Recent questions in JEEMAIN and NEET

If $f$ is a real-valued differentiable function satisfying $|f(x) - f(y)| \leq (x-y)^2, x, y \in R$ and $f(0) = 0$, then $f(1)$ equals :

asked Nov 5, 2018 by pady_1

0 answers

Let $f$ be differentiable for all $x$. If $f(1) = -2$ and $f'(x) \geq 2$ for $x \in [1,6]$, then :

asked Nov 5, 2018 by pady_1

0 answers

Suppose $f(x)$ is differentiable at $x=1$ and $ \displaystyle \lim_{h \to 0} \frac{1}{h} f(1+h) =5 $, then $f'(1)$ equals :

asked Nov 5, 2018 by pady_1

0 answers

If the roots of the equation $x^2 - bx + c = 0$ be two consecutive integers, then $b^2 - 4c$ equals :

asked Nov 5, 2018 by pady_1

0 answers

The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a-2)x -a - 1 = 0$ assume the least value is :

asked Nov 5, 2018 by pady_1

0 answers

The system of equations $\alpha x + y + z = \alpha -1$ $x + \alpha y + z = \alpha -1 $ $x + y + \alpha z = \alpha - 1$ has no solution, if $\alpha$ is :

asked Nov 5, 2018 by pady_1

0 answers

If $a^2+b^2+c^2 = -2$ and $f(x) = \begin{vmatrix} 1+a^2x & (1+b^2)x & (1+c^2) x \\ (1+a^2)x & 1+b^2x & (1+c^2)x \\ (1+a^2)x & (1+b^2)x & 1+c^2x \end{vmatrix}$, then $f(x)$ is a polynomial of degree :

asked Nov 5, 2018 by pady_1

0 answers

If $w = \frac{z}{z - \frac{1}{3} i } $ and $|w| = 1$, then $z$ lies on :

asked Nov 5, 2018 by pady_1

0 answers

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 :

asked Nov 5, 2018 by pady_1

1 answer

Let $ f : (-1, 1) \to B$ be a function defined by$f(x) = \tan^{-1} \frac{2x}{1-x^2}$, then $f$ is both one-one and onto when $B$ is the interval :

asked Nov 5, 2018 by pady_1

0 answers

If the coefficient of $x^7$ in $\begin{bmatrix} ax^2 + \begin{pmatrix} \frac{1}{bx} \end{pmatrix} \end{bmatrix}^{11} $ equals the coefficient of $x^{-7}$ in $\begin{bmatrix} ax^2 - \begin{pmatrix} \frac{1}{bx} \end{pmatrix} \end{bmatrix}^{11} $, then $a$ and $b$ satisfy the relation :

asked Nov 5, 2018 by pady_1

0 answers

If $A = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then which one of the following holds for all $n \geq 1$, by the principle of mathematical induction ?

asked Nov 5, 2018 by pady_1

0 answers

The value of $^{50}C_4 $ $\displaystyle\sum_{r = 1}^{6}$ $^{56-r}C_3$ is :

asked Nov 5, 2018 by pady_1

0 answers

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number :

asked Nov 5, 2018 by pady_1

0 answers

In a triangle PQR, $\angle{R} = \frac{\pi}{2}$. If $\tan (\frac{P}{2})$ and $\tan (\frac{Q}{2})$ are the roots of $ax^2 + bx + c = 0, a \neq 0$, then :

asked Nov 5, 2018 by pady_1

0 answers

If the coefficients of $r^{th}$, $(r+1)^{th}$ and $(r+2)^{th}$ terms in the binomial expansion of $(1 + y)^m$ are in AP, then $m$ and $r$ satisfy the equation :

asked Nov 5, 2018 by pady_1

0 answers

ABC is a triangle. Forces $\overrightarrow{P}, \overrightarrow{Q}, \overrightarrow{R}$ acting along $IA, IB$ and $IC$ respectively are in equilibrium, where $I$ is the incentre of $\Delta ABC$. Then $\overrightarrow{P} : \overrightarrow{Q} : \overrightarrow{R}$ is :

asked Nov 5, 2018 by pady_1

0 answers

The differential equation representing the family of curves $y^2 = 2c (x + \sqrt{c})$, where $c > 0$, is a parameter, is of order and degree as follows:

asked Nov 5, 2018 by pady_1

0 answers

Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ is :

asked Nov 5, 2018 by pady_1

0 answers

$ \displaystyle{\lim_{x \to \infty} [\frac{1}{n^2} \sec^2 \frac{1}{n^2} + \frac{2}{n^2} \sec^2 \frac{4}{n^2} + . . . . . . + \frac{n}{n^2} \sec^2 1]}$

asked Nov 5, 2018 by pady_1

0 answers

If the cube roots of unity are 1, $\omega, \omega^2$, then the roots of the equation $(x-1)^3 + 8 = 0$, are :

asked Nov 5, 2018 by pady_1

0 answers

If $A^2 - A + I = 0$, then the inverse of A is :

asked Nov 5, 2018 by pady_1

0 answers

Let $R = \{ (3,3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6) \}$ be a relation on the set $A = \{ 3, 6, 9, 12\}$. The relation is :

asked Nov 5, 2018 by pady_1

0 answers

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

asked Nov 5, 2018 by pady_1

1 answer

Let P be the point (1, 0) and Q a point on the locus $y^2=8x$. The locus of mid point of PQ is :

asked Nov 5, 2018 by pady_1

0 answers

If $C$ is the mid point of AB and P is any point outside AB, then :

asked Nov 5, 2018 by pady_1

0 answers

$t_{1/4}$ can be taken as the time taken for the concentration of a reactant to drop to $\frac{3}{4}$ of its initial value. If the rate constant for a first order reaction is $k$, the $t_{1/4}$ can be written as :

asked Nov 5, 2018 by pady_1

0 answers

An organic compound having molecular mass 60 is found to contain $C=20 \%, H=6.67 \%$ and $N = 46.67 \%$ while rest is oxygen. On heating it gives $NH_3$ along with a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is :

asked Nov 5, 2018 by pady_1

0 answers

The amount of solid $NH_4HS$ is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm pressure. Ammonium hydrogen sulphide decomposes to yield $NH_3$ and $H_2S$ gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm ? The equilibrium constant for $NH_2HS$ decomposition at this temperature is :

asked Nov 5, 2018 by pady_1

0 answers

If the bond dissociation energies of $XY, X_2$ and $Y_2$ (all diatomic molecules) are in the ratio of $1 : 1 : 0.5$ and $\Delta H_f$ for the formation of $XY$ is $-200 \; kJ \; mol^{-1}$. The bond dissociation energy of $X_2$ will be :

asked Nov 5, 2018 by pady_1

0 answers

p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is :

asked Nov 5, 2018 by pady_1

0 answers

Reaction of cyclohexanone with dimethlamine in the presence of catalic amount of an acid forms a compound. Water during the reaction is continuously removed. The compound formed is generally known as :

asked Nov 5, 2018 by pady_1

0 answers

The value of the 'spin only' magnetic moment for one of the following configurations is 2.84 BM. The correct one is :

asked Nov 5, 2018 by pady_1

0 answers

Which of the following factors may be regarded as the main cause of lanthanide contraction ?

asked Nov 5, 2018 by pady_1

0 answers

Which of the following statements in relation to the hydrogen atom is correct ?

asked Nov 5, 2018 by pady_1

0 answers

The structure of diborane $(B_2H_6)$ contains :

asked Nov 5, 2018 by pady_1

0 answers

The reaction is fastest when $X$ is :

asked Nov 5, 2018 by pady_1

0 answers

Equimolar solutions in the same solvent have :

asked Nov 5, 2018 by pady_1

0 answers

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

asked Nov 5, 2018 by pady_1

1 answer

Which of the following is fully fluorinated polymer ?

asked Nov 5, 2018 by pady_1

0 answers

Acid catalyzed hydration of alkenes except ethene leads to the formation of :

asked Nov 5, 2018 by pady_1

0 answers

Amongst the following the most basic compound is :

asked Nov 5, 2018 by pady_1

0 answers

Which types of isomerism is shown by 2, 3-dichlorobutane ?

asked Nov 5, 2018 by pady_1

0 answers

Which one of the following methods is neither meant for the synthesis nor for separation of amines ?

asked Nov 5, 2018 by pady_1

0 answers

Alkyl halides react with dialkyl copper reagents to give :

asked Nov 5, 2018 by pady_1

0 answers

Of the five isomeric hexanes, the isomer which can give two monochlorinated compound is :

asked Nov 5, 2018 by pady_1

0 answers

Among the following acids which has the lowest $pK_a$ value ?

asked Nov 5, 2018 by pady_1

0 answers

In both DNA and RNA, heterocylic base and phosphate ester linkages are at :

asked Nov 5, 2018 by pady_1

0 answers

Tertiary alkyl halides are practically inert to substitution by $S_N 2$ mechanism because of :

asked Nov 5, 2018 by pady_1

0 answers

The decreasing order of nucleophilicity among the nucleophiles :

asked Nov 5, 2018 by pady_1

0 answers

Ask Questions, Get Answers