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Recent questions tagged 2016
Questions
The Boolean Expression $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to :
jeemain
math
past papers
2016
90
asked
Dec 11, 2018
by
pady_1
1
answer
A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ}$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ}$. Then the time taken (in minutes) by him, from B to reach the pillar, is :
jeemain
math
past papers
2016
89
asked
Dec 11, 2018
by
pady_1
1
answer
If $0 \leq x \leq 2\pi$, then the number of real values of $x$, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$, is :
jeemain
math
past papers
2016
88
asked
Dec 11, 2018
by
pady_1
1
answer
Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?
jeemain
math
past papers
2016
87
asked
Dec 11, 2018
by
pady_1
1
answer
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?
jeemain
math
past papers
2016
86
asked
Dec 11, 2018
by
pady_1
1
answer
Let $\overrightarrow{a}, \; \overrightarrow{b}$ and $\overrightarrow{c}$ be three unit vectors such that $ \overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c} ) = \frac{\sqrt 3}{2} (\overrightarrow{b} + \overrightarrow{c})$. If $\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :
jeemain
math
past papers
2016
85
asked
Dec 11, 2018
by
pady_1
1
answer
If the line, $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$ lies in the plane, $lx + my - z =9$, then $l^2 + m^2$ is equal to
jeemain
math
past papers
2016
84
asked
Dec 11, 2018
by
pady_1
1
answer
The distance of the point $(1, −5, 9)$ from the plane $x−y+z=5$ measured along the line $x=y=z$ is :
jeemain
math
past papers
2016
83
asked
Dec 11, 2018
by
pady_1
1
answer
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :
jeemain
math
past papers
2016
82
asked
Dec 11, 2018
by
pady_1
1
answer
Let P be the point on the parabola, $y^2=8x$ which is at a minimum distance from the centre C of the circle, $x^2+(y+6)^2=1$. Then the equation of the circle, passing through C and having its centre at P is :
jeemain
math
past papers
2016
81
asked
Dec 11, 2018
by
pady_1
1
answer
If one of the diameters of the circle, given by the equation, $x^2+y^2−4x+6y−12=0$, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is :
jeemain
math
past papers
2016
80
asked
Dec 11, 2018
by
pady_1
1
answer
The centres of those circles which touch the circle, $x^2+y^2−8x−8y−4=0$, externally and also touch the x-axis, lie on :
jeemain
math
past papers
2016
79
asked
Dec 11, 2018
by
pady_1
1
answer
Two sides of a rhombus are along the lines, $x−y+1=0$ and $7x−y−5=0$. If its diagonals intersect at $(−1, −2)$, then which one of the following is a vertex of this rhombus ?
jeemain
math
past papers
2016
78
asked
Dec 11, 2018
by
pady_1
1
answer
If a curve $y = f(x)$ passes through the point $(1, -1)$ and satifies the differential equation, $y(1+xy) dx = x ;dy$, then $f(-\frac{1}{2})$ is equal to :
jeemain
math
past papers
2016
77
asked
Dec 11, 2018
by
pady_1
1
answer
The area (in sq. units) of the region $\{ (x,y) : y^2 \geq 2x $ and $x^2 + y^2 \leq 4x, \; x \geq 0, \; y \geq 0 \}$ is :
jeemain
math
past papers
2016
76
asked
Dec 11, 2018
by
pady_1
1
answer
$\begin{align*} \displaystyle{\lim_{n \to \infty} \begin{pmatrix} \frac{(n+1) (n+2) ...3n}{n^{2n}} \end{pmatrix} }^{1/n} \end{align*}$ is equal to :
jeemain
math
past papers
2016
75
asked
Dec 11, 2018
by
pady_1
1
answer
The integral $\begin{align*} \int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx \end{align*}$ is equal to : <br> where C is an arbitrary constant.
