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Recent questions and answers in JEEMAIN PAST PAPERS

Questions >> JEEMAIN and NEET >> JEEMAIN PAST PAPERS

JEEMAIN PAST PAPERS

Elimination of bromine from 2-bromobutane results in the formation of :

answered Feb 22, 2020 by aliochemist

1 answer

Statement 1 : The sum of the series $ 1 + ( 1 + 2+4) + (4+6+9) + (9+12+16) + .......+ (361 + 380+400)$ is $8000$. <br> Statement 2 : $\displaystyle\sum_{k=1}^{n} (k^3 - ( k-1)^3 ) = n^3$ for any natural number $n$.

answered Feb 12, 2020 by anjanachandran3g

1 answer

Let $f(x) = (x+1)^2 - 1, x \geq -1$ <br> Statement -1 : The set $\{ x : f(x) = f^{-1} (x) \} = \{0, -1\}$ <br> Statement-2: f is a bijection.

answered Feb 11, 2020 by bookinggo1

1 answer

Statement -1: The variance of first n even natural numbers is $\frac{n^2-1}{4}$ <br> Statement -2 :The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$

answered Feb 6, 2020 by laxmikntpanda25

1 answer

$\begin{align} \displaystyle{\lim_{n \to \infty} \begin{pmatrix} \frac{(n+1) (n+2) ...3n}{n^{2n}} \end{pmatrix} }^{1/n} \end{align}$ is equal to :

answered Feb 6, 2020 by priyanka.clay6

1 answer

The integral $\begin{align} \int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx \end{align}$ is equal to : <br> where C is an arbitrary constant.

answered Feb 6, 2020 by priyanka.clay6

1 answer

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 :

answered Feb 5, 2020 by priyanka.clay6

1 answer

Consider <br> $f(x) = \tan^{-1} \begin{pmatrix} \sqrt{\frac{1+\sin x}{1 - \sin x}} \end{pmatrix}, x \in (0, \frac{\pi}{2})$. A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point :

answered Feb 5, 2020 by priyanka.clay6

2 answers

For $x \in R, \; f(x) = | \log 2 - \sin x | $ and $g(x) = f( f(x))$, then :

answered Feb 5, 2020 by priyanka.clay6

1 answer

The events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14, then the probability that neither A nor B occurs, is :

answered Feb 4, 2020 by smitha.ds

1 answer

Let $p = \displaystyle{\lim_{x \to 0^+} (1 + \tan^2 \sqrt{x} )^{1/2x} }$ then $\log p$ is equal to :

answered Jan 30, 2020 by priyanka.clay6

1 answer

If the sum of the first ten terms of the series $(1 + \frac{3}{5})^2 + ( 2 + \frac{2}{5})^2 + (3 + \frac{1}{5})^2 + 4^2 + (4 + \frac{4}{5})^2......,$ is $\frac{16}{5} m$, then $m$ is equal to :

answered Jan 30, 2020 by priyanka.clay6

1 answer

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 :

answered Jan 30, 2020 by priyanka.clay6

1 answer

If the number of terms in the expansion of $\begin{pmatrix} 1 - \frac{2}{x} + \frac{4}{x^2} \end{pmatrix}^n, x \neq 0$ is 28, then the sum of the coefficients of all the terms in this expansion, is :

answered Jan 30, 2020 by priyanka.clay6

1 answer

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 :

answered Jan 30, 2020 by priyanka.clay6

1 answer

The system of linear equations <br> $ x + \lambda y - z = 0 $ <br> $\lambda x - y - z =0$ <br> $x + y - \lambda z = 0$ <br> has a non-trivial solution for :

answered Jan 30, 2020 by priyanka.clay6

1 answer

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

answered Jan 30, 2020 by priyanka.clay6

1 answer

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

answered Jan 30, 2020 by priyanka.clay6

1 answer

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

answered Jan 30, 2020 by priyanka.clay6

1 answer

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

answered Jan 29, 2020 by priyanka.clay6

1 answer

The integral $\begin{align} \int^{\frac{3\pi}{4}}_{\frac{\pi}{4}} \frac{dx}{1+ \cos x} \end{align}$ is equal to

answered Jan 28, 2020 by priyanka.clay6

1 answer

If, for a positive integer n, the quadratic equation, $x(x + 1) + (x + 1)(x + 2) +.....+ (x + \overline{n – 1})(x + n) = 10n$ has two consecutive integral solutions, then n is equal to

answered Jan 28, 2020 by priyanka.clay6

1 answer

The radius of a circle, having minimum area, which touches the curve $y = 4 - x^2$ and the lines, $y = |x|$ is

answered Jan 27, 2020 by priyanka.clay6

1 answer

Let $a, \; b, \; c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x+y) = f(x) + f(y) + xy, \forall x, y \in R$, then $ \displaystyle\sum_{n=1}^{10} f(n)$ is equal to

answered Jan 26, 2020 by priyanka.clay6

1 answer

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

answered Jan 25, 2020 by priyanka.clay6

1 answer

The value of $(^{21} C_1 - ^{10}C_1) + (^{21}C_2 - ^{19}C_2) + (^{21}C_3 -^{10}C_3) + (^{21}C_4 - ^{10}C_4) +...+(^{21}C_{10} - ^{10}C_{10})$ is

