If $P = \begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \\ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, $Q = P A P^{T}$, then $P^{T} Q^{2015} P$ is:
Previous 10 Questions — JEE Main 2016 (9 April Morning Shift)
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The point represented by $2 + i$ in the Argand plane moves $1$ unit eastwards, then $2$ units northwards and finally fr…
Topic: JEE Main 2016 (9 April Morning Shift)
If the equations $x^{2} + bx - 1 = 0$ and $x^{2} + x + b = 0$ have a common root different from $-1$, then $|b|$ is equ…
Topic: JEE Main 2016 (9 April Morning Shift)
The number of distinct real roots of the equation
$ \begin{vmatrix}
\cos x & \sin x & \sin x \\
\sin x & \cos x & \si…
Topic: JEE Main 2016 (9 April Morning Shift)
If the four-letter words (need not be meaningful) are to be formed using the letters from the word “MEDITERRANEAN” such…
Topic: JEE Main 2016 (9 April Morning Shift)
Let $x, y, z$ be positive real numbers such that
$x + y + z = 12$
and
$x^{3} y^{4} z^{5} = (0.1)(600)^{3}$.
Then $x^{3}…
Topic: JEE Main 2016 (9 April Morning Shift)
For $x \in \mathbb{R},; x \ne -1$,
if
$ (1+x)^{2016} + x(1+x)^{2015} + x^{2}(1+x)^{2014} + \ldots + x^{2016}
= \display…
Topic: JEE Main 2016 (9 April Morning Shift)
Next 10 Questions — JEE Main 2016 (9 April Morning Shift)
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For $x \in \mathbb{R}, x \ne 0$, let $f_{0}(x) = \dfrac{1}{1 - x}$ and $f_{n+1}(x) = f_{0}(f_{n}(x)),; n = 0,1,2,\ldots…
Topic: JEE Main 2016 (9 April Morning Shift)
The value of
$\displaystyle \sum_{r=1}^{15} r^{2} \left( \dfrac{{}^{15}C_{r}}{{}^{15}C_{r-1}} \right)$ is equal to:
Topic: JEE Main 2016 (9 April Morning Shift)
A circle passes through $(-2,4)$ and touches the $y$-axis at $(0,2)$. Which one of the following equations can represen…
Topic: JEE Main 2016 (9 April Morning Shift)
If $m$ and $M$ are the minimum and the maximum values of
$4 + \dfrac{1}{2}\sin^{2} 2x - 2\cos^{4} x,; x \in \mathbb{R}$…
Topic: JEE Main 2016 (9 April Morning Shift)
Let $a$ and $b$ respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies …
Topic: JEE Main 2016 (9 April Morning Shift)
In a triangle $ABC$, right angled at the vertex $A$, if the position vectors of $A,B$ and $C$ are respectively
$3\hat{i…
Topic: JEE Main 2016 (9 April Morning Shift)
If $A$ and $B$ are any two events such that $P(A) = \dfrac{2}{5}$ and $P(A \cap B) = \dfrac{3}{20}$, then the condition…
Topic: JEE Main 2016 (9 April Morning Shift)
If the mean deviation of the numbers
$1,, 1 + d,, \ldots,, 1 + 100d$
from their mean is $255$, then a value of $d$ is:
Topic: JEE Main 2016 (9 April Morning Shift)
The shortest distance between the lines
$\dfrac{x}{2} = \dfrac{y}{2} = \dfrac{z}{1}$
and
$\dfrac{x + 2}{-1} = \dfrac{y …
Topic: JEE Main 2016 (9 April Morning Shift)
The point $(2,1)$ is translated parallel to the line $L : x - y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in…
Topic: JEE Main 2016 (9 April Morning Shift)
