Area bounded by the curves \(y^2=9 x\) and \(y=3 x\) is:

The term of the perpetuity is:

The region represented by the system of inequalities \(x, y \geq 0, y \leq 6, x+y \leq 3\)

Match List-I with List-II
The function \(f(x)=2 x^3-15 x^2+36 x+5\) for \(x \in[2,5]\) has

List-I	List-II
(A) absolute maximum value	(I) 5
(B) absolute minimum value	(II) 60
(C) point of absolute maxima	(III) 3
(D) point of absolute minima	(IV) 32

Choose the correct answer from the options given below:

The rate of change of area of a circle with respect to its circumference when radius is 6 cm, is

Which of the following are examples of irregular trends in a time series?
(A) Decrease in production due to a sudden strike.
(B) The rise in prices before festivals.
(C) Unusual rise in income of the printing press due to the announcement of an election.
(D) Fall in crop yield due to floods.
Choose the correct answer from the options given below :

Match List-l with List-ll

List-l (Parametric Equations)	List-ll \(\frac{d y}{d x}\)
(A) \(x=\frac{2}{t}, y=2 t\)	(I) \(4 t^2\)
(B) \(x=t^3, y=3 t+2\)	(II) \(2(t+1)\)
(C) \(x=\log t, y=2 t^2\)	(III) \(-t^2\)
(D) \(x=e^t, y=2 t e^t\)	(IV) \(t^{-2}\)

Choose the correct answer from the options given below :

If a moneylender charges interest at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is :

In which of the following actinoid elements 6d subshell is vacant ?

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. 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. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Metallic radii of some transition elements are as follows:
Fe: 126 pm; Co: 125 pm; Ni: 125 pm; Cu: 128 pm
Which of these elements will have highest density?

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Malignant malaria is caused by -

Which one of the following equations is a homogeneous differential equation?

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: