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The equation of the tangent to the curve (1 + x^{2})y = 2  x where it crosses xaxis is
The area bounded by the parabola x = 4  y^{2} and the yaxis in square units, is
If x^{2} + x + 1 is a factor of ax^{3} + bx^{2} + cx +d,then the real root of ax^{3} + bx^{2} + cx + d = 0
If f: R → R is defined by f x = x − [ x ] , where [x] is the greatest integer not exceeding x, then the set of discontinuities of f is
The area bounded by the curve y=xsinx and xaxis between x=0 and x=2π is
The value of determinant ∆ of 3rd order is 9 then the value of ∆′^{2} where ∆′ is a determinant formed by cofactors of the element of ∆ is
If the function f is defined by then at what points is f differentiable
Integrating factor of differential equation cos x dy/dx+y sin x = 1 is
The number of solutions of dy/dx = (y+1)/(x1) when y (1) = 2 is :
If S is the set of all real x such that 2x  1/2x^{3} + 3x^{2} + x is positive, then S contains
If cos^{1}p + cos^{1}q+cos^{1}r = π, then p^{2} + q^{2} + r^{2} + 2pqr is equal to
Let cos^{1} p = α, cos^{1} q = β and cos^{1} r = γ
⇒ cosα = p, cosβ = q and cosγ = r
From question, α + β + γ = π
∴ cos (α + β) = cos (π  γ)
Squaring, we get p^{2}q^{2} + r^{2} + 2pqr = 1  p^{2}  q^{2} + p^{2}q^{2}
or, p^{2} + q^{2} + r^{2} + 2pqr = 1
If for [ x ] = 0 where [x] denotes the greatest integer not exceeding x, then
Which of the following is not a statement in logic ?
1. Earth is planet .
2. Plants are living object .
3. is rational number .
4. x^{2}  5x + 6 < 0, where x ∈ − R
If A is a square matrix of order 3 x 3 , then adj (adj A) is equal to
P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?
Total no. of ways delivering lectures = ^{4}P_{4} = 4! = 24
When two balls are drawn from a bag containing 2 white, 4 red and 6 black balls, the chance for both of them to be red is
The nth term of the series 3, √3, 1,... is 1/243, then n is
The coefficient of correlation between two variables x and y is 0.5, their covariance is 16. If the S.D. of x is 4, then the S.D. of y is equal to
The quartile deviation of daily wages (in Rs.) of 7 persons given below:
12, 7, 15, 10, 17, 17, 25 is
Roots of the equation 5x^{2}7x+k=0 are reciprocal of each other, then the value of k is
A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with yaxis, is such that sin^{2}β = 3sin^{2}θ, then cos^{2}θ equals:
The shortest distance between the lines (x  3)/3 = (y  8)/1 = (z  3)/1 and (x + 3)/3 = (y + 7)/2 = (z 6)/4 is
The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to
A circle touches the xaxis and also touches the cirlce with centre at (0, 3) and radius 2. The locus of the centre of the cirlce is
The locus of a point whose abscissa and ordinate are always equal is
If a=3, b=4, c=5 and a+b+c=0, the angle between a and b is
If vectors 3i+2jk and 6i4xj+yk are parallel, then the value of x and y are
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