Question(s) from Search: IIT

Fill in the blank

Let A, B, C be three vectors of length 3, 4, 5 respectively. Let A is perpendicular to B + C, B is perpendicular to C + A, and C is perpendicular to A + B then the length of the vector  is equal to  . . . .

The number of common tangents to the circles  and  is

a) 0

b) 1

c) 3

d) 4

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

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

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

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

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 =

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

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

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

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) (

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

a) −1

b)

c) −2

d) None of these

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

The value of  is

a) 0

b) 1

c) 2

d) 4

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

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)

For n > 0,  is

a)

b) π

c)

d)

The value of the definite integral  is

a) – 1

b) 2

c)

d)

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.

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

a)

b)

c)

d)

If f (x) = 3x – 5 then f ^-1 (x)

a) is given by

b) is given by

c)

d)

Evaluate

a) 0

b)

c)

d) 1

If   then  equals

a)

b)

c)

d) 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

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.