If
$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{
0 & {\cos x} & { - \sin x} \cr
{\sin x} & 0 & {\cos x} \cr
{\cos x} & {\sin x} & 0 \cr
} } \right| = 0} \right\},$
then $\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $ is equal to :
Previous 10 Questions — JEE Main 2017 (8 April Morning Shift)
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An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
Topic: JEE Main 2017 (8 April Morning Shift)
The value of $\tan^{-1}\left[\dfrac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right]$, $|x|
Topic: JEE Main 2017 (8 April Morning Shift)
Consider an ellipse, whose center is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\d…
Topic: JEE Main 2017 (8 April Morning Shift)
Let $z\in\mathbb{C}$, the set of complex numbers. Then the equation $2|z+3i|-|z-i|=0$ represents :
Topic: JEE Main 2017 (8 April Morning Shift)
Let f(x) = 210.x + 1 and g(x)=310.x $-$ 1. If (fog) (x) = x, then x is equal to :
Topic: JEE Main 2017 (8 April Morning Shift)
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in Engli…
Topic: JEE Main 2017 (8 April Morning Shift)
If the arithmetic mean of two numbers a and b, a>b>0, is five times their geometric mean, then $\dfrac{a+b}{a-b}$ is eq…
Topic: JEE Main 2017 (8 April Morning Shift)
Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remai…
Topic: JEE Main 2017 (8 April Morning Shift)
Let $A$ be any $3\times 3$ invertible matrix. Then which one of the following is not always true?
Topic: JEE Main 2017 (8 April Morning Shift)
If (27)999 is divided by 7, then the remainder is :
Topic: JEE Main 2017 (8 April Morning Shift)
Next 10 Questions — JEE Main 2017 (8 April Morning Shift)
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Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $\dfra…
Topic: JEE Main 2017 (8 April Morning Shift)
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appo…
Topic: JEE Main 2017 (8 April Morning Shift)
The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8\hat{i}-6\hat{j}$ and $3\hat{i}+4\…
Topic: JEE Main 2017 (8 April Morning Shift)
If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles…
Topic: JEE Main 2017 (8 April Morning Shift)
The integral $\int_{{\pi \over {12}}}^{{\pi \over 4}} {\,\,{{8\cos 2x} \over {{{\left( {\tan x + \cot x} \right)}^3}}…
Topic: JEE Main 2017 (8 April Morning Shift)
The area (in sq. units) of the smaller portion enclosed between the curves $x^2 + y^2 = 4$ and $y^2 = 3x$, is :
Topic: JEE Main 2017 (8 April Morning Shift)
The locus of the point of intersection of the straight lines,
$tx-2y-3t=0$,
$x-2ty+3=0\ (t\in\mathbb{R}),$ is :
Topic: JEE Main 2017 (8 April Morning Shift)
The curve satisfying the differential equation $y,dx-(x+3y^{2}),dy=0$ and passing through the point (1,1), also passes …
Topic: JEE Main 2017 (8 April Morning Shift)
If y = ${\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}},$
then (x2 $-$ …
Topic: JEE Main 2017 (8 April Morning Shift)
If a point P has co-ordinates (0,-2) and Q is any point on the circle $x^{2}+y^{2}-5x-y+5=0$, then the maximum value of…
Topic: JEE Main 2017 (8 April Morning Shift)
