A to Z Exams

If N denotes the set of all positive integers and if f:N->N is defined by f(n) = thesum of positive divisors of n then, f (2k, 3), where k is a positive integers is

The area (in square units) of the triangle formed by the lines x = 0,y = 0 and 3x + 4y = 12, is

If a point P moves such that its distances from the point A (1, 1) and the line x+ y + 2 = 0 are equal, then the locus of  P is

For a binomial variate X with n = 6, if P(X = 2) = 9P(X = 4), then its variance is

Box A contains 2 black and 3 red balls, while Box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B, is

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

In a ∆ABC, a(cos2 B + cos2 C) + cos A (c cos C + b cos B) is equal to

2 tan h -1 1/2  is equal to

sin -1(4/5) + 2 tan -1(1/3)  is equal to

If A+C =2B then(cos C - cos A) / (sin A -sin C) is equal to

The extreme values of  4 cos(x2) cos(π/3  + x2 ) cos(π/3 - x2) over IR are

The roots of the equation x3 - 3x - 2 = 0 are

The function f : c → c defined by  f(x) = (ax+b) / (cx+d) for x ε c where bd ≠ 0 reduces to a constant function, if

If f(x) = 10 cos x +(13+2x) sin x then f"(x) + f(x) is equal to

A stone thrown upward has its equation of motion s =490t - 4.9t2 then the maximum height reached by it is

The radius of a circle plate is increasing at the rate of  0.01 cm/s when the radius is at 12 cm . then the rate at which the area increases is

Observe the following statements A: f'(x) = 2x3 - 9x2  + 12x - 3 is increasing outside the interval (1, 2)R: f'(x) < 0 for x belongs to (1,2).Then which of the following is true

For any integer n ≥ 1, the number of positive divisors of n is denoted by d(n). Then for   a prime P, d(d(d(P7}}) =

The line among the following which touches the parabola y2=4ax, is

Which of the following equations gives a circle

The Cartesian form of the polar equation θ = tan -1 2 is

The area (in square units) bounded by the curves y2 = 4x and x2 = 4y in the plane is :

 If dx + dy =(x + y) ( dx- dy ) then log ( x  +  y ) is equal to

If PM is the perpendicular from P (2, 3) onto the line x + y = 3, then the co-ordinates of M are

The equation of the straight line perpendicular to 5x - 2y = 7 and passing through the point of intersection of the lines 2x + 3y = 1 and 3x + 4y = 6, is

The area of the triangle formed by the pair of straight lines (ax + by)2 - 3(bx - ay)2 = 0 and ax + by + c = 10, is

The product of the perpendicular distances from the origin on the pair of straight lines12x2 + 25xy + 12y2 + 10x + 11y + 2 = 0, is

The direction cosines of the line passing through P (2, 3, - 1) and the origin are

The point collinear with (1,-2,-3) and (2,0, 0) among the following is

The equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is