JEE Main 2016 (Offline)

If the line, \({{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z + 4} \over 3}\,\) lies in the planes, \(lx+my-z=9,\) then \({l^2} + {m^2}\) is equal to :

The distance of the point \((1,-5,9)\) from the plane \(x-y+z=5\) measured along the line \(x=y=z\) is :

A wire of length \(2\) units is cut into two parts which are bent respectively to form a square of side \(=x\) units and a circle of radius \(=r\) units. If the sum of the areas of the square and the circle so formed is minimum, then:

Consider :
f \(\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).\)
A normal to \(y =\) f\(\left( x \right)\) at \(x = {\pi \over 6}\) also passes through ...

The area (in sq. units) of the region \(\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}\) is :

If the number of terms in the expansion of \({\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,\) is 28, then the sum of the coefficients of all the terms in this expansion, is :

The centres of those circles which touch the circle, \({x^2} + {y^2} - 8x - 8y - 4 = 0\), externally and also touch the \(x\)-axis, lie on :

If one of the diameters of the circle, given by the equation, \({x^2} + {y^2} - 4x + 6y - 12 = 0,\) is a chord of a circle \(S\), whose centre is at \((-3, 2)\), then the radius of \(S\) is :

A value of \(\theta \,\) for which \({{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}\) is purely imaginary, is :

\(\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}\) is equal to:

If a curve \(y=f(x)\) passes through the point \((1,-1)\) and satisfies the differential equation, \(y(1+xy) dx=x\) \(dy\), then \(f\left( { - {1 \over 2}} \right)\) is equal to :

If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then $\mathrm{S}:$

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same di...

The eccentricity of the hyperbola whose length of the latus rectum is equal to \(8\) and the length of its conjugate axis is equal to half of the distance between its foci, is :

The integral \(\int {{{2{x^{12}} + 5{x^9}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}} dx\) is equal to :

For \(x \in \,R,\,\,f\left( x \right) = \left| {\log 2 - \sin x} \right|\,\,\)
and \(\,\,g\left( x \right) = f\left( {f\left( x \right)} \right),\,\,\) then :

Let \(p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}}\) then \(log\) \(p\) is equal to :

The Boolean expression
\(\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)\) is equivalent to :

If \(A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]\) and \(A\) adj \(A=A\) \({A^T},\) then \(5a+b\) is equal to :

The system of linear equations
\(\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr }\)
has a non-trivial solution for :

Let \(P\) be the point on the parabola, \({{y^2} = 8x}\) which is at a minimum distance from the centre \(C\) of the circle, \({x^2} + {\left( {y + 6} \right)^2} = 1\). Then the equation of the circle, passing through \(C\) and having its c...

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :

Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \({E_1}\) is the event that die \(A\) shows up four, \({E_2}\) is the event that die \(B\) shows up two and \({E_3}\) is the event that the sum of numbers on both dice...

The sum of all real values of \(x\) satisfying the equation \({\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}}\, = 1\) is :

If the sum of the first ten terms of the series \({\left( {1{3 \over 5}} \right)^2} + {\left( {2{2 \over 5}} \right)^2} + {\left( {3{1 \over 5}} \right)^2} + {4^2} + {\left( {4{4 \over 5}} \right)^2} + .......is\,{{16} \over 5}m,\) then m i...

If the \({2^{nd}},{5^{th}}\,and\,{9^{th}}\) terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

Two sides of a rhombus are along the lines, \(x - y + 1 = 0\) and \(7x - y - 5 = 0\). If its diagonals intersect at \((-1, -2)\), then which one of the following is a vertex of this rhombus?

If \(0 \le x < 2\pi\), then the number of real values of \(x\), which satisfy the equation \(\,\cos x + \cos 2x + \cos 3x + \cos 4x = 0\) is:

Let \(\overrightarrow a ,\overrightarrow b\) and \(\overrightarrow c\) be three unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow...