The area (in sq. units) of the triangle whose vertices are \((0,0),(a, 0),(0, b)\), is equal to

A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

Which of the following are correct about the Sinking Fund?
(A) It is a fixed term account.
(B) It is a set-up for a particular upcoming expense.
(C) A fixed amount at regular intervals is deposited in the Sinking Fund.
(D) It can be used in any emergency.
Choose the correct answer from the options given below:

Consider the following hypothesis test :
\( H_0 : \mu=18 \)
\( H_1 : \mu \neq 18 \)
If a sample of 48 provided a sample mean \(\bar{x}=17\),
and a sample standard deviation \(\sigma=4.5\),
then the value of the \(t\)-test statistic is :

If \(\int \frac{d x}{(x-1)^{3 / 4}(x+2)^{5 / 4}}=\alpha[1-g(x)]^\beta+c\), where \(c\) is a constant of integration, then which of the
following are true?
(A) \(\alpha=\frac{2}{3}\)
(B) \(\beta=\frac{3}{4}\)
(C) \(3 \alpha+4 \beta=5\)
(D) \(g(x)=\frac{3}{x+2}\)
Choose the correct answer from the options given below:

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

The corner points of the bounded feasible region determined by the system of linear inequalities are \((0,0),(2,4),(0,5)\) and \((4,0)\). If the maximum value of \(Z=a x+b y\), where \(a, b>0\) occurs at both \((2,4)\) and \((4,0)\), then

If 100 J of work is done to move electric charge equal to 4 C from a place where potential difference is \( -10 \text{ V} \) to another place where potential is V volt, then the value of V would be:

Hardy - Weinberg principle states that:

Observe the figures and answer the question.

Which of the following is not a constituent of bio-gas?

Read the passage carefully and answer
The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like NH3 and H2O) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lifted. It results in splitting of the d orbitals. The pattern of splitting depends upon the nature of the crystal field.
In tetrahedral coordination complexes, low-spin configurations are rare because:

A bubble in glass slab (\( \mu = 1.5 \)) when viewed from one side appears at 5 cm and 2 cm from otherside, then the thickness of the glass slab is:

Enzymes are biological catalysts. They accelerate biological reactions. Which of the following is not true about enzymes?