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Recent questions and answers in JEEMAIN-2013

Questions >> Archives >> JEEMAIN-2013

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

answered Apr 19, 2017 by meena.p

1 answer

The expression $\large\frac{\tan A}{1- \cot A} +\frac{\cot A}{1- \tan A}$ can be written as :

answered Apr 19, 2017 by meena.p

1 answer

If $y= \sec (\tan ^{-1}x)$, then $\large\frac{dy}{dx}$ at $x=1$ is equal to :

answered Apr 19, 2017 by meena.p

1 answer

Given : A circle,$2x^2+2y^2=5$ and an parabola , $y^2 = 4 \sqrt 5 x$ <br> Statement − I : An equation of a common tangent to these curves is $y =x +\sqrt 5$ <br> Statement − II : If the line, $y= mx+ \large\frac{\sqrt 5}{m} $$(m \neq 0)$ is their common tangent, then ‘m’ satisfies $m^4- 3m^2+2=0$

answered Apr 19, 2017 by meena.p

1 answer

The intercepts on x−axis made by tangents to the curve, $y= \int \limits_0^x |t| dt , x \in R$ which are parallel to the line $y = 2x,$ are equal to

answered Apr 19, 2017 by meena.p

1 answer

If $P=\begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} = 0 $ is the adjoint of $3 \times 3$ matrix $A$ and $|A|=4$ , then $\alpha$ is equal to :

answered Apr 18, 2017 by meena.p

1 answer

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC \perp CD$. If $\angle ADB = \theta, BC = p$ and $CD = q,$ then $AB$ is equal to :

answered Apr 18, 2017 by meena.p

1 answer

If z is a complex number of unit modulus and argument $\theta$, then $arg\bigg(\large\frac{1+z}{1+\bar{z}}\bigg)$ equals

answered Apr 18, 2017 by meena.p

1 answer

Let $T_n$ be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If $T_{n+1} − T_{n} = 1$ then the value of n is :

answered Apr 18, 2017 by meena.p

1 answer

The area (in square units) bounded by the curves $y=\sqrt x, 2y−x+3= 0$, x−axis, and lying in the first quadrant is :

answered Apr 18, 2017 by meena.p

1 answer

The term independent of x in expansion of $\bigg( \large\frac{x+1}{x^{2/3}-x^{1/3}+1} -\frac{x-1}{x-x^{1/2}} \bigg)^{10}$ is :

answered Apr 18, 2017 by meena.p

1 answer

The x−coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :

answered Apr 18, 2017 by meena.p

1 answer

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

answered Apr 18, 2017 by meena.p

1 answer

The equation of the circle passing through the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^2}{9} $$=1$ and having center at $(0,3)$ is :

answered Apr 17, 2017 by meena.p

1 answer

Statement − I : The value of the integral $\int\limits_{\pi/6} ^{\pi/3} \large\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\large\frac{\pi}{6}$. Statement − II : $\int\limits_{a}^{b} f(x)dx =\int \limits_a^b f(a+b-x)dx$

answered Apr 17, 2017 by meena.p

1 answer

$\lim\limits_{x \to 0} \large\frac{(1-cos 2x )(3+\cos x)}{x \tan 4x}$ is equal to

answered Apr 17, 2017 by meena.p

1 answer

If $\int f(x)=dx= \psi(x)$, then $\int x^5 f(x^3)dx $ is equal to :

answered Apr 17, 2017 by meena.p

1 answer

Consider : Statement − I : $(p \wedge \sim q) \wedge p ( \sim p \wedge q)$ is fallacy. Statement - II : $(p \to q) \longleftrightarrow ( \sim q \to \sim p)$ is a tautology

answered Apr 13, 2017 by meena.p

1 answer

If x, y, z are in A.P. and $\tan^{-1}x,\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P then :

answered Apr 12, 2017 by meena.p

1 answer

The circle passing through $(1, −2)$ and touching the axis of $x$ at $(3, 0)$ also passes through the point :

answered Apr 12, 2017 by meena.p

1 answer

If the equations $x^2 + 2x + 3 = 0$ and $ax^2+ bx + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is

answered Apr 12, 2017 by meena.p

1 answer

The number of values of k, for which the system of equations : $(k + 1)x + 8y = 4k\\ kx + (k + 3)y = 3k − 1 $ has no solution, is :

answered Apr 12, 2017 by meena.p

1 answer

A ray of light along $x+ \sqrt{3}y =\sqrt 3$ gets reflected upon reaching x−axis, the equation of the reflected ray is :

answered Apr 12, 2017 by meena.p

1 answer

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777, ……,$ is :

answered Apr 12, 2017 by meena.p

1 answer

The real number k for which the equation, $2x^3+3x+ k = 0$ has two distinct real roots in $[0, 1]$

answered Apr 11, 2017 by meena.p

1 answer

If the vector $\overrightarrow{AB} = 3 \hat i +4 \hat k$ and $\overrightarrow{AC} = 5 \hat i - 2 \hat j +4 \hat k$ are the sides of a triangle ABC, then the length of the median through A is :

answered Apr 11, 2017 by meena.p

1 answer

If the lines $\large\frac{x-2}{1} =\frac{y-3}{1} =\frac{z-4}{-k}$ and $\large\frac{x-1}{k} =\frac{y-4}{2} =\frac{z-5}{1}$ are coplanar, then k can have :

answered Apr 11, 2017 by meena.p

1 answer

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is :

answered Apr 10, 2017 by meena.p

1 answer

At present,a firm is manufacturing $2000 \;items$. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by $\large\frac{dp}{dx}$$=100 12 \sqrt {x}$. If the firm employs 25 more workers, then the new level of production of items is :

answered Apr 10, 2017 by meena.p

1 answer

Distance between two parallel planes $2x + y +2z = 8$ and $4x + 2y + 4z + 5 = 0$ is :

answered Apr 10, 2017 by meena.p

1 answer

Experimentally it was found that a metal oxide has formula $M_{0.98}O$. Metal M, is present as $M^{2+}$and $M^{3+}$ in its oxide. Fraction of the metal which exists as $M^{3+}$ would be :

answered Apr 7, 2017 by meena.p

1 answer

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was :

answered Apr 7, 2017 by meena.p

1 answer

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism :

answered Apr 7, 2017 by meena.p

1 answer

Stability of the species $Li_2 , Li^{-}_2$ and $Li^{+}_{2}$ increases in the order of

answered Apr 7, 2017 by meena.p

1 answer

An organic compound A upon reacting with $NH_3$ gives $B$.On heating, B gives $C$.$C$ in presence of $KOH$ reacts with $Br_2$ to give $CH_3CH_2NH_2.A$ is :

answered Apr 7, 2017 by meena.p

1 answer

The first ionisation potential of $Na$ is $5.1\;eV$. The value of electron gain enthalpy of $Na^+$ will be :

answered Apr 7, 2017 by meena.p

1 answer

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with $pH$ of $2$ ?

answered Apr 6, 2017 by meena.p

1 answer

Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest $E^0_{M^{3+} /m^{2+}}$ value ?

answered Apr 6, 2017 by meena.p

1 answer

Compound (A), $C_8H_9Br$, gives a white precipitate when warmed with alcoholic $AgNO_3$.Oxidation of (A) gives an acid (B) , $C_8H_6O_4$ . (B) easily forms anhydride on heating. Identify the compound (A) .

answered Apr 6, 2017 by meena.p

1 answer

Energy of an electron is given by $E= -2.178 \times 10^{18} J \bigg(\large\frac{Z^2}{n^2}\bigg)$. Wavelength of light required to excite an electron in an hydrogen atom from level $n = 1$ to $n = 2$ will be

answered Apr 6, 2017 by meena.p

1 answer

Which of the following represents the correct order of increasing first ionization enthalpy for $Ca, Ba, S, Se \;and\; Ar ?$

answered Apr 6, 2017 by meena.p

1 answer

The coagulating power of electrolytes having ions $Na^{+} ,Al^{3+}$ and $Ba^{2+}$ for arsenic sulphide sol increases in the order :

answered Apr 6, 2017 by meena.p

1 answer

Synthesis of each molecule of glucose in photosynthesis involves :

answered Apr 6, 2017 by meena.p

1 answer

Which of the following exists as covalent crystals in the solid state ?

answered Apr 5, 2017 by meena.p

1 answer

In which of the following pairs of molecules / ions , both the species are not likely to exist ?

answered Apr 5, 2017 by meena.p

1 answer

A gaseous hydrocarbon gives upon combustion $0.72\; g$. of water and $3.08\;g$ of $CO_2$. The empirical formula of the hydrocarbon is :

answered Apr 5, 2017 by meena.p

1 answer

Which of the following is the wrong statement ?

answered Apr 5, 2017 by meena.p

1 answer

Consider the following reaction : $xMnO_4^{-} +yC_2O_4^{2-} +zH^{+} \to xMn^{2+} +2yCO_2 +\large\frac{z}{2}$$H_2O$The values of x, y and z in the reaction are, respectively :

answered Apr 5, 2017 by meena.p

1 answer

The order of stability of the following carbocations is:

answered Apr 5, 2017 by meena.p

1 answer

Which of the following arrangements does not represent the correct order of the property stated against it ?

answered Apr 4, 2017 by meena.p

1 answer

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