The area (in square unit) of the triangle formed by \(x+y+1=0\) and the pair of straight lines \(x^2-3 x y+2 y^2=0\) is

A plane meets the \(X, Y, Z\)-axes in \(A, B, C\) respectively. If the centroid of the \(\triangle A B C\) is \((2,-3,5)\), then the perpendicular distance from origin to the given plane is

From a bag containing 4 white and 5 red balls, if 3 balls are drawn at random, then the mean of the number of red balls among the balls drawn, is

If \(\left(\mathrm{l}_1, \mathrm{~m}_1, \mathrm{n}_1\right),\left(\mathrm{l}_2, \mathrm{~m}_2, \mathrm{n}_2\right)\) are the direction cosines of two lines, then \(\left(1_1 m_2-1_2 m_1\right)^2+\left(m_1 n_2-m_2 n_1\right)^2+\) \(\left(\mathrm{n}_1 \mathrm{l}_2-\mathrm{n}_2 \mathrm{l}_1\right)^2+\left(\mathrm{l}_1 \mathrm{l}_2+\mathrm{m}_1 \mathrm{~m}_2+\mathrm{n}_1 \mathrm{n}_2\right)^2=\)

If the general solution of \(\frac{d y}{d x}=\frac{y^2}{x y-y^2-x^2}\) is \(\tan ^{-1}\left(\frac{y}{x}\right)=f(y)+C\), then \(f\left(e^3\right)=\)

The direction cosines of two lines are connected by the relations \(l+m-n=0\) and \(l m-2 m n+n l=0\). If \(\theta\) is the acute angle between those lines then \(\cos \theta=\)

A box contains 20% defective bulbs. Five bulbs are chosen randomly from this box. The probability that exactly 3 of the chosen bulbs are defective is

The equation of the line through the point \((-1,3)\) in symmetrical form, when the angle made by the line with the positive direction of \(X\)-axis is \(120^{\circ}\), is given by

The compounds formed when \(\mathrm{KMnO}_4\) is heated to \(513 \mathrm{~K}\) are ____

The pair of lines \(l x^2+2(l+m) x y+m y^2=0\) lies along two diameters of a circle and divides the circle into 4 sectors. If the area of bigger sector is 5 times the area of smaller sector, then \(\frac{l m}{(l+m)^2}=\)

A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is \(\sqrt{\frac{g h}{6}}\) and coefficient of friction is \(\frac{5}{3 \sqrt{3}}\). The time taken by the person to reach from A to B with maximum possible acceleration is

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

A bulb of resistance $280\Omega$ is supplied with a $200 \mathrm{V}$ $AC$ supply. What is the peak current?