Area of the triangle ABC with vertices \(\left(a, a^2\right),\left(b, b^2\right)\) and \(\left(c, c^2\right)\) is equal to :

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

If \(f(x)=|x|+|x-5|\), then which of the following statements are TRUE?
(A) \(f\) is a continuous function everywhere
(B) \(f\) is a continuous function except x = 5 and x = 0
(C) \(f\) is a continuous function except x = 0 but not differentiable at x = 5
(D) \(f\) is a continuous function everywhere but not differentiable at x = 0 and x = 5
Choose the correct answer from the options given below:

The shaded region shown in the figure is given by inequalities:

Derivative of \(\cos \left(\sin \left(x^2\right)\right)\) with respect to x is:

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which \(C\) can alone fill the tank. If pipe \(B\) can fill the tank 15 minutes faster than pipe \(A\) and 5 minutes slower than pipe \(C\), then the time required by pipe \(A\) to fill the tank alone is:

The feasible region associated with the inequality \(2 x+3 y>4\) is

If the dielectric constant and dielectric strength be denoted by k and x respectively, then good capacitor must have :

Which type of population interaction is exhibited by 'mycorrhizae'?

Answer the question on basis of passage given below :
Look at the following chemical reactions and answer the following question:
(A) \(C_7H_8 \xrightarrow{\text{Conc. HNO}_3, 0^\circ C} (B) \xrightarrow{Sn/HCl} (C) \xrightarrow{NaNO_2/H_3O^+} (D) \xrightarrow{H_2O, Heat} (E)\)
(E) \(CH_3I \xrightarrow{KMnO_4/H^+} (F) \xrightarrow{H_3O^+} (G) \xrightarrow{NaOH} (H)\)
Which of the following compounds will form dimer ?

The integral \(\int \frac{2 x+x^3}{1+x^2} d x\) is equal to :

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of
nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
Which of the following is non-reducing sugar?

The ratio of radii of the nuclei with the mass numbers given as 2, 16, 54 and 128, respectively, will be