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Question(s) from Search: IIT

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326

Let f(x) =

If f is continuous for all x, then k is equal to

a) 3

b) 5

c) 7

d) 9

Let f(x) =

If f is continuous for all x, then k is equal to

a) 3

b) 5

c) 7

d) 9

IIT 1981
03:32 min
327

Fill in the blank

The domain of the function f (x) =  is

a) [− 2, − 1]

b) [1, 2]

c) [− 2, − 1] ⋃ [1, 2]

d) None of the above

Fill in the blank

The domain of the function f (x) =  is

a) [− 2, − 1]

b) [1, 2]

c) [− 2, − 1] ⋃ [1, 2]

d) None of the above

IIT 1984
02:48 min
328

 

 

Then

a) 0

b) 1

c) 2

d) 4

 

 

Then

a) 0

b) 1

c) 2

d) 4

IIT 1981
01:26 min
329

The complex numbers  satisfying  are the vertices of the triangle which is

a) of zero area

b) right angle isosceles

c) equilateral

d) obtuse angled isosceles

The complex numbers  satisfying  are the vertices of the triangle which is

a) of zero area

b) right angle isosceles

c) equilateral

d) obtuse angled isosceles

IIT 2001
05:10 min
330

Let x and y be two real variables such that x > 0 and xy = 1. Find the minimum value of x + y.

a) 1

b) 2

c) 3

d) 4

Let x and y be two real variables such that x > 0 and xy = 1. Find the minimum value of x + y.

a) 1

b) 2

c) 3

d) 4

IIT 1981
01:44 min
331

ABC is an isosceles triangle in a circle of radius r. If AB = AC and h is the altitude from A to BC then the triangle ABC has perimeter , area A = . . . . .

Also  . . . . .

ABC is an isosceles triangle in a circle of radius r. If AB = AC and h is the altitude from A to BC then the triangle ABC has perimeter , area A = . . . . .

Also  . . . . .

IIT 1989
07:12 min
332

Let f(x) = x|x|. The set of points where f(x) is twice differentiable is .  .  .  .

a) ℝ

b) 0

c) ℝ − {0, 1}

Let f(x) = x|x|. The set of points where f(x) is twice differentiable is .  .  .  .

a) ℝ

b) 0

c) ℝ − {0, 1}

IIT 1992
02:00 min
333

Find the shortest distance of the point (0, c) from the parabola
y = x2, where 0 ≤ c ≤ 5.

a)

b)

c)

d)

Find the shortest distance of the point (0, c) from the parabola
y = x2, where 0 ≤ c ≤ 5.

a)

b)

c)

d)

IIT 1982
03:58 min
334

Both roots of the equation

( x – b) ( x – c) + (x – c) ( x – a) + (x – a) (x – b) = 0 are always

a) positive

b) negative

c) real

d) none of these

Both roots of the equation

( x – b) ( x – c) + (x – c) ( x – a) + (x – a) (x – b) = 0 are always

a) positive

b) negative

c) real

d) none of these

IIT 1980
02:52 min
335

 

a) – 1

b) 0

c) 1

d) 2

 

a) – 1

b) 0

c) 1

d) 2

IIT 1997
02:51 min
336

If  is purely real where ω = α + iβ, β ≠ 0 and z ≠ 1 then the set of real values of z is

a)  

b)  

c)  

d)  

If  is purely real where ω = α + iβ, β ≠ 0 and z ≠ 1 then the set of real values of z is

a)  

b)  

c)  

d)  

IIT 2006
05:43 min
337

Two vertices of an equilateral triangle are (- 1, 0) and (1, 0) and its third vertex lies above the X–axis, the equation of circumcircle is . . .

Two vertices of an equilateral triangle are (- 1, 0) and (1, 0) and its third vertex lies above the X–axis, the equation of circumcircle is . . .

IIT 1997
04:55 min
338

Two towns A and B are 60 meters apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all the 200 students is to be as small as possible then the school should be built at

a) Town B

b) 45 km from town A

c) Town A

d) 45 km from town B

Two towns A and B are 60 meters apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all the 200 students is to be as small as possible then the school should be built at

a) Town B

b) 45 km from town A

c) Town A

d) 45 km from town B

IIT 1982
01:37 min
339

If a continuous function f defined on the real line ℝ, assumes positive and negative values in ℝ then the equation f(x) = 0 has a root in ℝ. For example, it is known that if a continuous function f on ℝ is positive at some points and its minimum value is negative then the equation f(x) = 0 has a root in ℝ. Consider the function f(x) =  for all real x where k is a real constant.

The line y = x meets y =  for k ≤ 0 at

a) No point

b) One point

c) Two points

d) More than two points

If a continuous function f defined on the real line ℝ, assumes positive and negative values in ℝ then the equation f(x) = 0 has a root in ℝ. For example, it is known that if a continuous function f on ℝ is positive at some points and its minimum value is negative then the equation f(x) = 0 has a root in ℝ. Consider the function f(x) =  for all real x where k is a real constant.

The line y = x meets y =  for k ≤ 0 at

a) No point

b) One point

c) Two points

d) More than two points

IIT 2007
02:08 min
340

(One or more than one correct answer)
Let  and  be complex numbers such that  and . If has positive real part and  has negative imaginary part, then  may be

a) Zero

b) Real and positive

c) Real and negative

d) None of these

(One or more than one correct answer)
Let  and  be complex numbers such that  and . If has positive real part and  has negative imaginary part, then  may be

a) Zero

b) Real and positive

c) Real and negative

d) None of these

IIT 1986
05:31 min
341

If then ab + bc + ca lies in the interval

a)  

b)  

c)  

d)  

If then ab + bc + ca lies in the interval

a)  

b)  

c)  

d)  

IIT 1984
02:29 min
342

Find the values of x and y for which the following equation is satisfied

a) x = y = −1

b) x = y = 3

c) x = 1, y = 3

d) x = 3, y = −1

Find the values of x and y for which the following equation is satisfied

a) x = y = −1

b) x = y = 3

c) x = 1, y = 3

d) x = 3, y = −1

IIT 1980
05:23 min
343

The equation of the directrix of the parabola y2 + 4y + 4x +2 = 0 is

a) x = − 1

b) x = 1

c)

d)

The equation of the directrix of the parabola y2 + 4y + 4x +2 = 0 is

a) x = − 1

b) x = 1

c)

d)

IIT 2001
01:51 min
344

Let α, β be roots of the equation (x – a) (x – b) = c, c ≠ 0. Then the roots of the equation (x – α) (x – β) + c = 0 are

a) a, c

b) b, c

c) a, b

d) a + c, b + c

Let α, β be roots of the equation (x – a) (x – b) = c, c ≠ 0. Then the roots of the equation (x – α) (x – β) + c = 0 are

a) a, c

b) b, c

c) a, b

d) a + c, b + c

IIT 1992
02:15 min
345

The expression  is a polynomial of degree

a) 5

b) 6

c) 7

d) 8

The expression  is a polynomial of degree

a) 5

b) 6

c) 7

d) 8

IIT 1992
03:38 min
346

If f(x) =
then f(100) equals

a) 0

b) 1

c) 100

d) −100

If f(x) =
then f(100) equals

a) 0

b) 1

c) 100

d) −100

IIT 1999
02:18 min
347

Show that the area of the triangle on the argand diagram formed by the complex numbers z, iz, z + iz is   .

Show that the area of the triangle on the argand diagram formed by the complex numbers z, iz, z + iz is   .

IIT 1986
03:10 min
348

The angle between the tangents drawn from the point (1, 4) to the parabola  is

a)

b)

c)

d)

The angle between the tangents drawn from the point (1, 4) to the parabola  is

a)

b)

c)

d)

IIT 2004
02:56 min
349

The equation  has

a) No solution

b) One solution

c) Two solutions

d) More than two solutions

The equation  has

a) No solution

b) One solution

c) Two solutions

d) More than two solutions

IIT 1997
03:20 min
350

If the system of equations

x + ay = 0

az + y = 0

ax + z = 0

has infinite solutions then the value of a is

a) −1

b) 1

c) 0

d) No real values

If the system of equations

x + ay = 0

az + y = 0

ax + z = 0

has infinite solutions then the value of a is

a) −1

b) 1

c) 0

d) No real values

IIT 2003
04:39 min

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