If the roots of each of the equations \(2 x^2+x-1=0,3 x^2-10 x+3=0\) and \(6 x^2+11 x-2=0\) corresponds to probabilities of three events of a random experiment, then those events are

If \(f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right)\) is a real valued function then the range of \(f\) is

\(P\) and \(Q\) are the extremities of a focal chord of the parabola \(y^2=4 a x\). If \(P=(9,9)\) and \(Q=(p, q)\), then \(p-q=\)

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If X is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of X is

If \(a>0, \lim _{x \rightarrow a} \frac{a^x-x^a}{x^x-a^a}=-1\), then \(a\) is equal to

If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^4+x^2+1=0\) such that \(\alpha+\beta=-1, \gamma+\delta=1, \alpha^2=\beta\) and \(\gamma^2=-\delta\), then \(\alpha^{2023}+\beta^{2023}+\gamma^{2022}+\delta^{2022}=\)

If the ratio of the perpendicular distances of a variable point \(P(x, y, z)\) from the \(X\)-axis and from the \(Y Z\)-plane in \(2: 3\), then the equation of the locus of \(P\) is

The current gain of a transistor is 0.98 . If the transistor is used in a common emitter arrangement what would be the change in collector current corresponding to a change of \(0.5 \mathrm{~mA}\) in the base current?

An initially charged undriven \(L C R\) circuit having inductance \(L\), capacitance \(C\) and resistance \(R\) will be

In the hardening stage of plaster of paris, the compound formed is

A cylindrical metallic wire is stretched to increase its length. If the resistance of the wire is increased by $4\%$ then the percentage increase in its length is

The variance of the data : \(1,2,3,5,8,13,17\) is approximately

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?