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Distance between two parallel lines is unity. A point P lies between the lines at a distance 'a' from one of them. Find the length of a side of an equilateral triangle PQR such that Q lies on one of the parallel lines while R lies on the other.

$(a-b)cos\frac{C}{2}=csin\left(\frac{A-B}{2}\right)$

Solveis
equal to

(A)


(B)
(C)


(D)

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane 2x - y + z + 3 = 0 is the line

The plane passing through the point $(-2,-2-3)$ and containing the line through the points $(1,1,1)$ and $(1,-1,2)$ make intercepts $a,b,c$ along the $x,y,z$ axis respectively. Then the value of $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$ is:

Number of solutions of the equation $|x-1|+|x-2|+|x-3|=7$ is

If sin x +cosec x =2, then write the value of $si{n}^{n}x+cose{c}^{n}x.$

Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers what is the probability that this number has the same digits ?

If sum of $n$ of a series is given by $S_n=3n^2+3n$, then $n^{th}$ term of the series is

Let z be a complex number such that |z| = 5 . Find the maximum value of | z + 3 + 4i |

“The economies of China, India and Pakistan differ interms of sectoral growth.” Comment.

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis

The half life of a radioactive substance is 20 minutes. The time taken between 50 $\%$ decay and 87.5$\%$ decay of the substance will be

The area enclosed by the curve $y=\sqrt{4-x^2},y\ge \sqrt{2}\sin \left(\frac{x\pi }{2\sqrt{2}}\right)$ and the x-axis divided by the y - axis in the ratio

If the linear function is of the form $y=mx+c$, where $m<0$ and $c>0$, then the graph will be

$If\frac{2x}{2x^2+5x+2}$ > $\frac{1}{x+1},then$

If the mirror image of the point $(1,3,5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha ,\beta ,\gamma )$, then $5(\alpha +\beta +\gamma )$ equals:

At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of the contact to the point (-4,-3). Find the equation of the curve given that it passes through (-2,1).

For what value of k , the matrix $\left[\begin{array}{cc}2-k& 4\\ -5& 1\end{array}\right]$ is not invertible?

The solution of differential equation $(2x-y+1)dx+(2y-x+1)dy=0$ is

(where $c$ is integration constant)

If the curves, $\frac{x^2}{a}+\frac{y^2}{b}=1$ and $\frac{x^2}{c}+\frac{y^2}{d}=1$ intersect each other at an angle of ${90}^{\circ }$, then which of the following relations is $\text{TRUE}?$

The product of the roots of the equation $9x^2-18\left|x\right|+5=0$ is :

If tangents are drawn from points on the hyperbola $\frac{x^2}{4}-\frac{y^2}{9}=1$ to the circle $x^2+y^2=4,$ then the locus of the mid-point of the chord of contact is

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1,3$ and $8$, then a ratio of other two observations is :

What will be the input of $A$ & $B$ for the Boolean expression $\left(\overline{A+B}\right).\left(\overline{A.B}\right)=1$

Find the value of