Recent questions and answers in 2016

The Boolean Expression $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to :

answered Feb 27, 2020 by priyanka.clay6

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 :

answered Feb 27, 2020 by priyanka.clay6

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 :

answered Feb 20, 2020 by priyanka.clay6

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 ?

answered Feb 20, 2020 by priyanka.clay6

1 answer

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?

answered Feb 20, 2020 by priyanka.clay6

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 :

answered Feb 20, 2020 by priyanka.clay6

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

answered Feb 20, 2020 by priyanka.clay6

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 :

answered Feb 20, 2020 by priyanka.clay6

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 :

answered Feb 20, 2020 by priyanka.clay6

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 :

answered Feb 19, 2020 by priyanka.clay6

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 :

answered Feb 18, 2020 by priyanka.clay6

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 :

answered Feb 18, 2020 by priyanka.clay6

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 ?

answered Feb 18, 2020 by priyanka.clay6

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 :

answered Feb 18, 2020 by priyanka.clay6

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 :

answered Feb 6, 2020 by priyanka.clay6

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 :

answered Feb 6, 2020 by priyanka.clay6

1 answer

The integral $\begin{align} \int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx \end{align}$ is equal to : where C is an arbitrary constant.

answered Feb 6, 2020 by priyanka.clay6

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 :

answered Feb 5, 2020 by priyanka.clay6

1 answer

Consider $f(x) = \tan^{-1} \begin{pmatrix} \sqrt{\frac{1+\sin x}{1 - \sin x}} \end{pmatrix}, x \in (0, \frac{\pi}{2})$ . A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point :

answered Feb 5, 2020 by priyanka.clay6

2 answers