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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 ?
jeemain
2013
math
answered
Apr 19
by
meena.p
1
answer
The expression $\large\frac{\tan A}{1- \cot A} +\frac{\cot A}{1- \tan A}$ can be written as :
jeemain
2013
math
answered
Apr 19
by
meena.p
1
answer
If $y= \sec (\tan ^{-1}x)$, then $\large\frac{dy}{dx}$ at $x=1$ is equal to :
jeemain
2013
math
answered
Apr 19
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$
jeemain
2013
math
answered
Apr 19
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
jeemain
2013
math
answered
Apr 19
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 18
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 :
jeemain
2013
math
answered
Apr 17
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 : $\int\limits_{a}^{b} f(x)dx =\int \limits_a^b f(a+b-x)dx$
jeemain
2013
math
answered
Apr 17
by
meena.p
1
answer
$\lim\limits_{x \to 0} \large\frac{(1-cos 2x )(3+\cos x)}{x \tan 4x}$ is equal to
jeemain
2013
math
answered
Apr 17
by
meena.p
1
answer
If $\int f(x)=dx= \psi(x)$, then $\int x^5 f(x^3)dx $ is equal to :
jeemain
2013
math
answered
Apr 17
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
jeemain
2013
math
answered
Apr 13
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 :
jeemain
2013
math
answered
Apr 12
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 :
jeemain
2013
math
answered
Apr 12
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
jeemain
2013
math
answered
Apr 12
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 :
jeemain
2013
math
answered
Apr 12
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 :
jeemain
2013
math
answered
Apr 12
by
meena.p
1
answer
The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777, ……,$ is :
jeemain
2013
math
answered
Apr 12
by
meena.p
1
answer
The real number k for which the equation, $2x^3+3x+ k = 0$ has two distinct real roots in $[0, 1]$
jeemain
2013
math
answered
Apr 11
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 :
jeemain
2013
math
answered
Apr 11
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 :
jeemain
2013
math
answered
Apr 11
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 :
jeemain
2013
math
answered
Apr 10
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 :
jeemain
2013
math
answered
Apr 10
by
meena.p
1
answer
Distance between two parallel planes $2x + y +2z = 8$ and $4x + 2y + 4z + 5 = 0$ is :
jeemain
2013
math
answered
Apr 10
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 :
jeemain
2013
chemistry
answered
Apr 7
by
meena.p
1
answer
The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was :
jeemain
2013
chemistry
answered
Apr 7
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 :
jeemain
2013
chemistry
answered
Apr 7
by
meena.p
1
answer
Stability of the species $Li_2 , Li^{-}_2$ and $Li^{+}_{2}$ increases in the order of
jeemain
2013
chemistry
answered
Apr 7
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 :
jeemain
2013
chemistry
answered
Apr 7
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 :
jeemain
2013
chemistry
answered
Apr 7
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$ ?
jeemain
2013
chemistry
answered
Apr 6
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 ?
jeemain
2013
chemistry
answered
Apr 6
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) .
jeemain
2013
chemistry
answered
Apr 6
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
jeemain
2013
chemistry
answered
Apr 6
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 ?$
jeemain
2013
chemistry
answered
Apr 6
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 :
jeemain
2013
chemistry
answered
Apr 6
by
meena.p
1
answer
Synthesis of each molecule of glucose in photosynthesis involves :
jeemain
2013
chemistry
answered
Apr 6
by
meena.p
1
answer
Which of the following exists as covalent crystals in the solid state ?
jeemain
2013
chemistry
answered
Apr 5
by
meena.p
1
answer
In which of the following pairs of molecules / ions , both the species are not likely to exist ?
jeemain
2013
chemistry
answered
Apr 5
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 :
jeemain
2013
chemistry
answered
Apr 5
by
meena.p
1
answer
Which of the following is the wrong statement ?
jeemain
2013
chemistry
answered
Apr 5
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 :
jeemain
2013
chemistry
answered
Apr 5
by
meena.p
1
answer
The order of stability of the following carbocations is:
jeemain
2013
chemistry
answered
Apr 5
by
meena.p
1
answer
Which of the following arrangements does not represent the correct order of the property stated against it ?
jeemain
2013
chemistry
answered
Apr 4
by
meena.p
1
answer
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