Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively.
Both the pipes are opened together for some time and then pipe P is closed.
If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

If \(x=a t^2\) and \(y=2 a t\), then \(\frac{d^2 y}{d x^2}\) is

The values of \(a\) for which the function \(f(x)=a^x\) is increasing on \(R\) are given by :

Which of the following statements are true?
(A) If \(\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}\), then \(x, y, z\) are called direction ratios of \(\vec{r}\).
(B) For any two vectors \(\vec{a}\) and \(\vec{b}, \vec{a}+\vec{b}=\vec{b}+\vec{a}\).
(C) \(\vec{a} \perp \vec{b}\) if and only if \(\vec{a} \times \vec{b}=\overrightarrow{0}\).
(D) Projection of \(\vec{b}\) on \(\vec{a}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2}\).
Choose the correct answer from the options given below :

If \(A=\left[a_{i j}\right]\) is a square matrix of order 2 such that, \(a_{i j}=\left\{\begin{array}{ll}2, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.\), then \(\operatorname{det}\left(A^2\right)\) is:

If \(A^{-1}\) exists for the matrix \(A=\left[\begin{array}{ccc}1 & \lambda & -1 \\ -1 & 1 & 0 \\ \lambda & 1 & 1\end{array}\right]\) then

If \(A\) and \(B\) are square matrices of order 3 such that \(|A|=-1\) and \(|B|=5\), then the value of \(|3 A B|\) is

Match List - I and List - II

LIST – I (Name of vitamins)	LIST – II (Deficiency Disesse)
(A) Vitamin - A	(I) Increase in fragility of RBC
(B) Vitamin - E	(II) Increased blood clotting time
(C) Vitamin - C	(III) Xerophthalmia
(D) Vitamin - K	(IV) Scurvy

Choose the correct answer from the options given below:

A piece of copper and a piece of germanium are cooled from room temperature 20 C down to 80 K. The resistance of

The wave theory of light can not explain the phenomenon of

Arrange the given steps involved in gel electrophoresis used for separation of DNA fragments ?
(A) Exposure to UV light
(B) Staining with ethidium bromide
(C) Moving of DNA fragments towards anode
(D) Elution
Choose the correct options given below

Which of the following statements are true for the minimum deviation position of a prism?
(A). The angle of the prism is twice the angle of refraction.
(B). The refracted ray is parallel to the base of prism.
(C). The angle of incidence is equal to the angle of emergence.
(D). The angle of deviation is half the angle of a prism.
Choose the correct answer from the options given below:

Figure shows a coil C connected to a galvanometer G. When the North-pole of a bar magnet is pushed towards the coil, the pointer in the galvanometer deflects. Regarding this set up, the following statements are given:
(A) It indicates the presence of electric current in the coil.
(B) The deflection is found to be smaller when the magnet is pushed towards the coil faster.
(C) There is repulsion in the moving magnet and the magnetic pole induced in the coil facing towards the N pole of the magnet.
(D) If the bar magnet does not move, there is no induced current in the coil.
Choose the correct answer from the options given below: