(A) f(x) = |x| is continuous function on R (the set of real numbers)
(B) f(x) = [x] is continuous function on R
(C) f(x) = sin x is continuous function on R
(D) f(x) = tanx is continuous function on R
(E) f(x) = sinx + cosx is continuous function on R

If A is a skew-symmetric matrix of order \(n \times n\) and \(a_{i j}\) is the \((i, j)^{\text {th }}\) elements, then :

The direction ratios of the line perpendicular to the lines \(\frac{x-5}{2}=\frac{y+11}{-3}=\frac{z+3}{1}\) and \(\frac{x-7}{1}=\frac{y+2}{2}=\frac{z-4}{-2}\) are proportional to :

\(\int \frac{1}{x\left(x^5-1\right)} d x\) is equal to

Match the Integrating factor of the following Differential equations.

List - I	List - II
(A) \(\frac{d y}{d x}-y=\cos x\)	(I) \(e^x\)
(B) \(\frac{d y}{d x}=\cos x-y\)	(II) \(x^2\)
(C) \(x \frac{d y}{d x}+2 y=x^2\)	(III) \(\frac{1}{x^2}\)
(D) \(\frac{d y}{d x}=x+\frac{2}{x} y\)	(IV) \(e^{-x}\)

\(\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)\) is valid for which values of \(\lambda\) ?

\(\int_{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x\) is equal to

The capacity to generate a whole plant from any cell is called:

Match List-I with List-II

List-I (Physical property)	List-II (Expression)
(A) G (conductance)	(I) \(1/(RA)\)
(B) R (resistance)	(II) \(A/(\rho l)\)
(C) \(\kappa\) (Specific conductance)	(III) \(\kappa/c\)
(D) \(\Lambda_m\) (molar conductance)	(IV) \(l/(\kappa A)\)

Choose the correct answer from the options given below:

A resistor, an inductor and a capacitor are connected in series with a variable frequency source of alternating emf. At resonance, the amplitude of current depends on :
(A) Resistance
(B) Inductance
(C) Capacitance
(D) Frequency of source
Choose the correct answer from the options given below :

Choose the correct statements from following:
A. Resistivity of a conductor increases with increase in its length.
B. When a small resistor is connected in parallel across a galvanometer, it is converted into ammeter.
C. Current density is a vector quantity.
D. Potentiometer is used to measure the electric current.
E. Kirchoff's junction rule is based on the conservation of charge.
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
Process of accumulation of dark coloured amorphous substance is called:

If \(f(x)=x^3 \log _e x\), Then \(f^{\prime \prime}\left(e^2\right)\) is equal to