The function \(f(x)=\frac{x-2}{x+1}, x \neq-1\) is increasing when (Where \(R\) is a set of real numbers:

A specific characteristic of a sample is known as a:

The interval in which the function f given by \(f(x)=x^3+\frac{1}{x^3}, x \neq 0\) is increasing:

The corner points of a bounded feasible region determined by the following system of linear inequalities \(x+3 y \leq 60, x+y \geq 10, x \leq y, x \geq 0, y \geq 0\) are \((0,10),(5,5),(15,15)\) and (0,20). Let \(z=2 p x+q y, p, q>0\). If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

If \(x=4 t\) and \(y=\frac{4}{t}\), then \(\frac{d^2 y}{d x^2}\) is

In what ratio should a shopkeeper mix two types of rice, one costing ₹ \(20\) per kg and another costing ₹ \(40\) per kg to get a rice variety costing ₹ \(28\) per kg ?

The value of \(\left|\begin{array}{cc}\log _5 10 & 2 \\ 2 & \log _{10} 5\end{array}\right|\) is

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
Which Vitamin is known as Pyridoxine?

Which was the first discovered antibiotic ?

Match List - I with List - II.

List - I (Molecule)	List - II (Application)
(A) Statin	(I) Immunosuppressive agent
(B) Streptokinase	(II) Detergent formulations
(C) Cyclosporin A	(III) Blood-cholesterol lowering agent
(D) Lipase	(IV) Clot buster

Choose the correct answer from the options given below:

If the system of equations \(k x+y+z=0, x+k y-z=0, x-y+z=0\) has a non-zero solution, then the possible values of \(k\) are

Identify the incorrect statements from the following:
A. Phenylketonuria is an autosomal dominant trait.
B. Haemophilia is a sex linked recessive disease.
C. Thalassemia is an autosomal linked recessive blood disease.
D. Colour blindness is an autosomal linked recessive disorder.
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]\), then \(A^{-1}\) is equal to :