Which among the following is an actinoid element?
Calculate the number of atoms in 20 gram metal which crystallises to simple cubic structure having unit cell edge length 340 pm. (density of metal = 9.8 gcm–3)
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 =
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
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 \(\frac {dy}{dx}\) =?
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?
For the differential equation [1 + \((\frac {dy}{dx})^2\)]5/2 = 8 \((\frac {d^2y}{dx^2})\) has the order and degree_________respectively.
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
With reference to the principal values, if sin-1x + sin-1y + sin-1z = \(\frac {3π}{2}\), then x100 + y100 + z100 =?
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 \(\begin{bmatrix} 2 & 1 \\ 3 & 2\end{bmatrix}\) A \(\begin{bmatrix} -3 & 2 \\ 5 & -3\end{bmatrix}\) =\(\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}\), then A =?
The 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 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 \(\frac {dy}{dx}\) =?
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
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.)
If y = 4x – 5 is tangent to the curve y2 =px3 +q at (2, 3), then
