Recent questions in JEEMAIN-2016

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 :

asked May 26, 2017 by meena.p

1 answer

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

asked May 26, 2017 by meena.p

1 answer

If $f(x)$ is a differentiable function in the interval $(0, \infty)$ such that $f(1)=1$ and $\lim \limits_{t \to x} \large\frac{t^2f(x)-x^2f(t)}{t-x} $$=1$ fopr each $x >0$ then $f( \large\frac{3}{2})$ is equal to :

asked May 26, 2017 by meena.p

1 answer

The area (in sq. units) of the region described by $A=\{(x, y)|y ≥ x2−5x+4, x+y ≥ 1, y ≤ 0\}$ is :

asked May 26, 2017 by meena.p

1 answer

Bromination of cyclohexene under conditions given below yields :

asked May 26, 2017 by priyanka.c

1 answer

If $2 \int \limits_0^1 \tan ^{-1} x dx = \int \limits _0^1 \cot ^{-1} (1-x+x^2)dx$ then $\int \limits_0^1 \tan ^{-1} (1-x+x^2)dx$ is equal to :

asked May 26, 2017 by meena.p

1 answer

Sodium extract is heated with concentrated HNO3 before testing for halogens because :

asked May 26, 2017 by priyanka.c

1 answer

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

asked May 26, 2017 by priyanka.c

1 answer

If $\int \Large\frac{dx}{\cos ^3 x \sqrt {2 \sin 2x}}$$=(\tan x)^A+C(\tan x)^B +k$ where k is a constant of integration, then $A+B+C$ equals :

asked May 26, 2017 by meena.p

1 answer

The transition metal ions responsible for color in ruby and emerald are, respectively :

asked May 26, 2017 by priyanka.c

1 answer

The minimum distance of a point on the curve $y=x^2−4$ from the origin is :

asked May 26, 2017 by meena.p

1 answer

Which of the following is an example of homoleptic complex ?

asked May 26, 2017 by priyanka.c

1 answer

Identify the correct statement :

asked May 26, 2017 by priyanka.c

1 answer

If the tangent at a point $P,$ with parameter $t$, on the curve $x=4t^2+3, y=8t^3−1, t \in R,$ meets the curve again at a point Q, then the coordinates of Q are :

asked May 26, 2017 by meena.p

1 answer

Identify the incorrect statement :

asked May 26, 2017 by priyanka.c

1 answer

Assertion : Among the carbon allotropes, diamond is an insulator, whereas, graphite is a good conductor of electricity </br> Reason : Hybridization of carbon in diamond and graphite are $sp^3$ and $sp^2$, respectively.

asked May 26, 2017 by priyanka.c

1 answer

If the function $f(x) = \left\{ \begin{array}{l l} -x, & \quad x < 1 \\ a+\cos ^{-1} (x+b), & \quad 1 \leq x \leq 2 \end{array} \right.$ is differentiable at $x=1$, then $\large\frac{a}{b}$ is equal to :

asked May 26, 2017 by meena.p

1 answer

The commercial name for calcium oxide is :

asked May 26, 2017 by priyanka.c

1 answer

Identify the reaction which does not liberate hydrogen :

asked May 26, 2017 by priyanka.c

1 answer

If $\lim \limits_{x \to \infty}$ \bigg( 1+ \large\frac{a}{x}-\frac{4]{x^2} \bigg)^{2x} =e^3$, then 'a' is equal to :

asked May 26, 2017 by meena.p

1 answer

Extraction of copper by smelting uses silica as an additive to remove :

asked May 26, 2017 by priyanka.c

1 answer

The value of $\sum \limits_{r=1}^{15} r^2 \bigg( \large\frac{^{15} C_r}{^{15}C_{r-1}}\bigg)$ is equal to :

asked May 26, 2017 by meena.p

1 answer

The following statements concern elements in the periodic table. Which of the following is true ?

asked May 26, 2017 by priyanka.c

1 answer

Gold numbers of some colloids are : Gelatin : 0.005 - 0.01, Gum Arabic : 0.15 - 0.25; Oleate : 0.04 - 1.0; Starch : 15 - 25. Which among these is a better protective colloid ?

asked May 26, 2017 by priyanka.c

1 answer

The rate law for the reaction below is given by the expression $ k [A][B] \; A+B \to Product $ If the concentration of $B$ is increased from $0.1$ to $ 0.3 \;mole$, keeping the value of $A$ at $0.1 \; mole$, the rate constant will be :

asked May 26, 2017 by priyanka.c

1 answer

Let $x, y, z$ be positive real numbers such that $x+y+z=12$ and $x^3y^4z^5=(0.1) (600)^3$. Then $x^3+y^3+z^3$ is equal to :

asked May 26, 2017 by meena.p

1 answer

Oxidation of succinate ion produces ethylene and carbon dioxide gases. On passing $0.2 \; Faraday$ electricity through an aqueous solution of potassium succinate, the total volume of gases (at both cathode and anode) at STP ($1 \;atm$ and $273 K$) is :

asked May 26, 2017 by priyanka.c

1 answer

A solid $XY$ kept in an evacuated sealed container undergoes decomposition to form a mixture of gases $ X$ and $Y$ at temperature $T$. The equilibrium pressure is $10\; bar$ in this vessel. $ K_p$ for this reaction is :

asked May 26, 2017 by priyanka.c

1 answer

An aqueous solution of a salt $MX_2$ at certain temperature has a van’t Hoff factor of $2$. The degree of dissociation for this solution of the salt is :

asked May 25, 2017 by priyanka.c

1 answer

If $100 \; mole$ of $ H_2O_2$ decompose at $1 \; bar$ and $300 K,$ the work done $(kJ)$ by one mole of $O_2(g)$ as it expands against 1 bar pressure is:

asked May 25, 2017 by priyanka.c

1 answer

The bond angle $H-X-H$ is the greatest in the compound :

asked May 25, 2017 by priyanka.c

1 answer

Aqueous solution of which salt will not contain ions with the electronic configuration $1s^22s^22p^63s^23p^6$ ?

asked May 25, 2017 by priyanka.c

1 answer

Initially, the $root\; mean\; square\; (rms)$ velocity of $N2$ molecules at certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new $rms$ velocity will be :

asked May 25, 2017 by priyanka.c

1 answer

The volume of $0.1N$ dibasic acid sufficient to neutralize $1 g$ of a base that furnishes $0.04$ mole of $OH^{−}$ in aqueous solution is :

asked May 25, 2017 by priyanka.c

1 answer

The ratio $(R)$ of output resistance $r_0$, and the input resistance $r_i$ in measurements of input and output characteristics of a transistor is typically in the range :

asked May 25, 2017 by priyanka.c

1 answer

A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a commonemitter transistor configuration is :

asked May 25, 2017 by priyanka.c

1 answer

A galvanometer has a $50$ division scale. Battery has no internal resistance. It is found that there is deflection of $40$ divisions when $R=2400 Ω$. Deflection becomes $20$ divisions when resistance taken from resistance box is $4900 Ω$. Then we can conclude :

asked May 25, 2017 by priyanka.c

1 answer

For $x \in R,x \neq -1$, if $(1+x)^{2016} +x(1=x)^{2015} +x^2(1+x)^{2014}+.......+x^{2016}=\sum \limits_{i=0} ^{2016} a_i x^i $, then $a_{17}$ is equal to :

asked May 25, 2017 by meena.p

1 answer

If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :

asked May 25, 2017 by meena.p

1 answer

The number of distinct real roots of the equation $P=\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 $\bigg[ \large\frac{-\pi}{4} ,\frac{\pi}{4} \bigg]$ is :

asked May 25, 2017 by meena.p

1 answer

If $P=\begin{bmatrix} \large\frac{\sqrt 3}{2} & \frac{1}{2} \\ \large\frac{-1}{2} & \large\frac{\sqrt 3}{2} \end{bmatrix} $ , $A=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} $ and $Q= PAP^{T}$, then $P^Tq^{2015}P$ is :

asked May 25, 2017 by meena.p

1 answer

A thin $1 m$ long rod has a radius of $5 mm$. A force of $50 πkN$ is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 mm$, which of the following statements is false ?

asked May 25, 2017 by priyanka.c

1 answer

A particle of mass m is acted upon by a force $F$ given by the empirical law $F = \frac{R}{t^2} v(t)$. If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

asked May 25, 2017 by priyanka.c

1 answer

A modulated signal $C_m(t)$ has the form $C_m(t)=30 \; \sin \; 300πt+10\; (cos 200πt −\cos 400πt)$. The carrier frequency $f_c$, the modulating frequency (message frequency) $f_ω$, and the modulation index $µ$ are respectively given by :

asked May 25, 2017 by priyanka.c

1 answer

To get an output of 1 from the circuit shown in figure the input must be :

asked May 25, 2017 by priyanka.c

1 answer

If the equations $x^2+bx−1=0$ and $x^2+x+b=0$ have a common root different from $−1$, then $|b|$ is equal to :

asked May 25, 2017 by meena.p

1 answer

A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is

asked May 25, 2017 by priyanka.c

1 answer

The point represented by $2+i$ in the Argand plane moves $1 \;unit $ eastwards, then $2 \;units$ northwards and finally from there $2 \sqrt 2$ units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :

asked May 25, 2017 by meena.p

1 answer

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

asked May 25, 2017 by meena.p

1 answer

A photoelectric surface is illuminated successively by monochromatic light of wavelengths $ λ$ and $\frac{λ}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3\; times $ that in the first case, the work function of the surface is :

asked May 25, 2017 by priyanka.c

1 answer

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