For which value of \(k\), the given system of linear equations is inconsistent?
\(3 x+6 y+3 z=4\)
\(x+k y+2 z=6\)
\(z=7\)

The maximum profit that a company can make if the profit function is
\(P(x)=41+24 x-18 x^2\) is :

The two positive numbers whose sum is 16 and the sum of whose squares is minimum then the positive numbers are :

If matrix\(A_p=\left[\begin{array}{ll}p & (p+1) \\ p & (p-1)\end{array}\right], p \in \mathbb{N}\) (where \(\mathbb{N}\) is the set of natural numbers), then the value of \(\left|A_1\right|+\left|A_2\right|+\left|A_3\right|+\cdots+\left|A_{2025}\right|\) is:

Match List-I with List-II

List-I (Conditions)	List-II (Type of matrix)
(A) Square matrix \(A\)	(I) \(A=\left[a_{i j}\right]_{m \times m}\), where \(\left\{\begin{array}{ll}a_{i j}=0 & , i \neq j \\ a_{i j}=k & , i=j\end{array}\right.\) where \(k \neq 0\) is constant
(B) Scalar Matrix \(A\)	(II) \(A=\left[a_{i j}\right]_{m \times m}\)
(C) Diagonal matrix \(A\)	(III) \(A=\left[a_{i j}\right]_{m \times m}\), where \(\left\{\begin{array}{ll}a_{i j}=0 & , i \neq j \\ a_{i j}=1 & , i=j\end{array}\right.\)
(D) Identity matrix \(A\)	(IV) \(A=\left[a_{i j}\right]_{m \times m}\), where \(a_{i j}=0, i \neq j\)

Choose the correct answer from the options given below:

Let \(A\) and \(B\) be two invertible square matrices of same order, then which of the following is not correct?

The area bounded by the curve \(y=4+3 x-x^2\) and the \(x\)-axis is equal to

Select the correct statement/s from the following:
A. Spermatogonia always undergo meiotic cell division.
B. Primary spermatocytes divide by mitotic cell division.
C. Secondary spermatocytes have 23 chromosomes and undergo second meiotic division
D. Spermatozoa are transformed into spermatids.
Choose the correct answer from the options given below:

The potential energy of an electron in the first excited state of hydrogen atom is -6.8 eV. The kinetic energy of the electron in its ground state will be :

Alcohol is a depressant, which means that even small amounts of alcohol slow down the actions of parts of the brain, so alcohol lengthens the time you take to respond to a stimulus.
Different people react differently to alcohol. In some people, it increase their feelings of aggression, and releases their inhibitions so that they are more likely to be violent or commit other crimes.
An alcoholic needs to drink quite large quantities of alcohol regularly. This causes many parts of the body to be damaged, because alcohol is poisonous to cells. Probably, there are many factors which decide whether or not a person becomes alcoholic. Over a long period of time, it can cause loss of memory and confusion. One way in which the damage is done is that alcohol in the body fluids draws water out of cells by osmosis.
Alcohol lengthens the time one takes to respond to a stimulus. This occurs due to

A 300 turns rectangular coil of length 20 cm and breadth 12 cm is carrying a current of 12 A, when placed in a magnetic field of 6 T. The plane of the coil is making an angle of 60° with the magnetic field. What is the torque acting on the coil?

Which one of the following is also called 'Terror of Bengal'?

A body of mass 20 g and charge \( +50 \text{ }\mu\text{C} \) is suspended from the ceiling by a string. A horizontal electric field of 10 kV/m is applied.
The angle between the string and the vertical direction is :