The corner points of the bounded feasible region associated with the LPP: Maximize \(Z=p x+q y, p, q>0\) are (0, 0), (3.5, 0), \(\left(\frac{112}{59}, \frac{135}{59}\right)\) and (0,3). If the optimum value of Z occurs at both \(\left(\frac{112}{59}, \frac{135}{59}\right)\) and (0,3), then

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^5+x^3+x+2\right) d x\) is:

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

The function \(f(x)=x^2-x+1\) is

Derivative of \(\cos \left(\sin \left(x^2\right)\right)\) with respect to x is:

The value of the integral \(\int \frac{\log x^3}{x} d x\) is :

The sum of the products of elements of any row with the cofactors of corresponding elements is equal to:

An inductor of reactance 100 \( \Omega \) and resistor of resistance 100 \( \Omega \) are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is:

The half life of decaying \({ }^{14} C\) is 6000 years approximately. How much time is needed to decaying \(80 \%\) of \({ }^{14} C ?[\log 5=0.6990]\)

Match List-I with List-II

List-I	List-II
(A) Resistive Circuit	(I) No power dissipation
(B) Purely inductive or capacitive circuit	(II) Maximum power dissipated because \( X_L = X_C \)
(C) LCR series circuit	(III) Power dissipated only in resistor
(D) Power dissipated at resonance in LCR circuit	(IV) Maximum power dissipation

Choose the correct answer from the options given below :

Huygen's wave theory of light could not explain the phenomenon of :

A non-polar dielectric material is placed in an external electric field. Choose the correct statement(s) from the following:
(A) There will be no change in the positions of positive and negative charges inside the dielectric.
(B) The positive charges of molecules will shift opposite to the direction of the electric field.
(C) The negative charges of molecules will shift in the direction of the electric field.
(D) The positive charges of the molecules will shift in the direction of the field and negative charges of the molecules will shift opposite to the field.
Choose the correct answer from the options given below:

Choose the correct statements from the following:
A. Displacement current is due to time varying magnetic field.
B. The frequency of the electromagnetic wave naturally equals the frequency of oscillation of the charge.
C. Light carries energy from the Sun to the Earth.
D. Electromagnetic wave does not exert pressure.
E. Electromagnetic wave contains both electric and magnetic field.
Choose the correct answer from the options given below: