A convex lens of focal length 40 cm is placed in contact with a concave lens of focal length 20 cm. If an object is placed at 40 cm in front of the combination, the position of the image formed by the combination is

A 1.0 m long metallic rod is rotated with an angular frequency of \( 500 \, \text{rad s}^{-1} \) with one end hinged at the center and the other end at the circumference of a circular metallic ring of radius 1 m about an axis passing through the center and perpendicular to the plane of the ring. A constant and uniform magnetic field of 0.6 T parallel to the axis exists everywhere. The emf developed between the center and the ring is

A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is \(4 \times 10^{-3} Wb\). The self-inductance of the solenoid is

The time required for a 50 Hz alternating current to reach the peak value starting from zero

Identify the correct statement(s).
(A) In any lens, the optical centre is always at the centre of the lens.
(B) In a lens, if the curvature of its two surfaces is equal, the optical centre is at the centre of the lens.
(C) A light ray passing through the optical centre of a lens never shifts from the direction of the incident ray.
(D) A ray of light incident perpendicularly on a lens passes through its focus after refraction.
Choose the correct answer from the following given options.

In a cyclotron, if a deutron can gain a maximum energy of 40 MeV, then a proton can gain a maximum energy of _________

n the given diagram, the direction of current is given. Due to the presence of the current carrying wire, the loop ABCD will be

Match List I with List II.

LIST I	LIST II
A. Trichophyton	I. Typhoid
B. Rhino viruses	II. Pneumonia
C. Streptococcus	III. Common Cold
D. Salmonella	IV. Ringworm

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A charged particle carrying charge \(q = 1 \mu C\) moves in a uniform magnetic field with velocity \(v_1 = 10^6 \text{ m/s}\) at an angle of \(45^\circ\) with the x-axis in the xy-plane and experiences a force \(F_1 = 0.4\sqrt{2} \text{ N}\) along the negative z-axis. When the same particle moves with velocity \(v_2 = 10^6 \text{ m/s}\) along the z-axis, it experiences a force \(F_2\) in the y-direction. Find the magnitude of the magnetic field.

An electron in a hydrogen atom emits wavelengths during the transitions given below. Arrange these wavelengths in ascending order.
(A) from n = 3 to n = 2
(B) from n = 2 to n = 1
(C) from n = \( \infty \) to n = 1
(D) from n = \( \infty \) to n = 3
(E) from n = 4 to n = 1
Choose the correct answer from the options given below:

A monochromatic visible light consists of

Consider the following statement regarding sample parameter and statistic; statistical inference and t-test:
A. There are only three types of probability sampling: stratified, simple and systematic.
B. Since a = probability of the Type-I error, then \((1-\alpha)\) is probability of not rejecting \(H_o\) when \(H_a\) is true.
C. t-value is represented as; \(t=\frac{\text { Mean - Comparison value }}{\text { Standard error }}\)
D. A sample of less than 30 is considered to be sufficient to hold Central Limit Theorem (CLT).
E. A confidence interval consists of three components: confidence level, sample statistic and margin of error.

The two possible positions of an object kept in front of a lens of power +5.0 D, so that the image formed in both cases is four times magnified, are
(A) -30 cm
(B) -25 cm
(C) -15 cm
(D) -45 cm
Choose the correct answer from the options given below: