A resistor and a capacitor are connected in series with an alternating current source. The potential difference across resistor and capacitor are 90 V and 120 V respectively and rms value of current is 3 A. What is the power factor of the circuit?

The internal resistance of primary cell is \( 3 \Omega \). It generates a current of \( 0.3 \text{ A} \) in an external resistance of \( 22 \Omega \). The rate at which chemical energy is consumed in providing the current is:

Which of the following statements are correct?
(A) Total internal reflection occurs when a ray of light travels from a rarer transparent medium to a denser medium.
(B) In total internal reflection, the incident ray of light remains in the same medium after reflection.
(C) In total internal reflection, the angle of incidence inside the denser transparent medium is equal to the angle of reflection in the same medium.
(D) In total internal reflection inside a denser medium there is no angle of refraction
Choose the correct answer from the options given below:

A circular loop is placed in the plane of the paper in a magnetic field B. A current is induced in the loop in an anticlockwise direction. This is because the magnetic field B is

Resistance R1 is with 10 \(\Omega\) resistance in series and is in the first gap of meter bridge with R2 in the second gap. The balance point is at 50 cm. When the 10 \(\Omega\) resistance is removed then the balance point shifts to 40 cm. What is the value of R1?

A cylindrical, straight long wire having radius 'a' is carrying current 'I' uniformly distributed inside the wire. As per Ampere's circuital law, the magnetic field inside the wire at any distance r, (r < a) is given by:

Let \( i_E, i_C \) and \( i_B \) represent the emitter current, collector current and base current respectively in a transistor. Choose the correct statement from the following:

Identify the statements which are correct with respect to fertilization.
(A) Sperm comes in contact with zona pellucida layer of the ovum
(B) Acrosome secretions help the sperm to pass through the cells of corona radiata
(C) Entry of sperm into the cytoplasm of ovum induces the completion of the meiotic division of the secondary oocyte
(D) Fertilization can occur if the ovum and sperms are transported simultaneously to the ampullary region
Choose the correct answer from the options given below:

Choose the correct answer from the options given below:
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\) is \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{y-3}{-2}\)
B. Equation of line passing through (1, 2, 3) and parallel to the line given by \(\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}\) is \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z+3}{6}\).
C. Equation of line passing through the origin and (5, -2,3) is \(\frac{x}{5}=\frac{y}{-2}=\frac{z}{3}\).
D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is 2(x - 1) + 3(y - 2) - (z - 3) = 0.
E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is 2x + 3y + 4z = 1

The statement "all tax payers above 60 years in India" is an example of
(A) Sample
(B) Finite population
(C) Infinite population
(D) Statistical Interference

A point charge q is placed at the center of a cube of side L. The total electric flux passing through any three faces of this cube is:

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.
In the first transition series of elements (Sc to Zn), which element show least enthalpy of atomization?

The equation of the plane which passes through the point (3, 2, -1) and is perpendicular to the line with direction ratios 2, 1, 2 is: