For a full wave rectifier, if the input frequency is \(5 0 ~ H z\), the output frequency will be

As per the graph given below:

Match List - I with List - II

LIst - I (Function/Area/point)	List - II (Representation)
(A) Consumers Surplus	(I) y = g(x)
(B) Supply function	(II) v
(C) Demand function	(III) s
(D) Equilibrium point	(IV) y = f(x)

Choose the correct answer from the options given below:

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 :

If 525 = (10 + K) (mod 7) where \(K \in N\), then the least value of K is:

Central Limit Theorem implies that as the size of the sample increases, the distribution approaches:

Out of students in a school, it is known that \(65 \%\) reside in hostel and \(35 \%\) are day scholars. Previous year results report that \(40 \%\) of the students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination.At the end of the year, one student is chosen at random from the class.
If the selected student attains grade A, find the probability that the student is a hosteller.

An urn I contains \(3\) white and \(4\) blue balls, while urn II contains \(5\) white and \(6\) blue balls. One ball is drawn at random from one of the urns and it is found to be white. The probability that it was drawn from urn II is:

Two capacitors of capacitances \( C_1 \) and \( C_2 \) are connected in parallel.
If two-third of the total charge is shared by capacitor \( C_1 \), the ratio of \( C_1 \) to \( C_2 \) is given by:

Arrange the following steps of sewage treatment in correct sequence:
A. Flocs consume organic matter and reduces the BOD.
B. Removal of floating debris and grit.
C. Bacterial flocs allowed to sediment.
D. Primary effluent passed into aeration tank and agitated mechanically.
E. Effluent after secondary treatment is released into water bodies.
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (AC circuit)	List-II (Features)
(A) Only resistor in a circuit	(I) Current leads or lag the voltage
(B) Only capacitor in a circuit	(II) Voltage and Current are in phase
(C) Only inductor in a circuit	(III) The current lags the voltage by \(\frac{\pi}{2}\)
(D) Series LCR circuit \(X_C \neq X_L\) and \(R \neq 0\)	(IV) The current leads the voltage by \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-2 \hat{k}\). Then a vector of magnitude 24 , which is perpendicular to the vectors \(\vec{a}+\vec{b}\) and \(\vec{a}-\vec{b}\), is:

The area bounded by the curve \(y=2 x-x^2\) and the straight line \(y=-x\) is :

Read the passage carefully and answer the questions
The transition metals and their compounds are known for their catalytic activity. This activity is ascribed to their ability to adopt multiple oxidation states and to form complexes. Vanadium(V) oxide (in Contact Process), finely divided iron, and nickel (in Catalytic Hydrogenation) are some of the examples. Catalysts at a solid surface involve the formation of bonds between reactant molecules and atoms of the surface of the catalyst (first row transition metals utilise 3d and 4s electrons for bonding). This has the effect of increasing the concentration of the reactants at the catalyst surface and also weakening of the bonds in the reacting molecules (the activation energy is lowering). Also because the transition metal ions can change their oxidation states, they become more effective as catalysts.
\(TiCl_4 + Al(CH_3)_3\) is used as a catalyst in: