Evaluate \(: 3^{15} \bmod (7)\)

The solution set of the inequation \(\frac{7+5 x}{4} \geq \frac{x}{3}-10, x \in R\) is :

\(y=\log _e\left(\frac{1-x^2}{1+x^2}\right)\), then \(\frac{d y}{d x}\) is equal to:

The sum of order and degree of the differential equation \(y=x \frac{d y}{d x}+2 \sqrt{1+\left(\frac{d y}{d x}\right)^2}\) is

If \(A\) and \(B\) are any two events such that \(P(B)=P(A\) and \(B)\), then which of the following is correct:

The range of the function \(f(x)=\frac{1}{3-\sin 4 x}\) is:

The matrix \(A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \end{bmatrix}\) then \(A^{-1}\) is equal to:

In Kolbe's reaction, phenol undergoes :

The probability distribution function of a normal variate with mean \(\mu\) and variance \(\sigma^2\) is given by :
\(f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2},-\infty< x< \infty,-\infty < \mu < \infty, \sigma>0\)
If \(y=f(x)\) be the normal probability curve, then which of the following is correct?
(A) The normal curve is symmetrical about the line \(x=\mu\).
(B) Mean, median and mode of the distribution coincide.
(C) \(Y\)-axis is an asymptote to the normal curve.
(D) If \(x\) increases numerically, \(f(x)\) decreases rapidly.
Choose the correct answer from the options given below :

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
Oxidation state of scandium is

Which of the following functions from \(Z\) to \(Z\) is a bijective function? (where \(Z\) is set of integers)

Let \(\Delta = \begin{vmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{vmatrix}\), then \(\Delta\) lies in the interval

The particular solution of the differential equation \(x d y=\left(2 x^2+1\right) d x, x \neq 0\), given that \(y=1\) when \(x=1\) is: