All BASICSTANDARDADVANCED

Question(s) from Search: IIT

Search Results Difficulty Solution
426

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
427

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
428

Let z and ω be two complex numbers such that |z| ≤ 1 and |w| ≤ 1 then show that .

Let z and ω be two complex numbers such that |z| ≤ 1 and |w| ≤ 1 then show that .

IIT 1995
06:01 min
429

A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.

A is a point on the parabola . The normal at A cuts the parabola again at B. If AB subtends a right angle at the vertex of the parabola, find the slope of AB.

IIT 1982
06:08 min
430

If a, b, c, d are positive real numbers such that a + b + c + d = 2 then M = ( a + b ) ( c + d ) satisfies

a) 0 ≤ M ≤ 1

b) 1 ≤ M ≤ 2

c) 2 ≤ M ≤ 3

d) 3 ≤ M ≤ 4

If a, b, c, d are positive real numbers such that a + b + c + d = 2 then M = ( a + b ) ( c + d ) satisfies

a) 0 ≤ M ≤ 1

b) 1 ≤ M ≤ 2

c) 2 ≤ M ≤ 3

d) 3 ≤ M ≤ 4

IIT 2000
01:54 min
431

Show that the locus of a point that divides a chord of slope 2 of the parabola  internally in the ratio 1:2 is a parabola. Find its vertex.

Show that the locus of a point that divides a chord of slope 2 of the parabola  internally in the ratio 1:2 is a parabola. Find its vertex.

IIT 1995
06:25 min
432

Let α, β be the roots of  and γ, δ roots of . If α, β, γ, δ are in geometric progression then the integral values of p and q respectively are

a) −2, −32

b) −2, 3

c) −6, 3

d) −6, −32

Let α, β be the roots of  and γ, δ roots of . If α, β, γ, δ are in geometric progression then the integral values of p and q respectively are

a) −2, −32

b) −2, 3

c) −6, 3

d) −6, −32

IIT 2001
05:16 min
433

For what values of k does the following system of equations possess a non-trivial solution over the set of rationals? Find all the solutions.

x + y – 2z = 0

2x – 3y + z = 0

x – 5y + 4z = k

For what values of k does the following system of equations possess a non-trivial solution over the set of rationals? Find all the solutions.

x + y – 2z = 0

2x – 3y + z = 0

x – 5y + 4z = k

IIT 1979
05:23 min
434

Prove that there exists no complex number z such that  and .

Prove that there exists no complex number z such that  and .

IIT 2003
04:27 min
435

Three normals with slopes  are drawn from a point P not on the axis of the parabola . If  results in the locus of P being a part of the parabola, find the value of α.

Three normals with slopes  are drawn from a point P not on the axis of the parabola . If  results in the locus of P being a part of the parabola, find the value of α.

IIT 2003
05:59 min
436

Find the value of the expression

1.(2−ω)(2−+ 2.(3−ω)(3−+ … (n−1).(n−ω)(n−

where ω is an imaginary cube root of unity.

a) n(n−1)(+3n+4)

b) n(n+1)(+3n+4)

c) n(n−1)(+n+1)

d) n(n+1)(+n+1)

Find the value of the expression

1.(2−ω)(2−+ 2.(3−ω)(3−+ … (n−1).(n−ω)(n−

where ω is an imaginary cube root of unity.

a) n(n−1)(+3n+4)

b) n(n+1)(+3n+4)

c) n(n−1)(+n+1)

d) n(n+1)(+n+1)

IIT 1996
05:00 min
437

If  are positive real numbers whose product is a fixed number c then the minimum value of  is

a)

b)

c)

d)

If  are positive real numbers whose product is a fixed number c then the minimum value of  is

a)

b)

c)

d)

IIT 2002
02:06 min
438

If three complex numbers are in arithmetic progression then they lie on a circle in the complex plane.

a) True

b) False

If three complex numbers are in arithmetic progression then they lie on a circle in the complex plane.

a) True

b) False

IIT 1985
01:13 min
439

A solution of the differential equation  is

a)  y = 2

b)  y = 2x

c)  

d)  2

A solution of the differential equation  is

a)  y = 2

b)  y = 2x

c)  

d)  2

IIT 1999
01:47 min
440

For all x,  then the interval in which a lies is

a) a <

b)

c)

d)

For all x,  then the interval in which a lies is

a) a <

b)

c)

d)

IIT 2004
01:45 min
441

Let the three digit numbers A28, 3B9 and 62C where A, B, C are integers between 0 and 9, be divisible by a fixed number k. Show that the determinant
 

is divisible by k.

Let the three digit numbers A28, 3B9 and 62C where A, B, C are integers between 0 and 9, be divisible by a fixed number k. Show that the determinant
 

is divisible by k.

IIT 1990
04:45 min
442

If a and b are real numbers between 0 and 1 such that the points  form an equilateral triangle then a is equal to .  .  .  .

a)  

b)  

c)  

d)  

If a and b are real numbers between 0 and 1 such that the points  form an equilateral triangle then a is equal to .  .  .  .

a)  

b)  

c)  

d)  

IIT 1989
03:07 min
443

Let E be the ellipse  and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then

a) Q lies inside C but outside E

b) Q lies outside both C and E

c) P lies inside both C and E

d) P lies inside C but outside E

Let E be the ellipse  and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then

a) Q lies inside C but outside E

b) Q lies outside both C and E

c) P lies inside both C and E

d) P lies inside C but outside E

IIT 1994
04:15 min
444

Let a, b, c be the sides of a triangle where a ≠ c and λ ε R. If roots of the equation  are real then

a)

b)

c)

d)

Let a, b, c be the sides of a triangle where a ≠ c and λ ε R. If roots of the equation  are real then

a)

b)

c)

d)

IIT 2006
04:47 min
445

Find the value of the determinant

where a, b, c are respectively pth, qth and rth term of a harmonic

progression.

a) 0

b) 1

c) ½

d) None of the above

Find the value of the determinant

where a, b, c are respectively pth, qth and rth term of a harmonic

progression.

a) 0

b) 1

c) ½

d) None of the above

IIT 1997
04:23 min
446

If tangents are drawn to the ellipse  then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is

a)

b)

c)

d)

If tangents are drawn to the ellipse  then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is

a)

b)

c)

d)

IIT 2004
03:11 min
447

Let S is the set of all real x, such that  is positive, then S contains

a)

b)

c)

d)

Let S is the set of all real x, such that  is positive, then S contains

a)

b)

c)

d)

IIT 1986
04:28 min
448

Let pλ4 + qλ3 + rλ2 + sλ + t =  be an identity in λ where p, q, r, s, t are constants. Find the value of t.

a) 0

b) +1

c) –1

d) ±1

Let pλ4 + qλ3 + rλ2 + sλ + t =  be an identity in λ where p, q, r, s, t are constants. Find the value of t.

a) 0

b) +1

c) –1

d) ±1

IIT 1981
02:38 min
449

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

IIT 1994
02:27 min
450

A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .

A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .

IIT 1997
01:37 min

Play Selected  Login to save this search...