The integral \(\int e^x(\tan x+\log \sec x) d x\) is equal to :

The direction cosines of the line
\(x-y+z-5=0\) and \(x-3 y-6=0\) are:

The projection of the vector \(2 \hat{i}-\hat{j}+3 \hat{k}\) on the vector \(3 \hat{i}+2 \hat{j}+6 \hat{k}\) is :

For \(A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\) if \(M_{i j}\) and \(A_{i j}\) are the minor and the cofactor of \(a_{i j}\) respectively, then \(|A|\) equals to :
(A) \(a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}\)
(B) \(a_{21} A_{12}+a_{22} A_{22}+a_{23} A_{32}\)
(C) \(a_{11} M_{11}-a_{12} M_{12}+a_{13} M_{13}\)
(D) \(a_{11} M_{11}+a_{12} M_{12}+a_{13} M_{13}\)
Choose the correct answer from the options given below :

Rolle's theorem holds for the function \(x^3+b x^2+c x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), the respective values of \(b\) and \(c\) are :

Given \(\sum p_0 q_0=800, \sum p_0 q_1=1500, \sum p_1 q_1=1300\) and \(\sum p_1 q_0=900\), where subscripts 0 and 1 are used for base year and current year respectively. The Paasche's

Let R be the feasible region for a Linear Programming Problem and let \(z=a x+b y\) be the objective function. If R is bounded, then the objective function z has :

Which statement is not true for a detergent molecule ?

Match List-I with List-II

List-I	List-II
(A) Faraday's Law	(I) Current induced in a conductor moving perpendicular to a magnetic field
(B) Lenz's Law	(II) Direction of force on a straight current carrying conductor placed perpendicular to a magnetic field
(C) Fleming's right hand rule	(III) Magnitude of induced emf
(D) Fleming's left hand rule	(IV) Direction of induced current

Choose the correct answer from the options given below:

Choose the incorrect statement.

The rate of biomass production is called productivity. It is expressed in terms of -

Which of the following statements are correct ?
A. The saturation current is constant with collector plate potential for different frequencies of incident radiation.
B. The saturation current is different with collector plate potential for different frequencies of incident radiation.
C. The saturation current is different with collector plate potential for different intensity of incident radiation.
D. The saturation current is constant with collector plate potential for different intensity of incident radiation.
E. Below threshold frequency no photo electrons are emitted.
Choose the correct answer from the options given below :

The product \(( Y )\) in the following reaction is
\(2 C_6 H_5 CHO \xrightarrow[\text { Hest }]{\text { conc. } NaOH} Y+C_6 H_5 COONa\)