If xy = e(x – y) , then \(\frac {dy}{dx}\) =?
A round table conference is to be held among 20 countries. If two particular delegates wish to sit together, then such arrangements can be done in __________ways.
If surrounding air is kept at 20 °C and body cools from 80 °C to 70 °C in 5 minutes, then the temperature of the body after 15 minutes will be
The objective function of L.L.P. defined over the convex set attains its optimum value at
If \(\int \frac {2e^x + e^x}{3e^x + 4e^{-x}} \,dx\) = Ax + Blog( 3e2x + 4) + C, then values of A and B are respectively (where C is a constant of integration.)
The principal solutions of tan 3θ = –1 are
The general solution of differential equation \(e^{\frac {1}{2} (\frac {dy}{dx})}\) = 3x is (where C is a constant of integration.)
If y = 4x – 5 is tangent to the curve y2 =px3 +q at (2, 3), then
For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to
Which of the following statement pattern is a contradiction?
If a and b are two vectors such that I\(\vec {a}\)I + I\(\vec {b}\)I = \(\sqrt 2\) with \(\vec {a}\).\(\vec {b}\) = –1, then the angle between \(\vec {a}\) and \(\vec {b}\) is
Give that f(x) =\(\frac {1-cos4x}{x^2}\) if x < 0 ,f(x) = a if x = 0 , f(x) =\(\frac {\sqrt {x}}{\sqrt {16 + \sqrt {x} }- 4}\) if x > 0, is continuous at x = 0, then a will be
\(\int_{-π/2}^{π/2} f(x) \,dx\) =?Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)
In a triangle ABC, with usual notations ∠A = 60°, then (1 + \(\frac {a}{c}\) + \(\frac {b}{c}\))(1 + \(\frac {c}{b}\) - \(\frac {a}{b}\)) = ?
The general solution of the differential equation x2 + y2 – 2xy \(\frac {dy}{dx}\) = 0 is (where C is a constant of integration.)
The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤\(\frac {π}{4}\), is
The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is
Argument of \(\frac {1-i√3}{1+i√3}\) is
Probability of getting odd numbers in first 100 numbers.
A polygon has 44 diagonals. Then the number of sides of the polygon are
If $x = 1 + 2i$, then the value of $x^3 + 7x^2 - x + 16$ is