If \(\theta\) is an acute angle and the vector \(\vec{a}=(\sin \theta) \hat{i}+(\cos \theta) \hat{j}\) is perpendicular to the vector \(\vec{b}=\hat{i}-\sqrt{3} \hat{j}\) then \(\theta\) is equal to:

If the matrix \(A=\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]\) is skew-symmetric then values of \(x\) and \(y\) respectively are :

Area (in sq. units) of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is

The function \(f(x)=x^3, x \in R\), has:

In a pair of adjacent coils, if current in one coil changes from 0 A to 10 A in 0.25 s , causing a magnetic flux change of 15 Wb in the adjacent coil, the mutual inductance of the coils is :

The number of all possible matrices of order 3 with each entry either 0 or 1 is :

The value of \(\left|\begin{array}{lll}2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x\end{array}\right|\), where \(x \neq 0 ;\) is:

In humans, female, oogenesis is initiated

Human insulin was prepared by:

Match List-I with List-II

List-I (Physical quantity)	List-II (Formula)
(A) Current sensitivity of galvanometer	(I) \( \frac{\mu_0 I}{2R} \)
(B) Magnetic field at the centre of a circular coil	(II) \( \frac{NAB}{kR} \)
(C) magnetic field due to a long straight wire carrying a current	(III) \( \frac{NAB}{k} \)
(D) Voltage sensitivity of galvanometer	(IV) \( \frac{\mu_0 I}{2\pi R} \)

Choose the correct answer from the options given below:

Match List-I with List-II:

List-I (Physical quantity)	List-II (Unit)
(A) Magnetic moment	(I) N A\(^{-2}\)
(B) Magnetic field strength	(II) N m rad\(^{-1}\)
(C) Torsion constant	(III) A m\(^{-1}\)
(D) Magnetic permeability	(IV) A m\(^2\)

choose the correct answer from the options given below:

Match List - I with List - II.

LIST-I ((Function)y)	LIST-II (\((\) Derivative \() \frac{d y}{d x}\))
(A) \(y=\cos \sqrt{x}\)	(I) \(\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}\)
(B) \(y=\sqrt{\sin x}\)	(II) \(-3 x^2 \cos \left(x^3\right) \sin \left(\sin \left(x^3\right)\right)\)
(C) \(y=\sec (\tan \sqrt{x})\)	(III) \(\frac{\cos x}{2 \sqrt{\sin x}}\)
(D) \(y=\cos \left(\sin \left(x^3\right)\right)\)	(IV) \(-\frac{1}{2 \sqrt{x}} \sin \sqrt{x}\)

Choose the correct answer from the options given below:

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below: