Area of the region bounded by the curve \(y=\sqrt{x}\) and lines \(x+y=2, y=0\) is

Match List-l with List-ll
Let A and B be any two events

List-l	List-ll
(A) \(P \left( A ^{\prime}\right)\)	(I) \(\frac{P(A \cap B)}{P(A)} ; P(A) \neq 0\)
(B) \(P (\Phi)\)	(II) \(\frac{P(A \cap B)}{P(B)} ; P(B) \neq 0\)
(C) \(P ( A \mid B )\)	(III) \(1-P(A)\)
(D) \(P ( B \mid A )\)	(IV) \(0\)

Choose the correct answer from the options given below :

The total cost function is given by \(C(x)=\frac{1}{3} x^3-5 x^2+30 x-15\) and selling price per unit is Rs. 6. The profit is maximum if the value of x is:

The degree of the differential equation
\(\left[1+\left(\frac{d y}{d x}\right)\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is :

Which of the following are correct?
(A) A statistical hypothesis is a statement about the population parameter which may be true or false.
(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.
(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.
(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.
Choose the correct answer from the options given below :

The function \(f(x)=-2 x^3-9 x^2-12 x+5\) is :

The differential equation \(\frac{d y}{d x}+\frac{x}{y}=0\), represents the family of curves:

Arrange the following structures involved in embryogenesis in the correct
sequence.
(A) Zygote
(B) Blastocyst
(C) Blastomeres
(D) Morula
Choose the correct answer from the options given below:

Chromosome number of in human meiocyte is :

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, 3d series (Sc to Zn), 4d series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has Ac and elements from Rf to Cn. The two series of the inner transition metals; 4f (Ce to Lu) and 5f (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of s and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
Which of the following statements is correct?

Isotonic solutions must have the same
(A) Solute
(B) Density
(C) Elevation in boiling point
(D) Depression in freezing point
Choose the correct answer from the options given below :

The value of \(\tan ^2\left(\sec ^{-1} 2\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) is:

Identify the correct statement about the electric charges \( q_1 \) and \( q_2 \) from the figure given below.