Let \(A\) be a non-singular square matrix of order \(n\) with \(|\operatorname{adj} A|=64\) and \(|A|=4\), then ' \(n\) ' is :

The point estimate of the population standard deviation for the random sample \(5,8,10,7,10,14\) is :

Consider the matrices \(A=\left[\begin{array}{ccc}9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 / 5 & 0 & 0 \\ 0 & 1 / 4 & 0 \\ 0 & 0 & 1 / 3\end{array}\right]\). The value of \(\left|(A B)^{-1}\right|\) is

The value of the definite integral \(I=\int_0^2 x \sqrt{2-x} d x\) is :

If the lines \(\frac{x+3}{k-5}=\frac{y-1}{1}=\frac{5-z}{-2 k-1}\) and \(\frac{x+2}{-1}=\frac{2-y}{-k}=\frac{z}{5}\) are perpendicular, then the value of \(k\) is

Consider the LPP : Maximize \(z=5 x+3 y\) subject to \(3 x+5 y \leq 15,5 x+2 y \leq 10, x, y \geq 0\).
The optimal feasible solution occurs at

The feasible region represented by the constraints \(x+2 y \geq 100,2 x-y \leq 0.2 x+y \leq 200, x \geq 0, y \geq 0\) of an LPP is

Given below are some stages of human evolution. Arrange them in correct sequence (Past to Recent)
(A) Homo habilis
(B) Homo sapiens
(C) Homo neanderthalensis
(D) Homo erectus
Choose the correct answer from the options given below:

The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:

Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Correctly predict the final product and the type of reaction for the following reaction:
\(C _6 H _5- N _2^{+} Cl ^{-}+ C _6 H _5- OH \xrightarrow{ HO ^{-}}\)?

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?

Identify the correct statements with respect to human evolution
A. Modern Homo sapiens arose during ice age between 50,000 to 75,000 years.
B. Ramapithecus was more man-like.
C. The brain capacity of Homo erectus was about 650-800 cc.
D. Dryopithecus was more ape-like.
Choose the correct answer from the options given below:

In Antirrhinum (Snapdragon), a red flower was crossed with a white flower and in F\(_1\) generation all pink flowers were obtained. When pink flowers were self crossed, F\(_2\) generation showed white, red and pink flowers.
Choose the correct statements for this case:
(A) This experiment does not follow the Principle of Dominance.
(B) Pink colour in F\(_1\) is due to incomplete dominance.
(C) Ratio of F\(_2\) is 1 (red): 2 (pink): 1 (white).
(D) Law of segregation does not apply in this case.
Choose the correct answer from the options given below: