Which of the following is NOT correct about a Sinking Fund?

The value of \(k\) for which the system of equations
\(\begin{array}{l}x+y+z=1 \\x-k y+z=1\end{array}\)
\(x-y+z=1\)
has more than one solution is :

For the function \(f(x)=x^x, x>0\), which of the following are TRUE?
(A) \(f^{\prime}(x)=x^x(1+\log x)\)
(B) \(x=e\) is the critical point
(C) \(f\) is increasing in \(\left(\frac{1}{e}, \infty\right)\)
(D) \(f\) is increasing in \((0, \infty)\)
Choose the correct answer from the options given below :

The area bounded by \(y^2=x, y=5\) and the \(y\)-axis is:

\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) dx is equal to :

If \(x=2 a t, y=a t^2\), where ' a ' is a constant, then \(\frac{d^2 y}{d x^2}\) at \(x=2\) is :

The unit digit of \(12^{12}\) is :

Match List - I with List - II.

List - I	List - II
(A) To study crystal structure	(I) IR ray
(B) To study structure of nuclei	(II) X-ray
(C) Take haze photography	(III) UV-ray
(D) Can cause fluorescence	(IV) \( \gamma \)-ray

Choose the correct answer from th options given below :

In a magnetic field,
(A) a charged particle in motion can experience a force
(B) a charged particle at rest, experiences a force
(C) there is no change in the speed of the charged particle
(D) there is a change in the kinetic energy of the charged particle.
Choose the correct answer from the options given below:

Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Correctly predict the final product and the type of reaction for the following reaction:
\(C _6 H _5- N _2^{+} Cl ^{-}+ C _6 H _5- OH \xrightarrow{ HO ^{-}}\)?

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
In the above passage, the inheritance is an example of:

In an ecosystem, energy flow is:

In a large building, there are 20 bulbs of 40 W each, 5 bulbs of 100 W each, 5 fans of 80 W each, and 1 heater of 1 kW. The voltage supply is 220 V. The minimum capacity of the main fuse of the building should be