The value of differentiation of \(x^7+1\) with respect to \(x^6\) is

If \(\vec{a}=4 \hat{i}-2 \hat{j}+5 \hat{k}\) and \(\vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}\) represent, both in magnitude and direction, two adjacent sides of a parallelogram, then a unit vector parallel to the diagonal, which is coinitial with \(\vec{a}\) and \(\vec{b}\), is :

If \(\vec{a}=2 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\vec{c}=-\hat{i}+\hat{k}\) are three vectors, then the area (in sq, units) of the parallelogram whose diagonals are \((\vec{b}+\vec{c})\) and \((\vec{a}+\vec{c})\) is

If \(\left|\begin{array}{lll}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{array}\right|=0\), then the values of \(x\) are:

If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ 4 & 0 & b \\ -5 & 3 & 10\end{array}\right]\) is symmetric, then the value of \(5 a+2 b\) is :

If \(A\) is a non-singular square matrix of order 3 such that \(A^3=4 A^2\), then the value of \(|A|\) is:

\(\int \tan ^{-1} \sqrt{x} d x\) equals to : (Here \(C\) is an arbitrary constant)

If \(A\) is a square matrix such that \(A^2=A\), then \((I+A)^3-8 A\) is equal to:

The sum of the \(x\) coordinates of the corner points of the feasible region for the LPP :
Minimize \(z=3 x+2 y\) subject to constraints \(x+y \leq 14, x \geq 4, x \leq 8, y \geq 0\) is

Which one of the following is a low spin complex?

The point mutation arise due to change in :

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
The reagent which doesn't react with both acetone and benzaldehyde is :

The sickle cell anaemia is a