jeemain
math
past papers
2016
74
asked
Dec 11, 2018
by
pady_1
1
answer
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :
jeemain
math
past papers
2016
73
asked
Dec 11, 2018
by
pady_1
1
answer
Consider <br> $f(x) = \tan^{-1} \begin{pmatrix} \sqrt{\frac{1+\sin x}{1 - \sin x}} \end{pmatrix}, x \in (0, \frac{\pi}{2})$. A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point :
jeemain
math
past papers
2016
72
asked
Dec 11, 2018
by
pady_1
2
answers
For $x \in R, \; f(x) = | \log 2 - \sin x | $ and $g(x) = f( f(x))$, then :
jeemain
math
past papers
2016
71
asked
Dec 11, 2018
by
pady_1
1
answer
Let $p = \displaystyle{\lim_{x \to 0^+} (1 + \tan^2 \sqrt{x} )^{1/2x} }$ then $\log p$ is equal to :
jeemain
math
past papers
2016
70
asked
Dec 11, 2018
by
pady_1
1
answer
If the sum of the first ten terms of the series $(1 + \frac{3}{5})^2 + ( 2 + \frac{2}{5})^2 + (3 + \frac{1}{5})^2 + 4^2 + (4 + \frac{4}{5})^2......,$ is $\frac{16}{5} m$, then $m$ is equal to :
jeemain
math
past papers
2016
69
asked
Dec 11, 2018
by
pady_1
1
answer
If the $2^{nd},\; 5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :
jeemain
math
past papers
2016
68
asked
Dec 11, 2018
by
pady_1
1
answer
If the number of terms in the expansion of $\begin{pmatrix} 1 - \frac{2}{x} + \frac{4}{x^2} \end{pmatrix}^n, x \neq 0$ is 28, then the sum of the coefficients of all the terms in this expansion, is :
jeemain
math
past papers
2016
67
asked
Dec 11, 2018
by
pady_1
1
answer
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :
jeemain
math
past papers
2016
66
asked
Dec 11, 2018
by
pady_1
1
answer
The system of linear equations <br> $ x + \lambda y - z = 0 $ <br> $\lambda x - y - z =0$ <br> $x + y - \lambda z = 0$ <br> has a non-trivial solution for :
jeemain
math
past papers
2016
65
asked
Dec 11, 2018
by
pady_1
1
answer
If $A= \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \; adj \; A = A A^T$, then $5a + b$ is equal to :
jeemain
math
past papers
2016
64
asked
Dec 11, 2018
by
pady_1
1
answer
The sum of all real values of $x$ satisfying the equation <br> $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is :
jeemain
math
past papers
2016
63
asked
Dec 11, 2018
by
pady_1
1
answer
A value of $\theta$ for which $\frac{2 + 3 i \sin \theta}{1 - 2 i \sin \theta}$ is purely imaginary, is :
jeemain
math
past papers
2016
62
asked
Dec 11, 2018
by
pady_1
1
answer
If $f(x) + 2f (\frac{1}{x}) = 3x, \; x \neq 0$, and $S = \{ x \in R : f(x) = f(-x) \}$; then $S$ :
jeemain
math
past papers
2016
61
asked
Dec 11, 2018
by
pady_1
1
answer
The hottest region of Bunsen flame shown in the figure below is : <br>
jeemain
chemistry
past papers
2016
60
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following is an anionic detergent ?
jeemain
chemistry
past papers
2016
59
asked
Dec 11, 2018
by
pady_1
1
answer
Thiol group is present in :
jeemain
chemistry
past papers
2016
58
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following statements about low density polythene is FALSE ?
jeemain
chemistry
past papers
2016
57
asked
Dec 11, 2018
by
pady_1
0
answers
In the Hofmann bromamide degradation reaction, the number of moles of $NaOH$ and $Br_2$ used per mole of amine produced are :
jeemain
chemistry
past papers
2016
56
asked
Dec 11, 2018
by
pady_1
0
answers
The reaction of propene with $HOCl\; (Cl_2+H_2O)$ proceeds through the intermediate :
jeemain
chemistry
past papers
2016
55
asked
Dec 11, 2018
by
pady_1
0
answers
2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields : <br>
jeemain
chemistry
past papers
2016
54
asked
Dec 11, 2018
by
pady_1
0
answers
The absolute configuration of <br> <br> is :
jeemain
chemistry
past papers
2016
53
asked
Dec 11, 2018
by
pady_1
0
answers
The product of the reaction given below is : <br>
jeemain
chemistry
past papers
2016
52
asked
Dec 11, 2018
by
pady_1
0
answers
The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :
jeemain
chemistry
past papers
2016
51
asked
Dec 11, 2018
by
pady_1
0
answers
The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :
jeemain
chemistry
past papers
2016
50
asked
Dec 11, 2018
by
pady_1
1
answer
Which one of the following complexes shows optical isomerism ? <br> (en=ethylenediamine)
jeemain
chemistry
past papers
2016
49
asked
Dec 11, 2018
by
pady_1
0
answers
The pair having the same magnetic moment is : <br> [At. No : Cr = 24, Mn = 25, Fe = 26, Co = 27]
jeemain
chemistry
past papers
2016
48
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following compounds is metallic and ferromagnetic ?
jeemain
chemistry
past papers
2016
47
asked
Dec 11, 2018
by
pady_1
0
answers
The pair in which phosphorous atoms have a formal oxidation state of +3 is :
jeemain
chemistry
past papers
2016
46
asked
Dec 11, 2018
by
pady_1
0
answers
The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :
jeemain
chemistry
past papers
2016
45
asked
Dec 11, 2018
by
pady_1
0
answers
The main oxides formed on combustion of Li, Na and K in excess of air are, respectively :
jeemain
chemistry
past papers
2016
44
asked
Dec 11, 2018
by
pady_1
0
answers
Which one of the following statements about water is FALSE ?
jeemain
chemistry
past papers
2016
43
asked
Dec 11, 2018
by
pady_1
0
answers
Which one of the following ores is best concentrated by froth floatation method ?
jeemain
chemistry
past papers
2016
42
asked
Dec 11, 2018
by
pady_1
0
answers
Which of the following atoms has the highest first ionization energy ?
jeemain
chemistry
past papers
2016
41
asked
Dec 11, 2018
by
pady_1
0
answers
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