The half-lives of two radioactive specimens are \(T_1=5\) years and \(T_2=7.5\) years.
The ratio of their disintegration constants \(\lambda_1\) and \(\lambda_2\) is:

Match List-I with List-II

List-I (Electronic Device)	List-II (Function)
(A) Stabilizer	(I) Used to convert a.c. voltage into d.c. voltage
(B) Filter	(II) Used either for stepping up or stepping down the a.c. voltage
(C) Rectifier	(III) Used for constant output voltage even when the input voltage or load current changes
(D) Transformer	(IV) Used to remove any ripple in the rectified output voltage

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Match List-I with List-II

List-I (Electromagnetic Wave Wave)	List-II (Application)
(A) Microwaves	(I) Photographs during foggy season and night vision cameras
(B) X-rays	(II) Radar
(C) Gamma rays	(III) Photographs internal parts of human body
(D) Infrared Rays	(IV) Radiography for malignant tumors in cancer treatment

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A bar magnet held perpendicular to a uniform magnetic field experiences a torque \( T_1 \). By what angle should it be rotated to change the experienced torque to \( 0.5T_1 \)?

An electric dipole is placed in a non-uniform electric field, such that the dipole moment is parallel to the electric field. The dipole will experience

Choose a vector quantity from the following:

A straight wire of mass 200 g and length 1.5 m carrying a current of 2 A is placed in a uniform magnetic field at right angles to its direction, is suspended in mid air. The magnitude of magnetic field is : \(\left(g=9.8 m / s ^2\right)\)

Identify the incorrect statements with reference to dispersion of white light.
(A) Red light gets most deviated while passing through the prism.
(B) Thick lenses show chromatic aberrations due to dispersion.
(C) Refractive index of medium for different colours is different.
(D) Red light travels faster than violet light in the prism.
(E) While light, once dispersed, cannot be recombined.
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Resonant frequency of a LCR series circuit is 16 kHz. If the capacitance is increased to 16 times, then the new resonant frequency will become

A die is rolled in such a way that an even number is twice likely to occur as an odd number.
If the die is rolled twice, then the mean of the number of perfect squares in two tosses is :

A student is asked to observe his face in three different types of mirrors P, Q, R one by one by holding each mirror close to his face at same distance. Mirror P given exact and same size image, Q gives exact but smaller while R gives exact but larger image.
A. P is Convex mirror, Q is Plane, R is Concave
B. P is Plane, Q is Convex, R is Concave
C. P is Concave, Q is Plane, R is Convex
D. P is Convex, Q is Concave, R is Plane
Choose the correct answer from the options given below:

Which of the following structures are related to the male reproductive organ.
(A). Isthmus
(B). Sertoli cells
(C). Leydig cells
(D). Prostate
Choose the correct answer option given below.

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :