are the n roots of unity then show that .

If  are the n roots of unity then show that .

IIT 1984
02:49 min
335

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
336

If p, q, r are positive and are in arithmetic progression the roots of the quadratic  are all real for

a)

b)

c)

d)

If p, q, r are positive and are in arithmetic progression the roots of the quadratic  are all real for

a)

b)

c)

d)

IIT 1994
02:34 min
337

The number of distinct roots of
 = 0
in the interval   ≤ x ≤   is

a) 0

b) 2

c) 1

d) 3

The number of distinct roots of
 = 0
in the interval   ≤ x ≤   is

a) 0

b) 2

c) 1

d) 3

IIT 2001
04:03 min
338

(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
339

If α and β (α < β) are roots of the equation  where c < 0 < b then

a) 0 < α < β

b) α < 0 < β < | α |

c) α < β < 0

d) α < 0 < | α | < β

If α and β (α < β) are roots of the equation  where c < 0 < b then

a) 0 < α < β

b) α < 0 < β < | α |

c) α < β < 0

d) α < 0 < | α | < β

IIT 2000
02:20 min
340

If A =  and | A3| = 125 then the value of α is

a) ± 1

b) ±2

c) ± 3

d) ± 5

If A =  and | A3| = 125 then the value of α is

a) ± 1

b) ±2

c) ± 3

d) ± 5

IIT 2004
00:46 min
341

Let and  be the roots of the equation  where the coefficients p and q may be complex numbers. Let A and B represent  in the complex plane. If  and OB = OA where O is the origin, prove that .

Let and  be the roots of the equation  where the coefficients p and q may be complex numbers. Let A and B represent  in the complex plane. If  and OB = OA where O is the origin, prove that .

IIT 1997
04:53 min
342

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
343

For the equation  if one of the roots is square of the other then p is equal to

a)

b)

c) 3

d)

For the equation  if one of the roots is square of the other then p is equal to

a)

b)

c) 3

d)

IIT 2000
03:13 min
344

The number of solutions of  is

a) 3

b) 1

c) 2

d) 0

The number of solutions of  is

a) 3

b) 1

c) 2

d) 0

IIT 2001
02:44 min
345

If a, b, c be positive and not all equal, show that the value of the determinant  is negative.

If a, b, c be positive and not all equal, show that the value of the determinant  is negative.

IIT 1981
04:21 min
346

Without expanding a determinant at any stage show that
 = Ax + B

where A, B are non-zero constants

Without expanding a determinant at any stage show that
 = Ax + B

where A, B are non-zero constants

IIT 1982
04:06 min
347

True/False
If the complex numbers  represent the vertices of an equilateral triangle with  then .

a) True

b) False

True/False
If the complex numbers  represent the vertices of an equilateral triangle with  then .

a) True

b) False

IIT 1984
02:27 min
348

The order of the differential equation whose general solution is given by  is

a) 5

b) 4

c) 3

d) 2

The order of the differential equation whose general solution is given by  is

a) 5

b) 4

c) 3

d) 2

IIT 1998
03:42 min
349

If f (x) =

a) f (x) is a strictly increasing function

b) f (x) has a local maxima

c) f (x) is a strictly decreasing function

d) f (x) is bounded

If f (x) =

a) f (x) is a strictly increasing function

b) f (x) has a local maxima

c) f (x) is a strictly decreasing function

d) f (x) is bounded

IIT 2004
02:07 min
350

Let Δa =
Then show that  = c, a constant.

Let Δa =
Then show that  = c, a constant.

IIT 1989
05:34 min

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