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 =?
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 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
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 \(\frac {dy}{dx}\) =?
∫\(\frac {5(x^6+1)}{X+1}\)dx = (where C is a constant of integration.)
∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (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.)
Which among the following is correct decreasing order of covalent character of ionic bond?
Identify the correct decreasing order of ease of dehydrohalogenation of alkyl halides.
Which from following polymers is obtained using
The equation of the line perpendicular to 2x – 3y + 5 = 0 and making an intercept 3 with positive Y-axis is
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?
For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to
The objective function of L.L.P. defined over the convex set attains its optimum value at
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
Argument of \(\frac {1-i√3}{1+i√3}\) is
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
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
If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then equation of the circle is (Taken π=\(\frac {22}{7}\))
If the standard deviation of first n natural numbers is 2, then the value of n is
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.
The principal solutions of tan 3θ = –1 are
