The order of the differential equation of the family of curves \(y^2=4 a(x+a)\) where a is an arbitrary constant is :

The local minimum value of the function \(f(x)=|x|+2\), where \(x\) is a real number is :

\(\int e^{-x}\left(\cot x+\mid \operatorname{cosec}^2 x\right) d x\) =

The function \(f(x)=x^2-x+1\) is

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is

Two parallel plate capacitors of capacitances \(2 \mu F\) and \(3 \mu F\) are joined in series and connected to a battery of \(V\) volts. The values of potential across the two capacitors V1 and V2 and energy stored in them U1 and U2 are related as :

Let \(A=\left[\begin{array}{ccc}2 & -3 & 4 \\ 0 & 1 & 5 \\ -4 & 2 & 3\end{array}\right]\), and \(a_{i j}\) be any element of \(A, i, j \in\{1,2,3\}\), then which of the following are TRUE?
(A) Minor of \(a_{23}=16\)
(B) Minor of \(a_{23}=-8\)
(C) Cofactor of \(a_{23}=-16\)
(D) Cofactor of \(a_{23}=8\)
(E) Cofactor of \(a_{13}=4\)
Choose the correct answer from the options given below :

Which of the following is incorrect?

From the statements given below, choose the correct statement regarding the galvanic cell.

Arrange the given stages of menstrual cycle in correct sequence.
(A) Luteal phase
(B) Follicular phase
(C) Menstruation
(D) Next cycle begins
Choose the correct answer from the options given below:

Read the passage carefully. Attempt the questions.
In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of these regulatory mechanisms. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location. The malignant tumors, on the other hand are a mass of proliferating cells. These cells actively divide and starve the normal cells by competing for vital nutrients. Cells sloughed from such tumors reach distant sites through blood, and wherever they get lodged in the body, they start a new tumor there. This property is called metastasis. Transformation of normal cells into cancerous cells may be induced by physical, chemical or biological agents called carcinogens.
Benign tumors are normally remain confined to:

A bubble in glass slab (\( \mu = 1.5 \)) when viewed from one side appears at 5 cm and 2 cm from otherside, then the thickness of the glass slab is: