If \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]\) then product \(A B\) is :

The value of the determinant \(\left|\begin{array}{ccc}85 & 15 & 30 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{array}\right|\) is:

Match \(List - I\) with \(List - II\)

\(List - I\)	\(List - II\)
(A) \(\frac{d}{d x}\left(\sin x^2\right)\)	(I) \(\frac{1}{5}\)
(B) \(\frac{d}{d x}\left(e^{\sin x}\right)\)	(II) 0
(C) \(f(x)=\tan ^{-1} x\) then \(f^{\prime}(2)\)	(III) \(2 x \cos x^2\)
(D) If \(y=3 \cos x-2 \sin x\), then \(\frac{d^2 y}{d x^2}+y\)	(IV) \(e^{\sin x} \cos x\)

If \(\theta\) is the angle between the vectors \(2\hat{i} - 2\hat{j} + 4\hat{k}\) and \(3\hat{i} + \hat{j} + 2\hat{k}\), then value of \(\sin \theta\) is:

If the area of the triangle with vertices \(A(1,3), B(2,0), C(k, 2 k)\) is \(\frac{k^2}{2}\) sq. units, then the value(s) of \(k\) is/are:

Area of the region bounded by the curve \(y=\cos (x)\) and x -axis between \(x=0\) and \(x=\pi\) is :

The value of the determinant \(\left|\begin{array}{ccc}a \cos \theta & b \sin \theta & 0 \\ -b \sin \theta & a \cos \theta & 0 \\ 0 & 0 & c\end{array}\right|\) is :

Observe the given figure and answer the following questions:

Antibody is represented as:

When an insect feeds on the Bt plant, the insect dies due to the conversion of inactive protein to active protein in:

The electric field in a copper wire of cross-sectional area \( 4 \, mm^2 \) carrying a current of 1 A and having electrical conductivity of \( 6.25 \times 10^7 \, Sm^{-1} \) is

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), \(4 d\) series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has \(A c\) and elements from Rf to Cn. The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
In series Sc to Zn, the lowest enthalpy of atomization is shown by

Match List I with List II

LIST I	LIST II
A. Homology	I. Darwin's finches
B. Analogy	II. Single step large mutation
C. Adaptive radiation	III. Convergent Evolution
D. Saltation	IV. Divergent Evolution

Choose the correct answer from the options given below:

Which of the following statements is/are true?
(A) \(B^T A B\) is a skew-symmetric matrix if \(A\) is symmetric matrix
(B) \(B^T A B\) is a symmetric matrix if \(A\) is symmetric matrix
(C) \(B^T A B\) is a symmetric matrix if \(A\) is skew-symmetric matrix
(D) \(B^T A B\) is a skew-symmetric matrix if \(B\) is skew-symmetric matrix
(E) \(B^T A B\) is a symmetric matrix if \(B\) is symmetric matrix
Choose the correct answer from the options given below :