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Recent questions and answers in 2018

Questions >> JEEMAIN and NEET >> JEEMAIN PAST PAPERS >> 2018

The trans-alkenes are formed by the reduction of alkynes with ?

answered Feb 2, 2021 by abdulrahimshafiuyusuf

1 answer

Let the orthocenter and centroid of a triangle be A (-3, 5) and B (3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segement AC as diameter, is :

answered Dec 29, 2019 by priyanka.clay6

1 answer

Let A be the sum of the first 20 terms and B be sum of the first 40 terms of the series $1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2+2.6^2 + ...$ If $B - 2A = 100 \lambda$, then $\lambda$ is equal to :

answered Dec 29, 2019 by priyanka.clay6

1 answer

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

answered Dec 29, 2019 by priyanka.clay6

1 answer

PQR is a triangular park with PQ = PR = 200 m. A. T. V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively $45^{\circ},\; 30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is :

answered Dec 29, 2019 by priyanka.clay6

2 answers

The length of the projection of the line segment joining the points $(5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x+y+z=7$ is

answered Dec 29, 2019 by priyanka.clay6

1 answer

Let $\overrightarrow{u}$ be a vector coplanar with the vectors $\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} $ and $\overrightarrow{b} = \hat{j} + \hat{k}$. If $\overrightarrow{u}$ is perpendicular to and $\overrightarrow{a}$ and $\overrightarrow{u} \overrightarrow{b} = 24$, then $| \overrightarrow{u}|^2$ is equal to :

answered Dec 27, 2019 by priyanka.clay6

1 answer

Let $y = y(x)$ be the solution of the differential equation <br> $\sin x \frac{dy}{dx} + y \cos x = 4 x, \; x \subset (0, \pi)$. If $y (\frac{\pi}{2})=0$, then $y (\frac{\pi}{6})$ is equal to

answered Dec 27, 2019 by priyanka.clay6

1 answer

Let $S = \{ t \in R : f(x) = |x-\pi|. (e^{|x|} - 1) \sin |x|$ is not differentiable at $t\}$. Then the set $S$ is equal to :

answered Dec 27, 2019 by priyanka.clay6

1 answer

The integral <br> $\begin{align} \int \frac{\sin^2 x \cos^2 x}{(\sin^5 x + \cos^3 x \sin^2 x + \sin^3 x \cos^2x + \cos^5x)^2} \end{align} \; dx$ is equal to:<br> (where C is a constant of integration)

answered Dec 27, 2019 by priyanka.clay6

1 answer

If $\displaystyle\sum_{i=1}^{9} (x_i - 5) = 9$ and $ \displaystyle\sum_{i=1}^{9} (x_i - 5)^2 = 45$ then the standard deviation of the 9 items $x_1, \; x_2, .... x_9$ is :

answered Dec 27, 2019 by priyanka.clay6

1 answer

For each $t \in R$ let $[t]$ be the greatest integer less than or equal to $t$. Then <br> $ \displaystyle\lim_{x \to 0^-} x$ $\begin{pmatrix} [\frac{1}{x} +[\frac{2}{x}] +....+[\frac{15}{x}] \end{pmatrix}$

answered Dec 27, 2019 by priyanka.clay6

1 answer

Let $g(x) = \cos x^2, \; f(x) = \sqrt{x}$ and $\alpha, \;\beta \;(\alpha < \beta)$ be the roots of the quadratic equation $18x^2-9 \pi x + x^2 = 0$. Then the area (in sq. units) bounded by the curve $y=(gof)(x) $ and the lines $x = \alpha,\; x = \beta$ and $y =0$, is

answered Dec 27, 2019 by priyanka.clay6

1 answer

The value of $\begin{align} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin^2 x}{1+2^x} dx \end{align}$ is :

answered Dec 27, 2019 by priyanka.clay6

1 answer

A straight line through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

answered Dec 27, 2019 by priyanka.clay6

1 answer

Let $a_1, a_2, a_3,.....,a_{49}$ be in A.P. such that $\displaystyle\sum_{k=0}^{12} a_{4k+1}=416$ and $a_9 + a_{43} =66$. <br> If $a_1^2 + a_2^2....a_{17}^2=140\;m$ then $m$ is equal to :

answered Dec 27, 2019 by priyanka.clay6

1 answer

The sum of the co-effiicients of all odd degree terms in the expansion of $(x + \sqrt{x^3-1})^5 + (x-\sqrt{x^3 - 1})^5, (x>1)$ is :

answered Dec 26, 2019 by priyanka.clay6

1 answer

If $\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix}= (A + Bx)(x-A)^2$<br> then the ordered pair (A, B) is equal to :

answered Dec 26, 2019 by priyanka.clay6

1 answer

Tangent and normal are drawn at $P(16, 16)$ on the parabola $y^2 =16x$, which intersect the axis of the parabola at A and B, respectively. If $C$ is the centre of the circle through the points $P, \;A$ and $B$ and $\angle CPB=\theta$, then a value of $\tan \theta$ is :

answered Dec 26, 2019 by priyanka.clay6

1 answer

The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :

answered Dec 26, 2019 by priyanka.clay6

1 answer

Two sets A and B are as under : $A =\{ (a,b) \in R \times R : |a-5|<1$ and $|b-5| <1\} $; <br> $B= \{(a,b) \in R \times R$: <br> $4(a-6)^2 + 9(b-5)^2 \leq 36 \}$. Then ;

answered Dec 26, 2019 by priyanka.clay6

1 answer

Let $f(x) = x^2 + \frac{1}{x^2} $ and $g(x) = x - \frac{1}{x},\; x \in R -\{-1, 0, 1\}$. If $h(x) = \frac{f(x)}{g(x)}$, then the local minimum value of $h(x)$ is :

answered Dec 26, 2019 by priyanka.clay6

1 answer

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

answered Dec 26, 2019 by priyanka.clay6

2 answers

If sum of all the solutions of the equation $8 \cos x. (\cos (\frac{\pi}{6} + x) . \cos (\frac{\pi}{6} - x) - \frac{1}{2}) = 1$ in $[0, \pi]$ is $k \pi$, then $k$ is equal to :

answered Dec 26, 2019 by priyanka.clay6

1 answer

Let $S = \{x \in R : x \geq 0$ and $2|\sqrt{x} - 3| + \sqrt{x} (\sqrt{x} - 6) + 6 = 0\}$ Then $S$ :

answered Dec 26, 2019 by priyanka.clay6

1 answer

If the system of linear equations <br> $x+ ky + 3z=0$ <br> $3x + ky - 2z=0$ <br> $2x + 4y - 3z =0 $ <br> has a non-zero solution $(x, y, z)$, then $\frac{xz}{y^2}$ is equal to :

answered Dec 26, 2019 by priyanka.clay6

1 answer

If the curves $y^2 = 6x, \; 9x^2 + by^2=16$ intersect each other at right angles, then the value of $b$ is :

answered Dec 26, 2019 by priyanka.clay6

1 answer

Tangents are drawn to the hyperbola $4x^2 - y^2 = 36$ at the points P and Q. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :

answered Dec 25, 2019 by priyanka.clay6

1 answer

If $\alpha, \; \beta \in C$ are the distinct roots, of the equation $x^2 - x + 1 = 0$, then $\alpha^{101} + \beta^{107} $ is equal to :

answered Dec 25, 2019 by priyanka.clay6

1 answer

If $L_1$ is the line of intersection of the planes $2x- 2y+ 3z - 2 =0,\; x- y + z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y -z-3=0, \; 3x - y + 2z - 1=0$, then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$, is :

answered Dec 25, 2019 by priyanka.clay6

1 answer

If the tangent at (1, 7) to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x +12 y + c = 0$ then the value of $c$ is :

answered Dec 25, 2019 by priyanka.clay6

1 answer

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point ?

answered Mar 20, 2019 by sharmanamamish9636

1 answer

According to molecular orbital theory, which of the following will not be a viable molecule ?

asked Dec 11, 2018 by pady_1

0 answers

Which of the following compounds contain(s) no covalent bond(s) ? <br> $KCl, \; PH_3,\; O_2, \; B_2H_6, \;H_2SO_4$

asked Dec 11, 2018 by pady_1

0 answers

Which of the following are Lewis acids?

asked Dec 11, 2018 by pady_1

0 answers

The combustion of benzene $(l)$ gives $CO_2(g)$ and $H_2O (l)$. Given that heat of combustion of benzene at constant volume is $-3263.9 \; kJ\; mol^{-1}$ at $25^{\circ}C$; heat of combustion (in $kJ\; mol^{-1}$) of benzene at constant pressure will be - $(R = 8.314 \;JK^{-1} mol^{-1})$

asked Dec 11, 2018 by pady_1

0 answers

Which type of 'defect' has the presence of cations in the interstitial sites ?

asked Dec 11, 2018 by pady_1

0 answers

The oxidation states of $Cr$ in $[Cr(H_2O)_6]Cl_3, [Cr(C_6H_6)_2]$, and $K_2[Cr(CN)_2(O)_2(O_2)(NH_3)]$ respectively are :

asked Dec 11, 2018 by pady_1

0 answers

The predominant form of histamine present in human blood is ($pK_a$ , Histidine = 6.0)

asked Dec 11, 2018 by pady_1

0 answers

The compound that does not produce nitrogen gas by the thermal decomposition is :

asked Dec 11, 2018 by pady_1

0 answers

The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to made teeth enamel harder by converting $ [3Ca_3(PO_4)_2.Ca(OH)_2]$ to:

asked Dec 11, 2018 by pady_1

0 answers

An aqueous solution contains $0.10\; M \;H_2S$ and $0.20\; M \; HCl$. If the equilibrium constant for the formation of $HS^-$ from $H_2S$ is $1.0 \times 10^{-7}$ and that of $S^{2-}$ from $HS^-$ ions is $1.2 \times 10^{-13}$ then the concentration of $S^{2-}$ ions in aqueous solution is :

asked Dec 11, 2018 by pady_1

0 answers

When metal 'M' is treated with NaOH, a white gelatinous precipitate 'X' is obtained, which is soluble in excess of NaOH. Compound 'X' when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal M is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following compounds will be suitable for Kjeldahl's method for nitrogen estimation ?

asked Dec 11, 2018 by pady_1

0 answers

An aqueous solution contains an unknown concentration of $Ba^{2+}$. When $50\; mL$ of the $1M$ solution of $Na_2SO_4$ is added, $BaSO_4$ just begins to precipitate. The final volume is $500\; mL$. The solubility product of $BaSO_4$ is $1 \times 10^{-10}$. What is the original concentration of $Ba^{2+}$.

asked Dec 11, 2018 by pady_1

0 answers

Phenol on treatment with $CO_2$ in the presence of $NaOH$ followed by acidification produces a compound $X$ as the major product. $X$ on treatment with $(CH_3 CO_2)O$ in presence of catalytic amount of $H_2SO_4$ produced :

asked Dec 11, 2018 by pady_1

0 answers

The major product of the following reaction is : <br>

asked Dec 11, 2018 by pady_1

0 answers

Consider the following reaction and statements : <br> $[Co(NH_3)_4Br_2]^+ + Br^- \to [Co(NH_3)_3Br_3] + NH_3$ <br> (i) Two isomers are produced if the reactant complex ion is a cis-isomer. <br> (ii) Two isomers are produced if the reactant complex ions is a trans-isomer. <br> (iii) Only one isomer is produced if the reactant complex ion is a trans-isomer. <br> (iv) Only one isomer is produced if the reactant complex ion is a cis-isomer. <br> The correct statements are :

asked Dec 11, 2018 by pady_1

0 answers

Glucose on prolonged heating with $HI$ gives :

asked Dec 11, 2018 by pady_1

0 answers

At $518^{\circ}C$, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of $363 $ Torr, was $1.00 \; Torr\;s^{-1}$ when $5\%$ had reacted and $0.5\; Torr\; s^{-1}$ when $33\%$ had reacted. The order of the reaction is :

asked Dec 11, 2018 by pady_1

0 answers

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