List of top Questions asked in JEE Main- 2016

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :

For $x \, \in \, R , x \neq 0, x \neq 1,$ let $f_0(x) = \frac{1}{1-x}$ and $f_{n+1} (x) | = f_0 (f_n(x)), n = 0 , 1 , 2 , ...$ Then the value of $f_{100}(3) + f_1 \left(\frac{2}{3} \right) + f_2 \left( \frac{3}{2} \right)$ is equal to :

A satellite is revolving in a circular orbit at a height ' $h$' from the earth's surface (radius of earth $R ; h < < R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth?s gravitational field, is close to : (Neglect the effect of atmosphere.)

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C$ ln $(BD)$ holds true. Then which of the combination is not a meaningful quantity ?

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :

$'n'$ moles of an ideal gas undergoes a process $A \to B $ as shown in the figure. The maximum temperature of the gas during the process will be :

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

The number of distinct real roots of the equation, $\begin{vmatrix}\cos x&\sin x &\sin x\\ \sin x&\cos x&\sin x\\ \sin x&\sin x&\cos x\end{vmatrix}= 0$ in the interval $ \left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$ is :

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4 $ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it ?

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 the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :

At very high pressures, the compressibility factor of one mole of a gas is given by :

If $A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}$ and $A$ adj $A$ = $AA^T$ , then $5a + b$ is equal to :

Let $z = 1 + ai$ be a complex number, $a > 0$, such that $z^3$ is a real number. Then the sum $1 + z + z^2 +..... + z^{11}$ 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 $f \left( - \frac{1}{2} \right)$ is equal to :

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:

If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$, meets the coordinate axes at $A$ and $B$, $(A \neq B)$, then the locus of the midpoint of $AB$ is :

Equation of the tangent to the circle, at the point $(1, -1)$, whose centre is the point of intersection of the straight lines $x - y = 1$and $+ y = 3$is :

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the six trials of this experiment is :

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then :

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

Bromination of cyclohexene under conditions given below yields :

Which one of the following substances used in dry cleaning is a better strategy to control environmental pollution ?