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Recent questions and answers in 2018
Questions
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
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2018
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 :
jeemain
math
past papers
2018
60
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 :
jeemain
math
past papers
2018
59
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 :
jeemain
math
past papers
2018
58
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 :
jeemain
math
past papers
2018
57
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
jeemain
math
past papers
2018
56
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 :
jeemain
math
past papers
2018
55
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
jeemain
math
past papers
2018
54
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 :
jeemain
math
past papers
2018
53
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)
jeemain
math
past papers
2018
52
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 :
jeemain
math
past papers
2018
51
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$ $\begin{pmatrix} [\frac{1}{x} +[\frac{2}{x}] +....+[\frac{15}{x}] \end{pmatrix}$
jeemain
math
past papers
2018
50
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
jeemain
math
past papers
2018
49
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 :
jeemain
math
past papers
2018
48
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
jeemain
math
past papers
2018
47
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 :
jeemain
math
past papers
2018
46
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 :
jeemain
math
past papers
2018
45
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 :
jeemain
math
past papers
2018
44
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 :
jeemain
math
past papers
2018
43
answered
Dec 26, 2019
by
priyanka.clay6
1
answer
The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :
jeemain
math
past papers
2018
42
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 ;
jeemain
math
past papers
2018
41
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 :
jeemain
math
past papers
2018
40
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
jeemain
math
past papers
2018
39
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 :
jeemain
math
past papers
2018
38
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 $S$ :
jeemain
math
past papers
2018
37
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 :
jeemain
math
past papers
2018
36
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 :
jeemain
math
past papers
2018
35
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 :
jeemain
math
past papers
2018
34
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 :
jeemain
math
past papers
2018
33
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 :
jeemain
math
past papers
2018
32
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 :
jeemain
math
past papers
2018
31
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 ?
jeemain
chemistry
past papers
2018
89
answered
Mar 20, 2019
by
sharmanamamish9636
1
answer
According to molecular orbital theory, which of the following will not be a viable molecule ?
jeemain
chemistry
past papers
2018
90
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following compounds contain(s) no covalent bond(s) ? <br> $KCl, \; PH_3,\; O_2, \; B_2H_6, \;H_2SO_4$
jeemain
chemistry
past papers
2018
88
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following are Lewis acids?
jeemain
chemistry
past papers
2018
87
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 - $(R = 8.314 \;JK^{-1} mol^{-1})$
jeemain
chemistry
past papers
2018
86
asked
Dec 11, 2018
by
pady_1
0
answers
Which type of 'defect' has the presence of cations in the interstitial sites ?
jeemain
chemistry
past papers
2018
85
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 :
jeemain
chemistry
past papers
2018
84
asked
Dec 11, 2018
by
pady_1
0
answers
The predominant form of histamine present in human blood is ($pK_a$ , Histidine = 6.0)
jeemain
chemistry
past papers
2018
83
asked
Dec 11, 2018
by
pady_1
0
answers
The compound that does not produce nitrogen gas by the thermal decomposition is :
jeemain
chemistry
past papers
2018
82
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:
jeemain
chemistry
past papers
2018
81
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 :
jeemain
chemistry
past papers
2018
80
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 :
jeemain
chemistry
past papers
2018
79
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following compounds will be suitable for Kjeldahl's method for nitrogen estimation ?
jeemain
chemistry
past papers
2018
78
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 $Ba^{2+}$.
jeemain
chemistry
past papers
2018
77
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 :
jeemain
chemistry
past papers
2018
76
asked
Dec 11, 2018
by
pady_1
0
answers
The major product of the following reaction is : <br>
jeemain
chemistry
past papers
2018
75
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 :
jeemain
chemistry
past papers
2018
74
asked
Dec 11, 2018
by
pady_1
0
answers
Glucose on prolonged heating with $HI$ gives :
jeemain
chemistry
past papers
2018
73
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 :
jeemain
chemistry
past papers
2018
72
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following lines correctly show the temperature dependence of equilibrium constant $K$, for an exothermic reaction ? <br>
jeemain
chemistry
past papers
2018
71
asked
Dec 11, 2018
by
pady_1
0
answers
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