Recent questions tagged jee(main)-2019

The correct match between Item-I and Item-II is : Item - I (drug) Item - II (test) (A) Chloroxylenol (P) Carbylamine Test (B) Norethindrone (Q) Sodium Hydrogen carbonateTest (C) Sulphapyridine (R) Ferric chloride test (D) Penicillin (S) Bayer's test (1) A→Q...

The compounds A and B in the following reaction are, respectively: (1) A = Benzyl alcohol, B = Benzyl isocyanide (2) A = Benzyl alcohol, B = Benzyl cyanide (3) A = Benzyl chloride, B = Benzyl cyanide (4) A = Benzyl chloride, B = Benzyl isocyanide

Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it ? (1) $(4,\ -4)$ (2) $(5,\ 2\sqrt6)$ (3) $(8,\ 6)$ (4) $(6,\ 4\...

Three circles of radii $a,\ b,\ c\quad(a<b<c)$ touch each other externally. If they have x-axis as a common tangent, then : (1) ${1\over\sqrt a}={1\over\sqrt b}+{1\over\sqrt c}$ (2) $a,\ b,\ c$ are in A. P. (3) $\sqrt a,\ \sqrt b,\ \sqrt c$ are in A. P. (4)...

Equation of a common tangent to the circle, $x^2+y^2-6x=0$ and the parabola, $y^2=4x$, is : (1) $2\sqrt3y=12x+1$ (2) $2\sqrt3y=-x-12$ (3) $\sqrt3y=x+3$ (4) $\sqrt3y=3x+1$

The plane through the intersection of the planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to y-axis also passes through the point : (1) $(-3,\ 0,\ -1)$ (2) $(3,\ 3,\ -1)$ (3) $(3,\ 2,\ 1)$ (4) $(-3,\ 1,\ 1)$

If $a,b$ and $c$ be three distinct real numbers in G.P. and $a+b+c=xb$, then $x$ cannot be : (1) $4$ (2) $-3$ (3) $-2$ (4) $2$

Consider the set of all lines $px+pq+r=0$ such that $3p+2q+4r=0$. Which one of the following statements is true ? (1) The lines are all parallel. (2) Each line passes through the origin. (3) The lines are not concurrent (4) The lines are concurrent at the ...

The system of linear equaltions. $x+y+z=0$ $2x+3y+2z=5$ $2x+3y+(a^2-1)z=a+1$ (1) has infinitely many solutions for $a=4$ (2) is inconsistent when $|a|=\sqrt3$ (3) is inconsistent when $a=4$ (4) has a unique solution for $|a|=\sqrt3$

Let $\vec{a}=\hat{i}-\hat{j},\ \vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times\vec{c}+\vec{b}=0$ and $\vec{a}.\vec{c}=4$, then $|\vec{c}|^2$ is equal to : (1) $19\over2$ (2) $8$ (3) $17\over2$ (4) $9$

Let $a_1,a_2,......,a_{30}$ be an A.P., $S=\sum\limits_{i=1}^{30}a_i$ and $T=\sum\limits_{i=1}^{15}a_{(2i-1)}$. If $A_5=27$ and $S-2T=75$, then $a_{10}$ is equal to : (1) 57 (2) 47 (3) 42 (4) 52

$5$ students of a class have an average height $150\ cm$ and variance $18\ cm^2$. A new student, whose height is $156\ cm$, joined them. The variance(in $cm^2$) of the height of these six students is : (1) 22 (2) 20 (3) 16 (4) 18

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals : (1) 52/169 (2) 25/169 (3) 49/169 (4) 24/169

For $x\in R-\{0,1\}$, let $f_1(x)={1\over x}$, $f_2(x)=1-x$ and $f_3(x)={1\over1-x}$ be three given functions. If a function, $J(x)$ satisfies $(f_2.J.f_1)(x)=f_3(x)$ then $J(x)$ is equal to : (1) $f_3(x)$ (2) $f_1(x)$ (3) $f_2(x)$ (4) ${1\over x}f_3(x)$

Let $A=\left\{0\in\left({-\pi\over2},\pi\right):{3+2i\sin\theta\over1-2i\sin\theta}\text{ is purely imaginary}\right\}$ Then the sum of the elements in $A$ is : (1) $5\pi\over6$ (2) $2\pi\over3$ (3) $3\pi\over4$ (4) $\pi$

If $\theta$ denotes the acute angle between the curves, $y=10-x^2$ and $y=2+x^2$ at a point of there intersection, then $|\tan\theta|$ is equal to : (1) 4/9 (2) 7/17 (3) 8/17 (4) 8/15

If $A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$, then the matrix $A^{-50}$ when $\theta={\pi\over12}$, is equal to : (1) $\begin{bmatrix}{\sqrt3\over2}&{1\over2}\\-{1\over2}&{\sqrt3\over2}\end{bmatrix}$ (2) $\begin{bmatrix}{...

