A Wheatstone bridge has four resistors: R1= R2 = R3 = 1 \( \Omega \) and R4 = 2 \( \Omega \). In order to balance the bridge, resistor R4 has to be shunted by resistance of

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

A coil \(C_1\) is connected to a galvanometer G. Second coil \(C_2\) is connected to a battery through a tapping key. The steady current in the coil \(C_2\) produces a steady magnetic field. As coil \(C_2\) is moved towards the coil \(C_1\), the galvanometer shows a deflection. To obtain a large deflection, one or more of the following steps can be taken:
(A) Use a rod made of soft iron inside the coil \(C_2\)
(B) Connect the coil \(C_2\) to a more powerful battery
(C) Move the arrangement of coil \(C_2\) rapidly towards the coil \(C_1\)
(D) hold the key pressed continuously
Choose the correct answer from the options given below:

The external diameter of a 5 m long hollow copper tube is 10 cm and the thickness of its wall is 5 mm. If the specific resistance of copper be \( 1.7 \times 10^{-8} \, \Omega\text{-m} \), then its resistance would be approximately

Read the following statements carefully:
(A) The average power in an inductor over one complete cycle is zero.
(B) Self-inductance plays the role of inertia.
(C) Mutual inductance of a pair of coils depends on their separation as well as their relative orientation.
(D) The capacitive reactance increases with increase in frequency of applied a. c.
Choose the correct answer from the options given below :

Light from a point source in air falls on spherical glass surface (n = 1.4 and radius of curvature 20 cm). The distance of light source from the glass surface is 150 cm, At what position is the image formed?

The magnifying power of a compound microscope is high, if

If \(A\) and \(B\) are square matrices of the same order, then \((A+B)(A-B)\) is equal to

If \(y=x \sin y\), then \(\frac{d y}{d x}\) is:

Answer the question on the basis of passage given below :
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under laboratory conditions, but microbes do it easily. Ammonia forms a large number of complexes with transition metals. Hybridisation easily explains the ease of sigma donation capability of NH₃ and PH₃. Phosphine is an inflammable gas, it is prepared from white phosphorus.
NH₃ is a stronger base than PH₃ because:

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Identify the incorrect statement for Cannizaro reaction.

The angle between the lines \(\vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{j}-2 \hat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is:

Which of the following matrices is not invertible?