The feasible region associated with the inequality \(2 x+3 y>4\) is

The area (in sq., units) of the region bounded by the parabola \(y^2=4 x\) and the line \(x=1\) is:

Match List-l with List-ll.Find the derivatives from List-I.

List-l	List-II
(A) \(y=\sqrt{\sin x+y}\)	(I) \(\frac{-\sin x}{1+\cos y}\)
(B)\(\sin y=x \sin (a+y)\)	(II) \(\frac{\cos x}{2 y-1}\)
(C) \(y+\sin y=\cos x\)	(III) \(\frac{-1}{\sin ^2(x+y)}\)
(D) \(y=\tan (x+y)\)	(IV) \(\frac{\sin ^2(a+y)}{\sin a}\)

Choose the correct answer from the options given below:

Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time.

If \(y = x + \tan x\), then value of \(\frac{d^2y}{dx^2}\) at \(x = \frac{\pi}{4}\) is:

Choose the correct answer from the options given below:
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\) is \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{y-3}{-2}\)
B. Equation of line passing through (1, 2, 3) and parallel to the line given by \(\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}\) is \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z+3}{6}\).
C. Equation of line passing through the origin and (5, -2,3) is \(\frac{x}{5}=\frac{y}{-2}=\frac{z}{3}\).
D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is 2(x - 1) + 3(y - 2) - (z - 3) = 0.
E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is 2x + 3y + 4z = 1

If \(A\) is a square matrix of order \(3 \times 3\) and \(|A|=4\). The value of \(\mid(\operatorname{adj} A)\). \(A \mid\) is:

Shown below is the graph of parabola \(y^2=x\), the area (in sq. units) of the shaded region is:

Match List I with List - II.

List - I	List - II
(A) L.C. Oscillation	(I) Inductor supplied with AC
(B) \( Q = \frac{\omega_o L}{R} \)	(II) \( \frac{d^2q}{dt^2} + \frac{1}{LC}q = 0 \)
(C) Voltage leads current	(III) \( \frac{i_p}{i_s} = \frac{V_s}{V_p} \)
(D) Transformer	(IV) Sharpness of resonance curve

Choose the correct answer from the options given below :

Choose the correct statements from the following:
(A) Electromagnetic waves do not follow the principle of superposition.
(B)The variations in the electric field and in the magnetic field of electromagnetic waves, if any, never happen simultaneously.
(C) Electromagnetic waves are produced by accelerated charges
(D) The energy of electromagnetic waves is divided equally into electric and magnetic field vectors.
Choose the correct answer from the options given below:

Ex situ conservation include:

Arrange the given structures formed during spermatogenesis in correct sequence.
(A) Spermatozoa
(B) Secondary spermatocytes
(C) Spermatids
(D) Spermatogonia
Choose the correct answer from the options given below:

If \(y=\log _e\left(\sec \left(e^{x^2}\right)\right)\), then \(\frac{d y}{d x}=\)