Recent questions in JEEMAIN-2016

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are:

asked Jun 2, 2017 by priyanka.c

1 answer

The contrapositive of the following statement,
“If the side of a square doubles, then its area increases four times”, is :

asked May 30, 2017 by priyanka.c

1 answer

The angle of elevation of the top of a vertical tower from a point $A,$ due east of it is $45^0$ . The angle of elevation of the top of the same tower from a point $B$ , due south of $A$ is $30^0$ . If the distance between $A$ and $B$ is $54 \sqrt 2$ m , then the height of the tower (in metres), is :

asked May 30, 2017 by priyanka.c

1 answer

If $A>0, B>0$ and $Α + B = \frac{\pi}{6} ,$ then the minimum value of $\tan A + \tan B$ is :

asked May 30, 2017 by priyanka.c

1 answer

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

asked May 30, 2017 by priyanka.c

1 answer

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 :

asked May 30, 2017 by priyanka.c

1 answer

Let $ABC$ be a triangle whose circumcentre is at $P$ . If the position vectors of $A, B, C$ and $P$ are $\overrightarrow{a} , \overrightarrow{b}, \overrightarrow{c}$ and $\frac{\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}}{4}$ respectively, then the position vector of the orthocentre of this triangle, is :

asked May 30, 2017 by priyanka.c

1 answer

The number of distinct real values of $λ$ for which the lines $\begin{align} \frac{x-1}{1} = \frac{y-2}{2} = \frac{z+3}{\lambda^2} \end{align}$ and $\begin{align}\frac{x-3}{1} = \frac{y-2}{\lambda^2 } = \frac{z-1}{2} \end{align}$ are coplanar is:

asked May 30, 2017 by priyanka.c

1 answer

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

asked May 30, 2017 by priyanka.c

1 answer

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 ?

asked May 30, 2017 by priyanka.c

1 answer

$P$ and $Q$ are two distinct points on the parabola, $y2=4x,$ with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$ , then the minimum value of $t_1^2$ is :

asked May 30, 2017 by priyanka.c

1 answer

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 $2x+y=3$ is :

asked May 30, 2017 by priyanka.c

1 answer

A straight line through origin $O$ meets the lines $3y=10−4x$ and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio :

asked May 29, 2017 by priyanka.c

1 answer

A ray of light is incident along a line which meets another line, $7x−y+1=0$ , at the point $(0, 1).$ The ray is then reflected from this point along the line, $y+2x=1.$ Then the equation of the line of incidence of the ray of light is :

asked May 29, 2017 by priyanka.c

1 answer

The solution of the differential equation $\begin{align} \frac{dy}{dx} + \frac{y}{2} \sec x = \frac{\tan}{2\;y}, \end{align}$ where $0 \leq x < \frac{\pi}{2},$ and $y(0)= 1,$ is given by

asked May 29, 2017 by priyanka.c

1 answer

For $x \; \epsilon \;R, x ≠ 0,$ if $y(x)$ is a differentiable function such that $\begin{align} x \int_1^x y\; (t) \;dt = (x+1) \int_1^x t\; y \;(t)\; dt, \end{align}$ then $y(x)$ equals :
(where C is a constant.)

asked May 29, 2017 by priyanka.c

1 answer

The value of the integral $\begin{align} \int_4^{10} \frac{[x^2]dx}{[x^2 -28x + 196] + [x^2] } , \end{align}$ where $[x]$ denotes the greatest integer less than or equal to $x,$ is :

asked May 29, 2017 by priyanka.c

1 answer

The integral $\begin{align} \int \frac{dx}{(1+\sqrt x) \sqrt{x - x^2}} \end{align}$ to :
(where C is a constant of integration.)

asked May 29, 2017 by priyanka.c

1 answer

Let $C$ be a curve given by $y (x) = 1 + \sqrt{4x - 3}, x>\frac{3}{4}.$ If P is a point on $C$ , such that the tangent at $P$ has slope $\frac{2}{3},$ then a point through which the normal at $P$ passes is:

asked May 29, 2017 by priyanka.c

1 answer

Let $f(x)=sin^4x+cos^4x.$ Then f is an increasing function in the interval :

asked May 29, 2017 by priyanka.c

1 answer

If the tangent at a point on the ellipse $\large\frac{x^2}{27} +\frac{y^2}{3}$ $=1$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle $OAB$ is :

asked May 29, 2017 by meena.p

1 answer

Consider the following two statements : <br> P : If 7 is an odd number, then 7 is divisible by 2. <br> Q : If 7 is a prime number, then 7 is an odd number. <br> If $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of Q, then the ordered pair $(V_1, V_2)$ equals :

asked May 29, 2017 by meena.p

1 answer

If $m$ and $M$ are the minimum and the maximum values of $4 +\large\frac{1}{2}$ $\sin ^2 2x - 2 \cos ^4 x , x \in R$ then $M−m$ is equal to :

asked May 29, 2017 by meena.p

1 answer

The number of $x \in [0, 2 \pi]$ for which $| \sqrt{2 \sin ^4 x +18 \cos ^2 x} - \sqrt {2 \cos ^4 x +18 \sin ^2 x}|=1$ is :

asked May 29, 2017 by meena.p

1 answer

If $A$ and $B$ are any two events such that $P(A)= \large\frac{2}{5}$ and $P(A \cap B)=\large\frac{3}{20}$ ,then the conditional probability, $P(A |(A' \cup B')),$ where $A'$ denotes the complement of A, is equal to :

asked May 29, 2017 by meena.p

1 answer

Let $a, b \;\epsilon \; R, (a ≠ 0).$ If the function f defined as $f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \leq x < 1 \\ a , & 1 \leq x < \sqrt 2 \\ \frac{2b^2 - 4b}{x^3}, & \sqrt 2 \leq x < \infty \end{cases}$ is continuous in the interval $[0, ∞)$ , then an ordered pair $(a, b)$ is

asked May 29, 2017 by priyanka.c

1 answer

If the mean deviation of the numbers $1, 1+ d, ..., 1+100d$ from their mean is $255$ , then a value of $d$ is :

asked May 29, 2017 by meena.p

1 answer

In a triangle $ABC$ , right angled at the vertex $A$ , if the position vectors of A, B and C are respectively $3 \hat i + \hat j - \hat k , \hat i+3 \hat j +p \hat k$ and $5 \hat i+q \hat j -4 \hat k$ then the point $(p, q)$ lies on a line :

asked May 29, 2017 by meena.p

1 answer

The distance of the point $(1, −2, 4)$ from the plane passing through the point $(1, 2, 2)$ and perpendicular to the planes $x−y+2z=3$ and $2x−2y+z+12=0,$ is :

asked May 29, 2017 by meena.p

1 answer

$\begin{align}\lim_{x\to o}\frac{(1 - \cos2x)^2}{2x \; \tan x -x \tan 2x } \end{align}$ is :

asked May 29, 2017 by priyanka.c

1 answer

The shortest distance between the lines $\large\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\large\frac{x+2}{-1} = \frac{y-4}{8} =\frac{z-5}{4}$ lies in the interval

asked May 29, 2017 by meena.p

1 answer

The sum $\displaystyle\sum_{r =1}^{10} (r^2 + 1) \times (r!)$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2−18e+5=0$ . If $S(5, 0)$ is a focus and $5x=9$ is the corresponding directrix of this hyperbola, then $a^2−b^2$ is equal to

asked May 29, 2017 by meena.p

1 answer

Let $a_1, a_2, a_3, ......, a_n, .....$ be in A.P. If $a_3+a_7+a_11+a_15=72,$ then the sum of its $first\; 17\; terms$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer