JEE Advanced 2017 Paper 2 Offline

The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y \(-\) 2z = 5 and 3x \(-\) 6y \(-\) 2z = 7 is

f : R \(\to\) R is a differentiable function such that f'(x) > 2f(x) for all x\(\in\)R, and f(0) = 1 then

If \(f(x) = \left| {\matrix{ {\cos 2x} & {\cos 2x} & {\sin 2x} \cr { - \cos x} & {\cos x} & { - \sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right|\),then

If the line x = \(\alpha\) divides the area of region R = {(x, y) \(\in\)R2 : x3 \(\le\) y \(\le\) x, 0 \(\le\) x \(\le\) 1} into two equal parts, then

If \(I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx}\), then

If y = y(x) satisfies the differential equation\({8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4 + \sqrt {9 + \sqrt x } } } \right)}^{ - 1}}}\)dx, x > 0 and y(0) = \(\sqrt 7\), then y(256) =

If \(g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt\), then

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5 =

Let \(f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)\)for x \(\ne\) 1. Then

If f : R \(\to\) R is a twice differentiable function such that f"(x) > 0 for all x\(\in\)R, and \(f\left( {{1 \over 2}} \right) = {1 \over 2}\), f(1) = 1, then

How many 3 \(\times\) 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?

Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is

a12 = ?

If a4 = 28, then p + 2q =

If the triangle PQR varies, then the minimum value of cos(P + Q) + cos(Q + R) + cos(R + P) is

Let \(\alpha\) and \(\beta\) be non zero real numbers such that \(2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1\). Then which of the following is/are true?

|\(\overrightarrow{OX}\) \(\times\) \(\overrightarrow{OY}\)| = ?

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that\(\overrightarrow{OP}\) . \(\overrightarrow{OQ}\) + \(\overrightarrow{OR}\) . \(\overrightarrow{OS}\) = \(\overrightarrow{OR}\) . \(\overrightarrow{OP}\) + $$...