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

The area (in sq. units) bounded by the parabola \(y^2=4 a x\), its latus rectum and the \(x\)-axis in the first quadrant is:

For \(y \neq 0\), the particular solution of the differential equation \(2 y e^{x / y} d x+\left(y-2 x e^{x / y}\right) d y=0\) at the point \((1,1)\) is

Let \(X\) denotes the number of hours you study during a randomly selected school day. The random variable \(X\) has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List - I with List - II.

LIST - I	LIST - II
(A) Value of K	(I) \(\frac{1}{4}\)
(B) Probability you study at least two hours	(II) \(\frac{1}{8}\)
(C) Probability you study exactly two hours	(III) \(\frac{3}{8}\)
(D) Probability you study at most one hour	(IV) \(\frac{5}{8}\)

Choose the correct answer from the options given below:

Which of the following is not correct about the Compound Annual Growth Rate (CAGR)?

The value of integral \(\int_0^1 \sqrt{1-x^2} d x\) is :

The area bounded by the curve \(y=x|x|, x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:

If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
Which is most reactive hydrogen halide for cleavage of ethers?

Which of the following physical quantities have the same value for electron and photons of same wavelength?

Genes which code for a pair of contrasting traits are knows as:

\(\text{C}_3\text{H}_6\text{O}\) does not form a silver mirror with Tollen's reagent but forms an oxime with hydroxylamine. It can give positive:

Which one of the following set of constraints does the given shaded region represent?