∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)
If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is
If matrix A =\(\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}\) is such that AX = I, where I is 2 x 2 unit matrix, then X =
A random variable X has the following probability distribution then P (X ≥ 2) =?
If y = sec–1\((\frac {x + x^{-1}}{x - x^{-1}})\), then \(\frac {dy}{dx}\) =?
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
For the differential equation [1 + \((\frac {dy}{dx})^2\)]5/2 = 8 \((\frac {d^2y}{dx^2})\) has the order and degree_________respectively.
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?
With reference to the principal values, if sin-1x + sin-1y + sin-1z = \(\frac {3π}{2}\), then x100 + y100 + z100 =?
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
If a, b, c are position vectors of points A, B, C respectively, with 2a + 3b -5c = 0 , then the ratio in which point C divides segment AB is
The angle between two lines x +1 =y + 3 =z - 4 and \(\frac {x-4}{1}\) = \(\frac {y+2}{2}\) = \(\frac {z+1}{2}\) is
If \(\begin{bmatrix} 2 & 1 \\ 3 & 2\end{bmatrix}\) A \(\begin{bmatrix} -3 & 2 \\ 5 & -3\end{bmatrix}\) =\(\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}\), then A =?
20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is
If the standard deviation of first n natural numbers is 2, then the value of n is
The ratio in which the plane r.(\(\hat i\) -2\(\hat j\) + 3\(\hat k\) ) =17 divides the line joining the points -2\(\hat i\)+4\(\hat j\)+7\(\hat k\) and 3\(\hat i\)-5\(\hat j\)+8\(\hat k\) is
∫\(\frac {5(x^6+1)}{X+1}\)dx = (where C is a constant of integration.)
If xy = e(x – y) , then \(\frac {dy}{dx}\) =?
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
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.
The objective function of L.L.P. defined over the convex set attains its optimum value at
The principal solutions of tan 3θ = –1 are
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 general solution of differential equation \(e^{\frac {1}{2} (\frac {dy}{dx})}\) = 3x is (where C is a constant of integration.)
