If matrix \(A=\left[\begin{array}{ccc}x & 2 & 3 \\ a & y & -5 \\ b & c & 0\end{array}\right]\) isa skew-symmetric matrix, then
(A) x + y + c = 5
(B) c = 5
(C) a + b + c = 0
(D) a + b - c = 10
Choose the correct answer from the options given below:

Let \(\vec{a}=4 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=-2 \hat{i}+\hat{j}-2 \hat{k}\). Then
(A) \(\vec{a}\) is a unit vector
(B) \(\vec{a} \times \vec{b}=-\hat{i}+2 \hat{j}+2 \hat{k}\)
(C) \(\vec{a}\) and \(\vec{b}\) are parallel vectors
(D) \(\vec{a}\) and \(\vec{b}\) are neither parallel nor perpendicular vectors
Choose the \(\backslash\) textbf\{correct\} answer from the options given below :

The point on the curve \(\frac{x^2}{4}+\frac{y^2}{9}=1\) at which the tangent to the curve is parallel to the \(x\)-aris is

Two positive numbers whose sum is 60 and the product of the square of one number and other number is maximum are:

Differential equation of a parabola with vertex at origin and symmetric about \(x\)-axis is :

The general solution of the differential equation \(x\left(\frac{d y}{d x}\right)=y+x \tan \left(\frac{y}{x}\right)\) is

If \(x=a t^2\) and \(y=2 a t\), then \(\frac{d^2 y}{d x^2}=\)

The self-inductance of an inductance coil having 100 turns is 20 mH. The total flux through the coil for a current of 40 mA is :

Which one of the following structures is not the male sex accessory duct?

Benzene ring in phenol is expected to give the characteristic substitution or replacement reactions i.e. halogenation, nitration, sulphonation, alkylation etc. In these reactions, the attacking reagent is electrophile. The phenolic group activates the ortho and para positions in the ring due to conjugation. Disubstitution reactions are quite fast as the electron density in the ring has increased considerably. Phenols do not respond to nucleophilic substitution reactions as it is influenced by phenolic group.
Secondary alcohol among the following is:

(A)

(B) \(H _2 C = CH _2- CH _2 OH\)

(C) \(H _3 C - CH _2- CH _2 OH\)
(D)
(E)

Choose the correct answer from the options given below:

0.01 molal aqueous solutions of strong electrolytes \(NaCl , KCl , MgSO _4\) and \(K _2 SO _4\) are prepared.Which of the following statements is correct regarding their osmotic pressure ? (Assume complete dissociation of solute particles)

For a heavily doped n-type semiconductor, Fermi level lies:

The relative order of reactivity of \(1^\circ, 2^\circ, 3^\circ\) alcohol towards dehydration is :