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JEEMAIN PAST PAPERS
JEEMAIN PAST PAPERS
1998
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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 $n$.
jeemain
math
past papers
2012
4
answered
Feb 12
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.
jeemain
math
past papers
2009
86
answered
Feb 11
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 $\frac{n(n+1)(2n+1)}{6}$
jeemain
math
past papers
2009
88
answered
Feb 6
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 :
jeemain
math
past papers
2016
75
answered
Feb 6
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.
jeemain
math
past papers
2016
74
answered
Feb 6
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 :
jeemain
math
past papers
2016
73
answered
Feb 5
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 :
jeemain
math
past papers
2016
72
answered
Feb 5
by
priyanka.clay6
2
answers
For $x \in R, \; f(x) = | \log 2 - \sin x | $ and $g(x) = f( f(x))$, then :
jeemain
math
past papers
2016
71
answered
Feb 5
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 :
jeemain
math
past papers
2001
109
answered
Feb 4
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 :
jeemain
math
past papers
2016
70
answered
Jan 30
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 :
jeemain
math
past papers
2016
69
answered
Jan 30
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 :
jeemain
math
past papers
2016
68
answered
Jan 30
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 :
jeemain
math
past papers
2016
67
answered
Jan 30
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 :
jeemain
math
past papers
2016
66
answered
Jan 30
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 :
jeemain
math
past papers
2016
65
answered
Jan 30
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 :
jeemain
math
past papers
2016
64
answered
Jan 30
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 :
jeemain
math
past papers
2016
63
answered
Jan 30
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 :
jeemain
math
past papers
2016
62
answered
Jan 30
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 $S$ :
jeemain
math
past papers
2016
61
answered
Jan 29
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
jeemain
math
past papers
2017
30
answered
Jan 28
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
jeemain
math
past papers
2017
29
answered
Jan 28
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
jeemain
math
past papers
2017
28
answered
Jan 27
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
jeemain
math
past papers
2017
27
answered
Jan 26
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
jeemain
math
past papers
2017
26
answered
Jan 25
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
jeemain
math
past papers
2017
25
answered
Jan 25
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
jeemain
math
past papers
2017
24
answered
Jan 25
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
jeemain
math
past papers
2017
23
answered
Jan 25
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 :
jeemain
math
past papers
2017
22
answered
Jan 25
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
jeemain
math
past papers
2017
21
answered
Jan 25
by
priyanka.clay6
1
answer
$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2 x)^3}$ equals
jeemain
math
past papers
2017
20
answered
Jan 25
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 :
jeemain
math
past papers
2017
19
answered
Jan 23
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 :
jeemain
math
past papers
2017
18
answered
Jan 23
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 :
jeemain
math
past papers
1998
198
answered
Jan 12
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 ?
jeemain
chemistry
past papers
2006
78
answered
Jan 5
by
sharmaaparna1
1
answer
Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?
jeemain
chemistry
past papers
2004
146
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 :
jeemain
math
past papers
2005
18
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 :
jeemain
chemistry
past papers
2001
83
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 :
jeemain
math
past papers
2000
138
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 :
jeemain
math
past papers
2005
3
answered
Nov 19, 2019
by
manishsutradhar1992
1
answer
By which of the following reactions can one get N-methyl aniline from aniline ?
jeemain
chemistry
past papers
1998
91
answered
Nov 13, 2019
by
ushradha2000
1
answer
The optically inactive compound from the following is :
jeemain
chemistry
past papers
2015
52
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 :
jeemain
math
past papers
2006
141
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 :
jeemain
physics
past papers
1999
17
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
jeemain
physics
past papers
2009
24
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
jeemain
chemistry
past papers
2004
130
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 :
jeemain
math
past papers
1998
181
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 :
jeemain
chemistry
past papers
2011
83
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
jeemain
physics
past papers
2004
211
answered
Sep 6, 2019
by
ravi.coexcl
1
answer
Two simple pendulums of lengths $16 l$ and $l$ are in phase at the mean position at a certain time. If $T$ is the time period of shorter pendulum, the minimum time after which they will be again in phase :
jeemain
physics
past papers
1999
20
answered
Aug 30, 2019
by
chandrasekharmoyila1993
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 :
jeemain
chemistry
past papers
1998
53
asked
Dec 20, 2018
by
pady_1
0
answers
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