If \(\vec{a}, \vec{b}\) and \(\sqrt{3} \vec{a}+\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) is:

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are :

In a kilometer race, \(A\) beats \(B\) by 50 meters or by 5 seconds, then the time taken by \(A\) to complete the race is

The graph given below represents which of the following function?

A manufacturing unit makes two models, 'classic' and 'supreme' of the scooter.
Each piece of the classic model requires 9 labour hours for assembling and 1 labour hour for finishing.
Each piece of supreme model requires 12 labour hours for assembling and 3 labour hour for finishing.
Maximum labour hours available for assembling and finishing are 180 and 30 respectively.
Profit is Rs. 10000 on each classic piece and Rs. 15000 on each supreme piece.
Which option describes the LPP to maximize profit Z (where x and y are classic and supreme pieces)?

Let \(A\) be a matrix such that \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right]\) Then which of the following are TRUE?
(A) \(A\) is a non-singular matrix
(B) \(A^T=A\)
(C) \(A\) is not an invertible matrix
(D) \(A\) is not a skew-symmetric matrix
Choose the correct answer from the options given below :

The lines \(\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\) and \(\frac{x-3}{-3}=\frac{y-4}{-6}=\frac{z-5}{-9}\) are :

The vector equation of the line passing through the point \((-1,5,4)\) and perpendicular to the plane \(z=0\) is :

The magnetic flux linked to a coil changes from 10 \(\times 10^{-3}\) Wb to 6 \(\times 10^{-3}\) Wb in 0.01 s. The induced emf will be :

Which among the following is not a primary consumer?

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Which one of the following is not the cellular barrier of innate immunity?

Which among the following shows positive deviation from Raoult's law?

Match List-I with List-II

List-I (Formula)	List-II (Physical Quantity)
(A) \( \epsilon = -L \frac{dI}{dt} \)	(I) Self inductance
(B) \( \epsilon = -M \frac{dI}{dt} \)	(II) Mutual inductance
(C) \( L = \frac{\Phi}{I} \)	(III) Mutual Induced emf
(D) \( M = \frac{\Phi}{I} \)	(IV) Self Induced emf

Choose the correct answer from the options given below: