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Recent questions tagged jeemain 2016 maths set c 10042016

The contrapositive of the following statement,
“If the side of a square doubles, then its area increases four times”, is :

asked May 30, 2017 by priyanka.c

1 answer

The angle of elevation of the top of a vertical tower from a point $A,$ due east of it is $45^0$. The angle of elevation of the top of the same tower from a point $ B$, due south of $A$ is $30^0$. If the distance between $A$ and $B$ is $54 \sqrt 2$ m , then the height of the tower (in metres), is :

asked May 30, 2017 by priyanka.c

1 answer

If $A>0, B>0$ and $Α + B = \frac{\pi}{6} ,$ then the minimum value of $ \tan A + \tan B$ is :

asked May 30, 2017 by priyanka.c

1 answer

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

asked May 30, 2017 by priyanka.c

1 answer

The $mean$ of $5$ observations is $5$ and their $variance$ is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

asked May 30, 2017 by priyanka.c

1 answer

Let $ABC $ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\overrightarrow{a} , \overrightarrow{b}, \overrightarrow{c}$ and $\frac{\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}}{4}$ respectively, then the position vector of the orthocentre of this triangle, is :

asked May 30, 2017 by priyanka.c

1 answer

The number of distinct real values of $λ$ for which the lines $\begin{align} \frac{x-1}{1} = \frac{y-2}{2} = \frac{z+3}{\lambda^2} \end{align}$ and $\begin{align}\frac{x-3}{1} = \frac{y-2}{\lambda^2 } = \frac{z-1}{2} \end{align} $ are coplanar is:

asked May 30, 2017 by priyanka.c

1 answer

ABC is a triangle in a plane with vertices $A(2, 3, 5), B(−1, 3, 2)$ and $C(λ, 5, µ).$ If the median through $A$ is equally inclined to the coordinate axes, then the value of $(λ^3+µ^3+5)$ is :

asked May 30, 2017 by priyanka.c

1 answer

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does $NOT$ lie on it ?

asked May 30, 2017 by priyanka.c

1 answer

$P$ and $Q$ are two distinct points on the parabola, $y2=4x,$ with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$, then the minimum value of $ t_1^2$ is :

asked May 30, 2017 by priyanka.c

1 answer

Equation of the tangent to the circle, at the point $(1, −1)$, whose centre is the point of intersection of the straight lines $x−y=1$ and $2x+y=3$ is :

asked May 30, 2017 by priyanka.c

1 answer

A straight line through origin $O$ meets the lines $3y=10−4x$ and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio :

asked May 29, 2017 by priyanka.c

1 answer

A ray of light is incident along a line which meets another line,$ 7x−y+1=0$, at the point $(0, 1). $ The ray is then reflected from this point along the line, $y+2x=1.$ Then the equation of the line of incidence of the ray of light is :

asked May 29, 2017 by priyanka.c

1 answer

The solution of the differential equation $\begin{align} \frac{dy}{dx} + \frac{y}{2} \sec x = \frac{\tan}{2\;y}, \end{align}$ where $0 \leq x < \frac{\pi}{2},$ and $y(0)= 1,$ is given by

asked May 29, 2017 by priyanka.c

1 answer

For $ x \; \epsilon \;R, x ≠ 0,$ if $y(x)$ is a differentiable function such that $\begin{align} x \int_1^x y\; (t) \;dt = (x+1) \int_1^x t\; y \;(t)\; dt, \end{align}$ then $y(x) $ equals :
(where C is a constant.)

asked May 29, 2017 by priyanka.c

1 answer

The value of the integral $\begin{align} \int_4^{10} \frac{[x^2]dx}{[x^2 -28x + 196] + [x^2] } , \end{align}$ where $[x]$ denotes the greatest integer less than or equal to $x,$ is :

asked May 29, 2017 by priyanka.c

1 answer

The integral $\begin{align} \int \frac{dx}{(1+\sqrt x) \sqrt{x - x^2}} \end{align}$ to :
(where C is a constant of integration.)

asked May 29, 2017 by priyanka.c

1 answer

Let $C$ be a curve given by $y (x) = 1 + \sqrt{4x - 3}, x>\frac{3}{4}.$ If P is a point on $ C$, such that the tangent at $P$ has slope $\frac{2}{3},$ then a point through which the normal at $P$ passes is:

asked May 29, 2017 by priyanka.c

1 answer

Let $f(x)=sin^4x+cos^4x.$ Then f is an increasing function in the interval :

asked May 29, 2017 by priyanka.c

1 answer

Let $a, b \;\epsilon \; R, (a ≠ 0). $ If the function f defined as $f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \leq x < 1 \\ a , & 1 \leq x < \sqrt 2 \\ \frac{2b^2 - 4b}{x^3}, & \sqrt 2 \leq x < \infty \end{cases}$ is continuous in the interval $[0, ∞)$, then an ordered pair $(a, b)$ is

asked May 29, 2017 by priyanka.c

1 answer

$\begin{align}\lim_{x\to o}\frac{(1 - \cos2x)^2}{2x \; \tan x -x \tan 2x } \end{align} $ is :

asked May 29, 2017 by priyanka.c

1 answer

The sum $\displaystyle\sum_{r =1}^{10} (r^2 + 1) \times (r!)$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

Let $a_1, a_2, a_3, ......, a_n, .....$ be in A.P. If $a_3+a_7+a_11+a_15=72,$ then the sum of its $first\; 17\; terms$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

If the coefficients of $x^{−2}$ and $x^{−4}$ in the expansion of $\begin{align} \begin{bmatrix}x^{\frac{1}{3}}+ \frac{1}{2x^{\frac{1}{3}}} \end{bmatrix}^{18}, (x>0) \end{align}$ are $m$ and $n$ respectively, then $\frac{m}{n}$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

If $\begin{align}\frac{^{n+2}C_6}{^{n-2}P_2} = 11, \end{align}$ then $n$ satisfies the equation :

asked May 28, 2017 by priyanka.c

1 answer

If $A = \begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix},$ then the determinant of the matrix $(A^{2016} - 2A^{2015} - A^{2014})$ is :

asked May 28, 2017 by priyanka.c

1 answer

Let $A$ be a $3×3$ matrix such that $A^2−5A+7I=O$.
Statement - I : $A^{-1} = \frac{1}{7}(5I - A)$
Statement - II :The polynomial $A^3−2A^2−3A+I$ can be reduced to $5(A−4I).$
Then :

asked May 28, 2017 by priyanka.c

1 answer

Let $z=1+ai$ be a complex number, $a > 0$, such that $z^3$ is a real number. Then the sum $1+z+z^2+.....+z^{11}$ is equal to :

asked May 28, 2017 by priyanka.c

1 answer

If x is a solution of the equation, $\sqrt{2x + 1} - \sqrt{2x - 1} = 1, \begin{pmatrix} x \geq \frac{1}{2} \end{pmatrix}$, then $\sqrt{4x^2-1}$ is equal to :

asked May 28, 2017 by priyanka.c

1 answer

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt 2 \cos \theta \}$ and $Q = \{ \theta : \sin \theta + \cos \theta = \sqrt 2 \sin \theta $ be two sets. Then :

asked May 28, 2017 by priyanka.c

1 answer

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