In what ratio should a grocery shopkeeper mix two varieties of pulses worth Rs. 85 per kg and Rs. 100 per kg respectively, so as to get a mixture worth Rs. 92 per kg?

\(\cos \left(\frac{\pi}{6}-\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is equal to:

Maximum value of \(z=5 x+4 y\) subject to the constraints \(x-y \leq 0, x+y \leq 4, x \geq 0, y \geq 0\) occurs at the point \((a, b)\). Then \(4 a+5 b=\) \(\_\_\_\_\) ,

If A is a square matrix of order 3 and \(|A| = -2\) then, \(|-2A^{-1}|\) is:

If A is an invertible matrix of order 3, then

List-I	List-II
(A) \(|\operatorname{adj} A|\)	(I) \(8|A|\)
(B) \(|A(\operatorname{adj} A)|\)	(II) \(|A|^2\)
(C) \(|2 A|\)	(III) \(\frac{1}{|A|}\)
(D) \(\left|A^{-1}\right|\)	(IV) \(|A|^3\)

Choose the Correct answer from the options given below :

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is

The matrix A \(=\left[\begin{array}{ccc}2 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 5\end{array}\right]\) is :

Which of the following is a statistic?

Match List-l with List-ll

List-l (Microorganisms)	List-II (Commercial Uses)
(A) Lactobacillus	(I) Use for the production of butyric acid
(B) Saccharomyces cerevisiae	(II) Use for production of swiss cheese
(C) Propionibacterium sharmanii	(III) Use for making bread
(D) Clostridium butylicum	(IV) Improves nutritional quality of milk by increasing vitamin B12

Choose the correct answer from the options given below:

Read the given paragraph and answer the given question :
Parasitism has evolved in many taxonomic groups from plants to higher vertebrates. Many parasites have evolved to be host specific in such a way that both host and the parasite tend to co-evolve. In accordance with their life styles, parasite evolve special adaptations and complex life cycle.
Which are the intermediate hosts of human liver fluke?

Observe the figure and answer the following:

What is the ploidy of the zygote, antipodal cells and primary endosperm nucleus?

If half life for a first order reaction of A is 2 minutes, how long will it take \([\text{A}]\) to reach 10% of its initial concentration?

Read the passage carefully and answer the Questions
Carboxylic acids are the earliest organic compounds isolated from nature. These are also known as organic acids but are weaker acids as compared to mineral acids. However, they are more acidic than alcohols and phenols because of greater resonance stabilization of the parent acid and its conjugate base. The acidic strength is determined by the \(K _a\), which is called the acidity constant. The greater the value of \(K _a\), the greater the tendency of the acid to ionize and hence the stronger the acid. The acidic strength of the saturated aliphatic carboxylic acid depends upon the inductive effect and its position with respect to - COOH groups. Electron -donating substituents tend to decrease whereas electron-withdrawing substituents tend to increase the acidic strength. The acidic strength of the aromatic carboxylic acid, on the other hand depends upon both the inductive effect and the resonance effect of the substituents.
Which of the following groups when attached directly does not increase the acidity of the carboxylic acid?