Question(s) from Search: IIT

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 .

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.

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

a)

b)

c) 3

d)

The number of solutions of  is

a) 3

b) 1

c) 2

d) 0

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

Match the following

Normals are drawn at the points P, Q and R lying on the parabola  which intersect at (3, 0) then

If a polynomial of degree 3, then  equals

a)

b)

c)

d) a constant

If ε then  is always greater than or equal to

a) 2 tan

b) 1

c) 2

d)

If the expression  is real then the set of all possible values of x is .  .  .  .

a) x = 2nπ or mπ + π/4

b) x = nπ or mπ + π/4

c) x = 2nπ or 2mπ + π/4

d) x = nπ or 2mπ + π/4

(Assertion and reason)

The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if

a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1.

b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true

Statement 1 – The curve  is symmetric with respect to the line x = 1

Statement 2 – The parabola is symmetric about its axis.

If  then

a)

b)

c)

d)

Let P = (x, y) be any point on  with focii  and  equals

a) 8

b) 6

c) 10

d) 12

Let α, β be roots of the equation are the roots of the equation  then the value of r is equal to

a)

b)

c)

d)

Show that square of  is a rational number.

The determinants   are.

a) Identical

b) Not identical

c) Identical if a = b = c

d) None of the above

Given that x = −9 is a root of  = 0

.

a) {2, 7}

b) {−2, −7}

c) {2, 0}

d) {0, 7}

An ellipse has OB as a semi-minor axis. F, F’ are its focii and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is . . . . .

If x = 9 is the chord of contact of the hyperbola  then the equation of the corresponding pair of tangents is

a)

b)

c)

d)

Solve for x

The rational number which equals the numbers with recurring decimals is

a)

b)

c)

d)

If a, b, c are in Geometric Progression then the equations  
have a common root if  are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) None of these

The circle  intersects hyperbola  in four points then

a)

b)

c)

d)

Solve for x in the following equation

Let T_r be the r^th term of an Arithmetic Progression for  If for some positive integers m, n we have  and  then T_mn equals

a)

b)

c)

d)

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then  is

a) 0.4

b) 0.8

c) 1.2

d) 1.4