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Recent questions and answers in 2017

Questions >> JEEMAIN and NEET >> JEEMAIN PAST PAPERS >> 2017

The area (in sq. units) of the region $\{ (x, y) : x \geq 0, \; x + y \leq 3, \; x^2 \leq 4y$ and $ y \leq 1 + \sqrt{x} \}$ is :

answered Apr 15, 2020 by karthikgoud20b

2 answers

The integral $\begin{align} \int^{\frac{3\pi}{4}}_{\frac{\pi}{4}} \frac{dx}{1+ \cos x} \end{align}$ is equal to

answered Jan 28, 2020 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

answered Jan 28, 2020 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

answered Jan 27, 2020 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

answered Jan 26, 2020 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

answered Jan 25, 2020 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

answered Jan 25, 2020 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

answered Jan 25, 2020 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

answered Jan 25, 2020 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 :

answered Jan 25, 2020 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

answered Jan 25, 2020 by priyanka.clay6

1 answer

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2 x)^3}$ equals

answered Jan 25, 2020 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 :

answered Jan 23, 2020 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 :

answered Jan 23, 2020 by priyanka.clay6

1 answer

The eccentriciy of an ellipse whose centre is at the origin is $\frac{1}{2}$. If one of its directrices is $x = -4$, then the equation of the normal to it at $(1, \frac{3}{2})$ is

answered Jan 21, 2020 by priyanka.clay6

1 answer

Let $I_n = \int \tan^n x\; dx, \; (n > 1)$. If $I_4 + I_6 = a \tan^5 x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to

answered Jan 21, 2020 by priyanka.clay6

1 answer

The distance of the point $(1, 3, -7)$ from the plane passing through the point $(1, -1, -1)$, having normal perpendicular to both the lines $\frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-4}{3}$ and $\frac{x-2}{2} = \frac{y+1}{-1} = \frac{z+7}{-1}$, is

answered Jan 21, 2020 by priyanka.clay6

1 answer

For any three positive real numbers $a, \;b$ and $c,\; 9(25a^2 + b^2 ) + 25(c^2 – 3ac) = 15b(3a + c)$, Then

answered Jan 21, 2020 by priyanka.clay6

1 answer

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$, then $adj (3A^2 + 12A)$ is equal to :

answered Jan 21, 2020 by priyanka.clay6

1 answer

A vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that $AP = 2 AB$. If $\angle{BPC} = \beta$, then $\tan \beta$ is equal to

answered Jan 21, 2020 by priyanka.clay6

1 answer

If $(2+\sin x) \frac{dy}{dx} +(y+1) \cos x = 0$ and $y(0)=1$, then $y(\frac{\pi}{2})$ is equal to :

answered Jan 21, 2020 by priyanka.clay6

1 answer

If for $x \in (0, \frac{1}{4})$, the derivative of $\tan^{-1} \begin{pmatrix} \frac{6x \sqrt{x}}{1-9x^3} \end{pmatrix}$ is $\sqrt{x}. g(x)$, then $g(x)$ equals :

answered Jan 21, 2020 by priyanka.clay6

1 answer

If the image of the point P(1, -2, 3) in the plane $2x + 3y - 4z + 22 =0$ measured parallel to the line, $\frac{x}{1} = \frac{y}{4} = \frac{z}{5}$ is $Q$, then $PQ$ is equal to :

answered Jan 21, 2020 by priyanka.clay6

1 answer

Twenty meters of wires is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

answered Jan 18, 2020 by priyanka.clay6

1 answer

Let $k$ be an integer such that the triangle with vertices $(k, -3k),\; (5, k)$ and $(-k, 2)$ has area 28 sq. units. Then the orthocentre of this triangle is at the point :

answered Jan 18, 2020 by priyanka.clay6

1 answer

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1& 1 \\ 1 & -\omega^2-1& \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$, then $k$ is equal to :

answered Jan 18, 2020 by priyanka.clay6

1 answer

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = $\frac{1}{4}$ and P (All the three events occur simultaneously) = $\frac{1}{6}$. Then the probability that at least one of the events occurs, is :

answered Jan 18, 2020 by priyanka.clay6

1 answer

If $5(\tan^2 x – \cos^2 x) = 2 \cos2x + 9$, then the value of $\cos 4 x$ is :

answered Jan 18, 2020 by priyanka.clay6

1 answer

The following statement $(p \to q)\; [(\sim p \to q) \to q]$ is :

answered Jan 18, 2020 by priyanka.clay6

1 answer

If S is the set of distinct values of 'b' for which of the following system of linear equations <br> $x + y + z = 1$ <br> $x + ay + z = 1$ <br> $ax + by + z = 0$ <br> has no solution, then S is :

answered Jan 18, 2020 by priyanka.clay6

1 answer

Which of the following species is not paramagnetic?

answered May 23, 2019 by ganeshbaruah0

1 answer

Which of the following reactions is an example of a redox reaction ?

answered May 23, 2019 by ganeshbaruah0

1 answer

The group having isoelectronic species is :

answered Apr 9, 2019 by madhu17032014

1 answer

Sodium salt of an organic acid 'X' produces effervescence with conc. $H_2SO_4$. 'X' reacts with the acidified aqueous $CaCl_2$ solution to give a white precipitate which decolourises acidic solution of $KMnO_4$. 'X' is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine ?

asked Dec 11, 2018 by pady_1

0 answers

A water sample has ppm level concentration of following anions <br> $F^- = 10, \; SO_4^{2-} = 100; \; NO_3^- = 50$ <br> The anion/anions that make/makes the water sample unsuitable for drinking is/are :

asked Dec 11, 2018 by pady_1

0 answers

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be :

asked Dec 11, 2018 by pady_1

0 answers

The major product obtained in the following reaction is : <br>

asked Dec 11, 2018 by pady_1

0 answers

The radius of the second Bohr orbit for hydrogen atom is : <br> (Planck's constant $h= 6.6262 \times 10^{-34} Js$; mass of electron = $9.1091 \times 10^{-31} kg$; charge of electron $e = 1.60210 \times 10^{-19}C$; permittivity of vacuum $\in_0 = 8.854185 \times 10^{-12} kg^{-1}m^{-3}A^{2}$)

asked Dec 11, 2018 by pady_1

0 answers

Which of the following molecules is least resonance stabilized ?

asked Dec 11, 2018 by pady_1

0 answers

Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by $10\;kJ\; mol^{–1}$ . If $k_1$ and $k_2$ are rate constants for reactions $R_1$ and $R_2$ respectively at $300\; K$, then $ln(k_2/k_1)$ is equal to : $(R = 8.314 \;J mol^{–1} K ^{–1} )$

asked Dec 11, 2018 by pady_1

0 answers

3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following compounds will form significant amount of meta product during mono-nitration reaction ?

asked Dec 11, 2018 by pady_1

0 answers

The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are :

asked Dec 11, 2018 by pady_1

0 answers

The correct sequence of reagents for the following conversion will be : <br>

asked Dec 11, 2018 by pady_1

0 answers

Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is :

asked Dec 11, 2018 by pady_1

0 answers

The increasing order of the reactivity of the following halides for the $S_N1$ reaction is : <br>

asked Dec 11, 2018 by pady_1

0 answers

$pK_a$ of a weak acid (HA) and $pK_b$ of a weak base $(BOH)$ are $3.2$ and $3.4$, respectively. The pH of their salt (AB) solution is :

asked Dec 11, 2018 by pady_1

0 answers

On treatment of $100 \;mL$ of $ 0.1 \;M$ solution of $CoCl_3.6H_2O$ with excess $AgNO_3;\; 1.2 \times 10^{22}$ ions are precipitated. The complex is :

asked Dec 11, 2018 by pady_1

0 answers

The major product obtained in the following reaction is : <br>

asked Dec 11, 2018 by pady_1

0 answers

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