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Find the value of k, if area of triangle is 4 sq unit and vertices are
$(-2,0),(0,4),(0,k)$

General value of x satisfying the equation tan^2x+sec2x=1 is

What is the equation of the line if the line have slope $\frac{1}{3}$ and passing through the point (2,3)?

The condition that the straight line $lx+my=n$ may be a normal to the hyperbola $b^2{x}^2-a^2{y}^2=a^2{b}^2$ is given by

1. 11

The weight of coffee in 70 jars is shown in the following table :

$\begin{array}{ccccccc}\text{Weight (in grams)}:& 200-201& 201-202& 202-203& 203-204& 204-205& 205-206\\ \text{Frequency}:& 13& 27& 18& 10& 1& 1\end{array}$

Determine the variance and standard deviation of the above distribution.

If a function $f:\{1,2,3,4\}\to \{1,2,3,4,5,6,7,8,9\}$ is defined, then the function $f$ can be

Choose the correct answer in Question
Distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y+ 8z =12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) $\frac{2}{\sqrt{29}}units$

The number of ways in which 8 red roses and 5 white roses of different sizes can be made out to form a garland so that no two white roses come together is

A circle with centre $(a,b)$ passes through the origin. The equation of the tangent to the circle at the origin is

Let $A=\left[a_{ij}\right]$ be a $4\times 4$ matrix. If $a_{ij}=\{\begin{array}{c}2,\text{when}i=j\\ 0,\text{when}i\ne j\end{array}$,
then the value of $\left\{\frac{\text{det(adj(adjA))}}{7}\right\}$ is
(where $\{.\}$ represents the fractional part function)

I alternately toss a fair coin and throw a fair die, until I, either toss a head or throw the face two. If I toss the coin first, then the probability that I throw the face two before I toss a head, is

If a$x^2+bx+c=0,a,b,cϵR$ , has no real root, then

The derivative of $si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ with respect to $ta{n}^{-1}\left(\frac{2x}{1-x^2}\right)$ is

1. -0.03125

Integrate the rational functions.
$\int \frac{x}{(x+1)(x+2)}dx.$

If ${\cos }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{12}{13}={\cos }^{-1}k,$ then the value of $k$ is

The order and degree of the differential equation ${[4+{\left(\frac{dy}{dx}\right)}^2]}^{2/3}=\frac{d^{2}y}{d{x}^2}$ are

The number of integral value(s) of $a$ for which ${\log }_e(x^2+5x)={\log }_e(x+a+3)$ has exactly one solution is

Calculate the mean
deviation about median age for the age distribution of 100 persons
given below:

An ellipse is drawn by taking a diameter of the circle $(x-1{)}^2+y^2=1$ as its semi-minor axis and a diameter

of the circle $x^2+(y-2{)}^2=4$ as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the

coordinate axes, then the equation of the ellipse is

The number of integers $n$ for which $n^2-4n+46$ is a perfect square, is

If the radius of a spherical balloon increases by $0.1\%$ then its volume increases approximately by

The graph of $y=|x^3+1|$ is

In how many ways $n$ married couples can be arranged around a table so that men and women are alternate and each woman is not adjacent to her husband?

Find
X and Y,
if

(i) and

(ii) and

Consider the family of lines $(x-y-6)+\lambda (2x+y+3)=0$ and $(x+2y-4)+\mu (3x-2y-4)=0.$ If the lines of these two families are at right angle to each other, then the locus of their point of intersection is

The time taken to travel 20 mi is 2 h, which can be represented as ordered pair (2,20). The time taken for every extra 1 mi is 10 min. Find the expression for the time taken with resepect to distance travelled.

Let

and

be two unit vectors andθ
is the angle between them. Then
is
a unit vector if

(A)
(B)

(C)

(D)

In $△ABC,R,r,r_1,r_2,r_3$ denote the circumradius, inradius, the exradii opposite to the vertices $A,B,C$ respectively. Given that $r_1:r_2:r_3=1:2:3$.
The value of $R:r$ is