The degree of the differential equation
\(\left[1+\left(\frac{d y}{d x}\right)\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is :

If three points \(A \left(a_1, b_1\right), B \left(a_2, b_2\right)\) and \(C \left(a_3, b_3\right)\) are collinear and D is the determinant of their coordinates with a column of 1s, then:

The probability distribution of a random variable X is given below:
\(\begin{array}{lllll} X & 0 & 1 & 2 & 3 \\ P ( X ) & k & & \\ & & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}\end{array}\)
then the value of \(P(X \leq 2)+P(X>2)\) is :

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where k > 0 is 30 sq. units, then the value of k is

Consider the LPP, Min \(Z=3 x-2 y\) subject to the conditions
\(
\begin{array}{l}
4 x+3 y \geq 12 \\
4 x+y \geq 4 \\
x \geq 0, y \geq 0
\end{array}
\)
then which of the following is correct?

The area of the region bounded by \(y=2 x-x^2\) and \(x\)-axis is :

For the LPP :
Maximise \(z=4 x+y\)
subject to constraints
\(x+y \leq 50, \quad 3 x+y \leq 90, \quad x \geq 0, y \geq 0\) the maximum value of \(z\) is :

Match List-I with List-II

List-(I) Function	Lis-(II) Derivative
(A) \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2},|x|<1\)	(I) \(\frac{d y}{d x}=\frac{1}{2 y-1}\)
(B) \(y=\sqrt{x+y}, x+y>0, y \neq \frac{1}{2}\)	(II) \(\frac{d y}{d x}=10^x \log _e 10\)
(C) \(y=\log _{10} x, x>0\)	(III) \(\frac{d y}{d x}=0\)
(D) \(y=10^*\)	(IV) \(\frac{d y}{d x}=\frac{1}{x \log _e 10}\)

Choose the correct answer from the options given below:

Arrange the following alkyl halides in increasing order of reactivity towards SN2 reaction :
(A) 1-Bromobutane
(B) 1-Bromo-2,2-dimethylpropane
(C) 1-Bromo-2-methylbutane
(D) 1-Bromo-3-methylbutane
Choose the correct answer from the options given below :

Development of fruits without fertilization is known as -

In a region of constant potential,

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?

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6, 10, 15, 12, 9, 8 will be :-