JEE Advanced 2018 Paper 1 Offline

Let P1 : 2x + y \(-\) z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?

For each positive integer n, let \({y_n} = {1 \over n}(n + 1)(n + 2)...{(n + n)^{{1 \over n}}}\). For x\(\in\)R, let [x] be the greatest integer less than or equal to x. If \(\mathop {\lim }\limits_{n \to \infty } {y_n} = L\), then the va...

A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F2 takes away the region which lies between the sides PQ and a curve of the form y = xn (n > 1). If the a...

Let f : [0, \(\infty\)) \(\to\) R be a continuous function such that\(f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt}\) for all x \(\in\) [0, \(\infty\)). Then, which of the following statement(s) is (are) TRUE?

Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing throug...

For a non-zero complex number z, let arg(z) denote the principal argument with \(-\) \(\pi\) < arg(z) \(\le\) \(\pi\). Then, which of the following statement(s) is (are) FALSE?

Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point o...

The number of real solutions of the equation $$\eqalign{
& {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = 1}^\infty {} {{\left( {{x \over 2}} \right)}^i}} \right) \cr
& = {\pi \over 2} - {\cos ...

The value of \({({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}}\) is ....................

For every twice differentiable function \(f:R \to [ - 2,2]\) with \({(f(0))^2} + {(f'(0))^2} = 85\), which of the following statement(s) is(are) TRUE?

Let f : R \(\to\) R and g : R \(\to\) R be two non-constant differentiable functions. If f'(x) = (e(f(x) \(-\) g(x))) g'(x) for all x \(\in\) R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?

The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is .................

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

Let a, b, c three non-zero real numbers such that the equation \(\sqrt 3 a\cos x + 2b\sin x = c,x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]\), has two distinct real roots \(\alpha\) and \(\beta\) with $$\alpha + \beta = {\pi...

Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ...., and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, .... . Then, the number of elements in the set X ...

In a \(\Delta\)PQR = 30\(^\circ\) and the sides PQ and QR have lengths 10\(\sqrt 3\) and 10, respectively. Then, which of the following statement(s) is(are) TRUE?

Let a and b be two unit vectors such that a . b = 0. For some x, y\(\in\)R, let \(\overrightarrow c = x\overrightarrow a + y\overrightarrow b + \overrightarrow a \times \overrightarrow b\). If | \(\overrightarrow c\)| = 2 and the ve...