Which of the following statements is INCORRECT?

A point source S is placed at a distance of 12 cm from a converging lens of focal length 10 cm on its principal axis. Where should a diverging mirror of focal length 14 cm be placed from the lens so that a real image is formed on the source itself?

In a transformer, the input current and voltage are 3 A and 50 V respectively. The ratio of the number of turns in the primary coil to secondary coil is 5 : 3. The output current and voltage, respectively, are

A wire of length 10 m and diameter 0.4 mm has a resistance of \( 2 \, \Omega \). The resistivity of the wire is

The radius of curvature of each surface of a double convex lens is 15 cm and the refractive index of the medium of the lens is 1.5. What is the focal length of the lens?

Match List-I with List-II (here symbols have their usual meanings)

List-I (Physical Quantity / Law)	List-II (Formula)
(A) Snell's law	(I) \( t/\mu \)
(B) Apparent Shift	(II) \( c/v \)
(C) Refractive Index	(III) \(\frac{\mu_2}{\mu_1}\)
(D) Apparent depth	(IV) \( t(1 - \frac{1}{\mu}) \)

Choose the correct answer from the options given below:

Three identical resistors are connected first in series to an electrical voltage V. Let I be the total current flowing in the circuit. These resistors are disconnected and again connected in parallel with the same source. Which of the following statements are true?
(A) The potential difference across each resistor is V/3 in series connection
(B) The potential difference across all three resistors in parallel connection is 3V
(C) The current flowing in each resistor in series connection is the same as I
(D) The current flowing through each resistor in parallel combination is equal to 31
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Productivity in the Ecosystem The flow of energy through a terrestrial ecosystem starts with the harnessing of sunlight by autotrophs. The radiant energy is converted by photosynthesis to organic compounds is known as productivity. The productivity is expressed in units of energy per unit of area per unit time. The amount of organic matter present at any given time is biomass. The productivity of any ecosystem is affected by many parameters like weather conditions, nutrient availability etc. The productivity of any ecosystem does vary seasonally and yearly.
The Net Primary Productivity of an ecosystem are represented by:

The order of a null matrix is:

Match List-I with List-II
The function \(f(x)=2 x^3-15 x^2+36 x+5\) for \(x \in[2,5]\) has

List-I	List-II
(A) absolute maximum value	(I) 5
(B) absolute minimum value	(II) 60
(C) point of absolute maxima	(III) 3
(D) point of absolute minima	(IV) 32

Choose the correct answer from the options given below:

If the objective function Z = px + qy is maximum at (2,-2) and the maximum value is 8, such that p = 3q, then the values of p and q respectively are:

If the matrix \(\left[\begin{array}{ccc}0 & 7 & -12 \\ -7 & 0 & -5 \\ 2 a & 5 & 3 b\end{array}\right]\) is skew-symmetric, then the value of \((4 a+3 b)\) is :

Geometry of \(\left[ Ni ( CN )_4\right]^{2-}\) and \(\left[ NiCl _4\right]^{2-}\) are: