If y = 4x – 5 is tangent to the curve y2 =px3 +q at (2, 3), then
For the differential equation [1 + \((\frac {dy}{dx})^2\)]5/2 = 8 \((\frac {d^2y}{dx^2})\) has the order and degree_________respectively.
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
∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)
With reference to the principal values, if sin-1x + sin-1y + sin-1z = \(\frac {3π}{2}\), then x100 + y100 + z100 =?
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 =
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 =?
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
The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤\(\frac {π}{4}\), is
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 \(\frac {dy}{dx}\) =?
The general solution of differential equation \(e^{\frac {1}{2} (\frac {dy}{dx})}\) = 3x is (where C is a constant of integration.)
The general solution of the differential equation x2 + y2 – 2xy \(\frac {dy}{dx}\) = 0 is (where C is a constant of integration.)
∫\(\frac {5(x^6+1)}{X+1}\)dx = (where C is a constant of integration.)
\(\int_{-π/2}^{π/2} f(x) \,dx\) =?Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)
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
Which of the following statement pattern is a contradiction?
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.)
For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to
The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is
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.
Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
