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 objective function of L.L.P. defined over the convex set attains its optimum value at
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
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?
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 slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
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
In a triangle ABC, with usual notations ∠A = 60°, then (1 + \(\frac {a}{c}\) + \(\frac {b}{c}\))(1 + \(\frac {c}{b}\) - \(\frac {a}{b}\)) = ?
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.
A random variable X has the following probability distribution then P (X ≥ 2) =?
Which of the following statement pattern is a contradiction?
\(\int_{-π/2}^{π/2} f(x) \,dx\) =?Where f(x) = sin |x| + cos |x|, x ∈ \((-\frac {π}{2}, \frac {π}{2})\)
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
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 y = sec–1\((\frac {x + x^{-1}}{x - x^{-1}})\), then \(\frac {dy}{dx}\) =?
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 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.)
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.)
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
The area of the region bounded by the y-axis, y = cos x, y = sin x, when 0 ≤ x ≤\(\frac {π}{4}\), is
