If \(f(x) = \frac{x^6}{6} - 2x^2\), then \(f''(4)\) =?

If \(\left|\begin{array}{ccc}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a\end{array}\right|=86\), then product of all values of \(a\) is :

If \(A=\left[\begin{array}{cc}2 & -3 \\ 3 & 4\end{array}\right]\) then, the value of \(A^2-6 A\)

Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{c}=3 \hat{i}+\hat{j}\) be three vectors. If \((\vec{a}+\lambda \vec{b})\) is perpendicular to \(\vec{c}\), then the value of \(\lambda\) is

\(A=\left[\begin{array}{lll}0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1\end{array}\right]\)
\(A^{-1}=\left[\begin{array}{ccc}\frac{1}{2} & -4 & \frac{5}{2} \\ -\frac{1}{2} & 3 & -\frac{3}{2} \\ \frac{1}{2} & y & \frac{1}{2}\end{array}\right]\)
Find the value of \(8 x+5 y\)

If \(A\) is a \(3 \times 3\) matrix such that \(|\operatorname{adj} A|=9\) and \(\left|k A^{-1}\right|=9\), then the value of \(k\) are :

Consider two lines \(l_1\) and \(l_2\) with cartesian equations \(\frac{x}{2}=\frac{1-y}{-2}=\frac{z}{1}\) and \(\frac{2 x-5}{16}=\frac{y-2}{-1}=\frac{z-5}{4}\) respectively. Which of the following is/are true?
(A) Direction ratio of \(l_1\) are \(2,2,1\)
(B) Direction cosines of \(l_1\) are \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
(C) Direction ratio of \(l_2\) are \(16,-1,4\)
(D) Angle between \(l_1\) and \(l_2\) is \(\cos ^{-1}\left(\frac{38}{3 \sqrt{273}}\right)\)
Choose the correct answer from the options given below:

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
"Maltose" disaccharide is composed of

Identify the carbohydrate which is not a polysaccharide

The magnetic moment of \(Cu ^{2+}\) ion \(( Z =29)\) is :

Using monochromatic light for diffraction in a single slit of width 0.1 mm , with a central maximum of 5 mm width on a screen 50 cm away, the wavelength of light used is :

Two conducting circular loops of radii a and b are placed in the same plane with their centre coinciding. If \( a \gg b \), the mutual inductance M between then will be directly proportional to:

Which of the following is not an In situ conservation approach?