answered Jan 25, 2020 by priyanka.clay6

1 answer

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

answered Jan 25, 2020 by priyanka.clay6

1 answer

It two different numbers are taken from the set $\{0,1,2,3,....., 10\}$; then the probability that their sum as well as absolute difference are both multiple of 4, is

answered Jan 25, 2020 by priyanka.clay6

1 answer

The normal to the curve $y(x-2)(x-3) = x+6$ at the point where the curve intersects the y-axis passes through the point :

answered Jan 25, 2020 by priyanka.clay6

1 answer

Let $\overrightarrow{a} = 2 \hat{i} +\hat{j} - 2 \hat{k}$ and $\overrightarrow{b} = \hat{i} + \hat{j}$. Let $\overrightarrow{c}$ be a vector such that $| \overrightarrow{c} - \overrightarrow{a} | = 3, \; |(\overrightarrow{a} \times \overrightarrow{b} ) \times \overrightarrow{c} |=3$ and the angle between $\overrightarrow{c}$ and $\overrightarrow{a} \times \overrightarrow{b} $ be $30^{\circ}$. The $\overrightarrow{a}.\overrightarrow{c}$ is equal to

answered Jan 25, 2020 by priyanka.clay6

1 answer

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2 x)^3}$ equals

answered Jan 25, 2020 by priyanka.clay6

1 answer

The function $f : R \to \begin{bmatrix}-\frac{1}{2}, \frac{1}{2} \end{bmatrix}$ defined as $f(x) = \frac{x}{1+x^2}$, is :

answered Jan 23, 2020 by priyanka.clay6

1 answer

A hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $(\pm 2, 0)$. Then the tangent to this hyperbola at $P$ also passes through the point :

answered Jan 23, 2020 by priyanka.clay6

1 answer

If $\overrightarrow{\alpha}$ and $\overrightarrow{\beta}$ are non zero and different vector such that $|\overrightarrow{\alpha} + \overrightarrow{\beta}| = |\overrightarrow{\beta} - \overrightarrow{\alpha}|$, then the angle between $\overrightarrow{\alpha} $ and $\overrightarrow{\beta}$ is :

answered Jan 12, 2020 by pranavindurkar111

1 answer

A metal, M forms chlorides in its $+2$ and $+4$ oxidation states. Which of the following statements about these chlorides is correct ?

answered Jan 5, 2020 by sharmaaparna1

1 answer

Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?

answered Dec 23, 2019 by prathamkhandelwal9622

1 answer

If $z_1$ and $z_2$ are two non-zero complex numbers such that $|z_1+z_2| = |z_1| + |z_2|$, then arg $z_1$ - arg $z_2$ is equal to :

answered Dec 22, 2019 by koteswararaopeddi850

1 answer

In a nuclide, one a.m.u of mass is dissipated into energy to bind its nucleons. The energy equivalent of this mass is :

answered Dec 20, 2019 by azharwahab950

1 answer

If $c$ is a parameter, then the differential equation whose solution is $y = c^2 + \frac{c}{x'}$ is :

answered Dec 19, 2019 by nikhiiraavi

1 answer

If in a frequency distribution, the Mean and Medium are 21 and 22 respectively, then its Mode is approximately :

answered Nov 19, 2019 by manishsutradhar1992

1 answer

By which of the following reactions can one get N-methyl aniline from aniline ?

answered Nov 13, 2019 by ushradha2000

1 answer

The optically inactive compound from the following is :

answered Oct 26, 2019 by sarvesh143dsp

1 answer

If $(a, a^2)$ falls inside the angle made by the lines $y=\frac{x}{2}, \;x > 0$ and $y = 3x,\; x > 0$, then $a$ belongs to :

answered Oct 20, 2019 by titankeshav

1 answer

Taking that earth revolves round the sun in a circular orbit of radius $15 \times 10^{10}m$, with a time period of 1 year the time taken by another planet, which is at a distance of $540 \times 10^{10}m$, to revolve round the sun in circular orbit once, will be :

answered Oct 14, 2019 by pskswamy1973

1 answer

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where g = the acceleration due to gravity on the surace of the earth) in terms of R, the radius of the earth is

answered Oct 14, 2019 by meena.clay6

1 answer

The half-life of a radioisotope is four hours. If the inital mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

answered Oct 1, 2019 by gurupadabethua1956

1 answer

$\begin{align} \int_0^{\pi/2} \sin^6 x \cos^5 x \; dx \end{align}$ is equal to :

answered Sep 26, 2019 by baskar.chakrapani

1 answer

Ozonolysis of an organic compound gives formaldehyde as one of the products.. This confirms the presence of :

answered Sep 16, 2019 by vanshikasharma1115

1 answer

A coil having n turns and resistance $4 R \Omega$. This combination is moved in time t seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

answered Sep 6, 2019 by ravi.coexcl

1 answer

10.6 g of a substance of molecular weight 106 was dissolved in 100 mL. 10 mL of this solution was pipetted out into a 1000 mL flask and made up to the mark with distilled water. The molarity of the resulting solution is :

asked Dec 20, 2018 by pady_1

0 answers

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