The interval in which the function \(f(x)=2 x^3+3 x^2-12 x+1\) is strictly increasing, is

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-2 \hat{k}\). Then a vector of magnitude 24 , which is perpendicular to the vectors \(\vec{a}+\vec{b}\) and \(\vec{a}-\vec{b}\), is:

Three pipes \(A, B\) and \(C\) can fill a tank in \(12\) hours, \(15\) hours and \(20\) hours respectively. If A is open all the time and \(B\) and \(C\) are open for one hour each alternately, in how many hours will the tank be full?

The linear programming problem: Minimise \(Z=3 x+2 y\)
Subject to constraints: \(x+y \geq 8, \quad 3 x+5 y \leq 15, \quad x \geq 0, y \geq 0\) has

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis :

The function f defined by \((x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is continuous at x = 3 if

The value of \(|\vec{a}-\vec{b}|\), if two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|=1,|\vec{b}|=4\), and \(\vec{a} \cdot \vec{b}=5\) is :

Match List-I with List-I

LIST – I (Common Name)	LIST – II (IUPAC Name)
(A) oxalic acid	(I) Ethanedioic acid
(B) Adipic acid	(II) Alpha - hydroxy propanoic acid
(C) Lactic acid	(III) Hexanedioic acid
(D) Phthalic acid	(IV) Benzene-1,2-dicarboxylic acid

Choose the correct answer from the options given below:

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

The amount of urea required to make a 500 mL solution of \(20 \%( w / w )\) concentration is

Which of the following has the highest molar conductivity?

Read the Passage carefully and answer the the questions
Insulin consists of two short polypeptide chains : chain A and chain B, that are linked together by disulphide bridges. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis of diseases. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (α-1-antitrypsin) used to treat emphysema. Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment.
Deficiency of adenosine deaminase (ADA) can be permanently cured by -

An ac source has a frequency of 60 Hz. The time taken for the voltage to change from peak value to zero is :