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Recent questions and answers in 2015
Questions
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
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2015
Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a} +\overrightarrow{b} |= \sqrt{3}$. If $\overrightarrow{c} = \overrightarrow{a} + 2\overrightarrow{b} + 3(\overrightarrow{a} \times \overrightarrow{b})^2$, then $2|\overrightarrow{c}|$ is equal to:
jeemain
math
past papers
2015
85
answered
Apr 7
by
priyanka.clay6
1
answer
Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :
jeemain
math
past papers
2015
86
answered
Apr 7
by
priyanka.clay6
1
answer
A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs 54 and per day mean wage of all the workers is Rs 60, then per day mean wage of the night shift workers (in Rs) is :
jeemain
math
past papers
2015
87
answered
Apr 7
by
priyanka.clay6
1
answer
In a $\Delta ABC, \; \frac{a}{b} = 2 + \sqrt{3}$ and $\angle{C} = 60^{\circ}$. Then the ordered pair $(\angle{A}, \angle{B})$ is equal to :
jeemain
math
past papers
2015
88
answered
Apr 7
by
priyanka.clay6
1
answer
If $f(x)=2 \tan^{-1}x+\sin^{-1} (\frac{2x}{1+x^2}),\; x>1$, then $f(5)$ is equal to:
jeemain
math
past papers
2015
89
answered
Apr 7
by
priyanka.clay6
1
answer
The contrapositive of the statement "If it is raining, then I will not come", is :
jeemain
math
past papers
2015
90
answered
Apr 7
by
priyanka.clay6
1
answer
If the shortest distance between the lines $\frac{x-1}{\alpha} = \frac{y+1}{-1} = \frac{z}{1},\; (\alpha \neq -1)$ and $x+y+z+1=0=2x-y+z+3$ is $\frac{1}{\sqrt{3}}$, then a value of $\alpha$ is :
jeemain
math
past papers
2015
84
answered
Apr 3
by
priyanka.clay6
1
answer
An ellipse passes through the foci of the hyperbola, $9x^2 - 4y^2 = 36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2}$ , then which of the following points does not lie on the ellipse ?
jeemain
math
past papers
2015
82
answered
Apr 3
by
priyanka.clay6
1
answer
If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$ (for some fixed $k$) at a point $(\alpha, \beta)$; then $(\alpha, \beta)$ is:
jeemain
math
past papers
2015
81
answered
Apr 3
by
priyanka.clay6
1
answer
If $y+3x =0$ is the equation of a chord of the circle, $x^2+y^2-30x=0$, then the equation of the circle with this chord as diameter is :
jeemain
math
past papers
2015
80
answered
Apr 2
by
priyanka.clay6
1
answer
Let $L$ be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at $P$. If $L_1$ is the line perpendicular to $L$ and passing through the point $(-2, 1)$, then the point of intersection of $L$ and $L_1$ is :
jeemain
math
past papers
2015
79
answered
Apr 2
by
priyanka.clay6
1
answer
The points $(0, \frac{8}{3})\; (1,3)$ and $(82, 30)$
jeemain
math
past papers
2015
78
answered
Apr 2
by
priyanka.clay6
1
answer
If the points $(1, 1, \lambda)$ and $(-3, 0, 1)$ are equidistant from the plane, $3x+4y+12z+13=0$, then $\lambda$ satisfies the equation :
jeemain
math
past papers
2015
83
answered
Apr 2
by
priyanka.clay6
1
answer
If $y(x)$ is the solution of the differential equation $(x+2) \frac{dy}{dx} = x^2+4x-9,\; x \neq -2$ and $y(0)=0$, then $y(-4)$ is equal to :
jeemain
math
past papers
2015
77
answered
Apr 2
by
priyanka.clay6
1
answer
The area (in square units) of the region bounded by the curves $y + 2x^2 =0$ and $y+3x^2 =1$, is equal to :
jeemain
math
past papers
2015
76
answered
Apr 2
by
priyanka.clay6
1
answer
For $x>0$, let $f(x) = \begin{align*} \int_1^x \frac{\log t}{1+t} dt \end{align*}$. Then $f(x) + f(\frac{1}{x})$ is equal to :
jeemain
math
past papers
2015
75
answered
Apr 2
by
priyanka.clay6
1
answer
The integral $\begin{align*} \int \frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}\end{align*}$ is equal to:
jeemain
math
past papers
2015
74
answered
Apr 1
by
priyanka.clay6
1
answer
Let the tangents drawn to the circle, $x^2+y^2 = 16$ from the point $P(0,h)$ meet the $x$-axis at point A and B. If the area of $\Delta APB$ is minimum, then $h$ is equal to :
jeemain
math
past papers
2015
73
answered
Apr 1
by
priyanka.clay6
1
answer
If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2+cx,\; x \in [-1, 1]$, at the point $x= \frac{1}{2}$, then $2b+c$ equals :
jeemain
math
past papers
2015
72
answered
Apr 1
by
priyanka.clay6
1
answer
The distance, from the origin of the normal to the curve, $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $ t = \frac{\pi}{4}$, is:
jeemain
math
past papers
2015
71
answered
Apr 1
by
priyanka.clay6
1
answer
$\displaystyle{\lim_{x \to 0} \frac{e^{x^2}-\cos x}{\sin^2x}}$ is equal to :
jeemain
math
past papers
2015
70
answered
Apr 1
by
priyanka.clay6
1
answer
The value of $\displaystyle\sum_{r=16}^{30} (r+2)(r-3)$ is equal to :
jeemain
math
past papers
2015
69
answered
Apr 1
by
priyanka.clay6
1
answer
If $A = \begin{bmatrix} 0 & -1 \\ 1& 0 \end{bmatrix}$, then which one of the following statement is not correct ?
jeemain
math
past papers
2015
65
answered
Mar 31
by
priyanka.clay6
1
answer
The least value of the product $xyz$ for which the determinant $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix}$ is non negative, is:
jeemain
math
past papers
2015
64
answered
Mar 31
by
priyanka.clay6
1
answer
If $2 + 3i$ is one of the roots of the equation $2x^3 - 9x^2 + kx - 13 = 0, \; k \in R$, then the real root of this equation :
jeemain
math
past papers
2015
63
answered
Mar 31
by
priyanka.clay6
1
answer
The largest value of $r$ for which the region represented by the set $\{ \omega \in C | \omega - 4 - i | \leq r \}$ is contained in the region represented by the set $\{z \in C / |z-1| \leq |z+i| \}$, is equal to :
jeemain
math
past papers
2015
62
answered
Mar 31
by
priyanka.clay6
1
answer
If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$, then the first of these terms in the expansion is :
jeemain
math
past papers
2015
68
answered
Mar 31
by
priyanka.clay6
1
answer
Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :
jeemain
math
past papers
2015
67
answered
Mar 31
by
priyanka.clay6
1
answer
The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :
jeemain
math
past papers
2015
66
answered
Mar 31
by
priyanka.clay6
1
answer
In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements : <br> (a) 5% families own both a car and a phone. <br> (b) 35% families own either a car or a phone. <br> (c) 40,000 families live in the town. <br> Then :
jeemain
math
past papers
2015
61
answered
Mar 31
by
priyanka.clay6
1
answer
Permanent hardness in water cannot be cured by :
jeemain
chemistry
past papers
2015
43
answered
Mar 24
by
sangethamadhu82
1
answer
Which of the following is not an assumption of the kinetic theory of gases ?
jeemain
chemistry
past papers
2015
32
answered
Mar 10
by
4216212
1
answer
The optically inactive compound from the following is :
jeemain
chemistry
past papers
2015
52
answered
Oct 26, 2019
by
sarvesh143dsp
1
answer
An aqueous solution of a salt $X$ turns blood red on treatment with $SCN^-$ and blue on treatment with $K_4 [Fe(CN)_6 ]$. $X$ also gives a positive chromyl chloride test. The salt $X$ is :
jeemain
chemistry
past papers
2015
47
answered
Jan 3, 2019
by
dhirendrachauhanchauhan7922
1
answer
The cation that will not be precipitated by $H_2S$ in the presence of $dil. HCl$ is :
jeemain
chemistry
past papers
2015
60
asked
Dec 11, 2018
by
pady_1
0
answers
<br> is used as :
jeemain
chemistry
past papers
2015
59
asked
Dec 11, 2018
by
pady_1
0
answers
Complete hydrolysis of starch gives :
jeemain
chemistry
past papers
2015
58
asked
Dec 11, 2018
by
pady_1
0
answers
Match the polymers in column-A with their main uses in column-B and choose the correct answer : <br>
jeemain
chemistry
past papers
2015
57
asked
Dec 11, 2018
by
pady_1
0
answers
Arrange the following amines in the order of increasing basicity.
jeemain
chemistry
past papers
2015
56
asked
Dec 11, 2018
by
pady_1
0
answers
In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which $\alpha$ - hydrogen has been replaced by halogen. This reaction is known as :
jeemain
chemistry
past papers
2015
55
asked
Dec 11, 2018
by
pady_1
0
answers
A compound $A$ with molecular formula $C_{10}H_{13}Cl$ gives a white precipitate on adding silver nitrate solution. $A$ on reacting with alcoholic KOH gives compound $B$ as the main product. $B$ on ozonolysis gives $C$ and $D$. $C$ gives Cannizaro reaction but not aldol condensation. $D$ gives aldol condensation but not Cannizaro reaction. $A$ is :
jeemain
chemistry
past papers
2015
54
asked
Dec 11, 2018
by
pady_1
0
answers
<br> A is :
jeemain
chemistry
past papers
2015
53
asked
Dec 11, 2018
by
pady_1
0
answers
$1.4\; g$ of an organic compound was digested according to Kjeldahl's method and the ammonia evolved was absorbed in $60 \;mL$ of $M/10\; H_2 SO_4$ solution. The excess sulphuric acid required $20\; mL$ of $M/10 \;NaOH$ solution for neutralization. The percentage of nitrogen in the compound is :
jeemain
chemistry
past papers
2015
51
asked
Dec 11, 2018
by
pady_1
0
answers
Photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth. X is :
jeemain
chemistry
past papers
2015
50
asked
Dec 11, 2018
by
pady_1
0
answers
The correct statement on the isomerism associated with the following complex ions, <br> (a) $[Ni(H_2O)_5NH_3]^{2+},$<br>(b)$[ Ni(H_2O)_4 (NH_3)_2]^{2+} $ and <br> (c)$[Ni(H_2O)_3 (NH_3)_3]^{2+} $ is :
jeemain
chemistry
past papers
2015
49
asked
Dec 11, 2018
by
pady_1
0
answers
Which molecule/ion among the following cannot act as a ligand in complex compounds ?
jeemain
chemistry
past papers
2015
48
asked
Dec 11, 2018
by
pady_1
0
answers
The geometry of $XeOF_4$ by VSEPR theory is :
jeemain
chemistry
past papers
2015
46
asked
Dec 11, 2018
by
pady_1
0
answers
The least number of oxyacids are formed by :
jeemain
chemistry
past papers
2015
45
asked
Dec 11, 2018
by
pady_1
0
answers
The correct order of thermal stability of hydroxides is :
jeemain
chemistry
past papers
2015
44
asked
Dec 11, 2018
by
pady_1
0
answers
In the isolation of metals, calcination process usually results in :
jeemain
chemistry
past papers
2015
42
asked
Dec 11, 2018
by
pady_1
0
answers
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