The half life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value ?

An electromagnetic wave moves in vacuum. Its speed is c.
Choose the correct options about the characteristics of electromagnetic waves:
(A) \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \)
(B) Electromagnetic waves are transverse in nature.
(C) Both the electric field and magnetic field vibrate perpendicular to the direction of propagation of waves
(D) Electromagnetic waves are longitudinal in nature.
Choose the correct answer from the options given below:

After how many half lives a radioactive substance will decay to 6.25% of its original value :

The de-Broglie wavelength of neutron at \( 127^\circ \text{C} \) is : (Given Boltzmann constant, \( k = 1.38 \times 10^{-23} \text{ J mole}^{-1} \text{K}^{-1}, h = 6.63 \times 10^{-34} \text{ Js} \), mass of neutron \( m = 1.66 \times 10^{-27} \text{ kg} \))

A bar magnet is cut into two equal halves along a plane parallel to the magnetic axis. The one parameter which remains unchanged is

Three capacitors of capacitance, \( 3 \, \mu \text{F}, 9 \, \mu \text{F} \) and \( 18 \, \mu \text{F} \) respectively are connected once in series and then in parallel. The ratio of equivalent capacitance in series to parallel is :

In the systematic study of the photoelectric effect experiment, the stopping potential depends (for a given metal):

The female reproductive system consists of :
(A) Ovaries
(B) External genitalia
(C) Cervix and vagina
(D) Oviducts and uterus
Choose the most appropriate answer from the options given below:

The curve \(y = f ( x )\) is normal probability curve, then which of the following statements are correct?
(A) mean, median and mode of the distribution coincide.
(B) the area bounded by the curve \(y = f ( x )\) and \(x\)-axis is one unit.
(C) The curve is symmetrical about the line \(x =\mu\), where \(\mu\) is the mean.
(D) y -axis is an asymptote to the curve.
Choose the correct answer from the options given below :

Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (α-1-antitrypsin). This protein is used to treat:

The angular momentum of an electron in the third orbit of a hydrogen atom is
(Given: \( h = 6.6 \times 10^{-34} \text{ Js} \))

Match List - I with List - II

List - I (Differential Equations)	List - II (Order and degree)
(A) \(ydx + xlog(y/x)dy - 2xdy = 0\)	(I) Order: 2, degree:1
(B) \(\left(\frac{d^3 y}{d x^3}\right)^2+3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^2\)	(II) Order :1, degree:1
(C) \(\frac{d y}{d x}+\log \left(\frac{d y}{d x}\right)+x=y\)	(III) Order: 3, degree:2
(D) \(\left(\frac{d s}{d t}\right)^4+2 s \frac{d^2 s}{d t^2}=0\)	(IV) Order: 1, degree: Not defined

Choose the correct answer from the options given below:

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), 4d series (Y to Cd), \(5 d\) series ( La and Hf to Hg ) and 6 d series which has \(A c\) and elements from \(R f\) to \(C n\). The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (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 is not regarded as transition metal?