Recent questions in JEEMAIN PAST PAPERS

Let ABCD be a parallelogram such that $\overrightarrow{AB} = \overrightarrow{q}, \overrightarrow{AD} = \overrightarrow{p}$ and $\angle{BAD}$ be an acute angle. If $\overrightarrow{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\overrightarrow{r}$ is given by

asked Dec 11, 2018 by pady_1

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A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

asked Dec 11, 2018 by pady_1

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Consider the function $f(x) = |x-2| + |x-5|, x \in R$. Statement 1: $f'(4) = 0$ Statement 2 : $f$ is continuous in [2, 5], differentiable in (2, 5) and $f(2) = f(5)$.

asked Dec 11, 2018 by pady_1

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An ellipse is drawn by taking a diameter of the circle $(x-1)^2 + y^2 = 1$ as its semiminor axis and a diameter of the circle $x^2+(y-2)^2 = 4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipseis

asked Dec 11, 2018 by pady_1

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Let $X = \{1, 2, 3, 4, 5\}$. The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X, Z \subseteq X$ and $ Y \cap Z$ is empty, is

asked Dec 11, 2018 by pady_1

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The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

asked Dec 11, 2018 by pady_1

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If $\begin{align}g(x) = \int_0^x \cos \; 4t \; dt \end{align}$, then $g(x+ \pi)$ equals

asked Dec 11, 2018 by pady_1

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Let P and Q be $3 \times 3$ matrices with $P \neq Q$. If $P^3 = Q^3$ and $P^2Q= Q^2P$, then determinant of $(P^2+Q^2)$ is equal to

asked Dec 11, 2018 by pady_1

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If $z \neq 1$ and $\frac{z^2}{z-1}$ is real, then the point represented by the complex number $z$ lies

asked Dec 11, 2018 by pady_1

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Three numbers are chosen at random without replacement from $\{1, 2, 3, ....,8 \}$. The probability that their minimum is 3, given that their maximum is 6, is

asked Dec 11, 2018 by pady_1

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If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1}$ intersect, then $k$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If $f : R \to R$ is a function defined by $f(x) = [x] \cos (\frac{2x-1}{2}) \pi$, where $[x]$ denotes the greatest integer function, then $f$ is

asked Dec 11, 2018 by pady_1

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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

asked Dec 11, 2018 by pady_1

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The area bounded between the parabolas $x^2 = \frac{y}{4}$ and $x^2= 9y$ and the straight line $y = 2$ is

asked Dec 11, 2018 by pady_1

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Let $a, b \in R$ be such that the function $f$ given by $f(x) = In \; |x| + bx^2 + ax, \; \; x \neq 0$ has extreme values at $x = -1$ and $x = 2$ Statement 1 : $f$ has focal maximum at $x = -1$ and at $x = 2$ Statement 2 : $ a = \frac{1}{2}$ and $b = \frac{-1}{4}$

asked Dec 11, 2018 by pady_1

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Let $x_1, x_2, ....., x_n$ be $n$ observations, and let $\overline{x}$ be their arithematic mean and $\sigma^2$ be their variance. Statement 1 : Variance of $2x_1, 2x_2, ....,2x_n$ is $4 \sigma^2$ Statement 2 : Arithmetic mean of $2x, 2x_2, .... , 2x_n$ is $4 \overline{x}$.

asked Dec 11, 2018 by pady_1

1 answer

If the line $2x + y = k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio $ 3 : 2$, then $k$ equals

asked Dec 11, 2018 by pady_1

1 answer

An equation of a plane parallel to the plane $ x - 2y + 2z - 5 = 0 $ and at a unit distance from the origin is

asked Dec 11, 2018 by pady_1

0 answers

In a $\Delta PQR$, if $ 3 \sin P + 4 \cos Q = 6 $ and $4 \sin Q + 3 \cos P = 1$, then the angle R is equal to

asked Dec 11, 2018 by pady_1

1 answer

If 100 times the $100^{th}$ term of an AP with non zero common difference equal the 50 times its $50^{th} $ term, then the $150^{th}$ term of this AP is

asked Dec 11, 2018 by pady_1

1 answer

If $n$ is a positive integer, then $(\sqrt{3} + 1)^{2n} - (\sqrt{3} - 1)^{2n}$ is

asked Dec 11, 2018 by pady_1

1 answer

Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} $ and $Au_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} $, then $u_1 + u_2$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

Statement 1 : An equation of a common tangent to the parabola $y^2 = 16 \sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$ is $y = 2x + 2\sqrt{3}$. Statement 2 : If the line $y = mx + \frac{4 \sqrt{3}}{m}, (m \neq 0)$ is a common tangent to the parabola $y^2 = 16 \sqrt{3}x $ and the ellipse $2x^2 + y^2 = 4$, then $m$ satisfies $m^2 + 2m^2 = 24$.

asked Dec 11, 2018 by pady_1

1 answer

If the integral $\begin{align} \int \frac{5 \tan x}{\tan x - 2} dx = x + a \;In |\sin x - 2 \cos x | + k \end{align}$, then $a$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The negation of the statement "If I become a teacher, then I will open a school" is

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

2 answers

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate if $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage began is

asked Dec 11, 2018 by pady_1

1 answer

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overrightarrow{c} = \hat{a} + 2 \hat{b}$ and $\overrightarrow{d} = 5 \hat{a} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

asked Dec 11, 2018 by pady_1

1 answer

The equation $e^{\sin x }- e^{- \sin x} - 4 = 0 $ has

asked Dec 11, 2018 by pady_1

1 answer

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by diferential equation $\frac{dV(t)}{dt} = -k(T-t)$, where $k>0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is

asked Dec 11, 2018 by pady_1

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Identify the compound that exhibits tautomerism.

asked Dec 11, 2018 by pady_1

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The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of $10 \; dm^3$ to a volume of $100\; dm^3$ at $27^ {\circ} C$ is :

asked Dec 11, 2018 by pady_1

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In a face centred cubic lattice, atom A occupies the corner position and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is :

asked Dec 11, 2018 by pady_1

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Phenol is heated with a solution of mixture of $KBr$ and $KBrO_3$. The major product obtained in the above reaction is

asked Dec 11, 2018 by pady_1

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Which of the following reagents may be used to distinguish between phenol and benzoic acid?

asked Dec 11, 2018 by pady_1

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Silver Mirror test is givn by which one of the following compounds ?

asked Dec 11, 2018 by pady_1

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A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

1 answer

The structure of $IF_7$ is :

asked Dec 11, 2018 by pady_1

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Which of the following statements regarding sulpher is incorrect ?

asked Dec 11, 2018 by pady_1

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The outer electron configuration of Gd (Atomic No:64) is :

asked Dec 11, 2018 by pady_1

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Which of the following statement is wrong ?

asked Dec 11, 2018 by pady_1

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A 5.2 molal aqueous solution of methyl alcohol, $CH_3OH$, is supplied. What is the mole fraction of methyl alcohol in the solution ?

asked Dec 11, 2018 by pady_1

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In context of the lanthanoids, which of the following statements is not correct ?

asked Dec 11, 2018 by pady_1

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The hybridization of orbitals of N atom in $NO_3^-, NO_2^+$ and $NH_4^+$ are respectively :

asked Dec 11, 2018 by pady_1

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The magnetic moment (spin only) of $[NiCl_4]^{2-}$ is

asked Dec 11, 2018 by pady_1

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The rate of a chemical reaction doubles for every $10^{\circ}C$ rise of temperature. If the temperature is raised by $50^{\circ}C$, the rate of the reaction increases by about :

asked Dec 11, 2018 by pady_1

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Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?

asked Dec 11, 2018 by pady_1

1 answer

Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at $-6^{\circ} C$ will be : [$K_f$ for water = 1.86 $K \; kg\; mol^{-1}$, and molar mass of ethylene glycol = 62 $g\; mol^{-1}$ )

asked Dec 11, 2018 by pady_1

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Which of the following facts about the complex $[Cr (NH_3)_6] Cl_3$ is wrong ?

asked Dec 11, 2018 by pady_1

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