Let $0<\theta<{\pi\over2}$. If the eccentricity of the hyperbola ${x^2\over\cos^2\theta}-{y^2\over\sin^2\theta}=1$ is greater than 2, then the length of its latus rectum lies in the interval : (1) $(2,3]$ (2) $(3,\infty)$ (3) $(3/2,2]$ (4) $(1,3/2]$

The equation of the line passing through $(-4,3,1)$, parallel to the plane $x+2y-z-5=0$ and intersecting the line ${x+1\over-3}={y-3\over2}={z-2\over-1}$ is : (1) ${x+4\over-1}={y-3\over1}={z-1\over1}$ (2) ${x+4\over3}={y-3\over-1}={z-1\over1}$ (3) ${x+4\...

For any $\theta \in\left({\pi\over4},{\pi\over2}\right)$, the expression $3(\sin\theta-\cos\theta)^4+6(\sin\theta+\cos\theta)^2+4\sin^6\theta$ equals : (1) $13-4\cos^6\theta$ (2) $13-4\cos^4\theta+2\sin^2\theta\cos^2\theta$ (3) $13-4\cos^2\theta+6\cos^4\...

If $\cos^{-1}\left({2\over3x}\right)+\cos^{-1}\left({3\over4x}\right)={\pi\over3}\quad\left(x>{3\over4}\right)$ then x is equal to : (1) $\sqrt{145}\over12$ (2) $\sqrt{145}\over10$ (3) $\sqrt{146}\over12$ (4) $\sqrt{145}\over11$

The value of $\int\limits_0^\pi|\cos x|^3 \mathrm dx$ (1) 2/3 (2) 0 (3) −4/3 (4) 4/3

If the Boolean expression $(p\oplus q)\land(\sim p\odot q)$ is equivalent to $p\land q$, where $\oplus,\odot\in\{\land,\lor\}$, then the ordered pair $(\oplus,\odot)$ is : (1) $(\land,\lor)$ (2) $(\lor,\lor)$ (3) $(\land,\land)$ (4) $(\lor,\land)$

$\lim\limits_{y\to0} {\sqrt{1+\sqrt{1+y^4}}-\sqrt2\over y^4}$ (1) exists and equals $1\over4\sqrt2$ (2) does not exist (3) exists and equals $1\over2\sqrt2$ (4) exists and equals $1\over2\sqrt2(\sqrt2+1)$

Let $f:R\to R$ be a function defined as : $f(x)=\begin{cases}5,&\text{if}&x\leq1\\a+bx,&\text{if}&1<x<3\\b+5x,&\text{if}&3\leq x<5\\30,&\text{if}&x\geq5\end{cases}$ Then, $f$ is : (1) continuous if $a=5$ and $b=5$ (2) continuous if $a=-5$ and $b=10$ (3) ...

The alkaline earth metal nitrate that does not crystallise with water molecules, is : (1) Sr(NO3)2 (2) Mg(NO3)2 (3) Ca(NO3)2 (4) Ba(NO3)2

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexs is : (1) 5.92 (2) 3.87 (3) 6.93 (4) 4.90

20 mL of 0.1 MH2SO4 solution is added to 30 mL of 0.2 M NH4OH solution. The pH of the resulatant mixture is : [pkb of NH4OH = 4.7]. (1) 9.4 (2) 5.0 (3) 9.0 (4) 5.2

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a a container of volume 10 m3 at 1000 K. given R is the gas constant in JK–1 mol–1m, x is : (1) $2R\over4+12$ (2) $2R\over4–R$ (3) $4–R\over2R$ (4) $4+R\over2R$

In general, the properties that decrease and increase down a group in the periodic table, respectively, are : (1) electronegativity and electron gain enthalpy. (2) electronegativity and atomic radius. (3) atomic radius and electronegativity. (4) electron ...