The area of the region enclosed by \(y=x+2\) and \(y=x^2+x-2\) 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 :

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

A relation \(R\) in the set \(A=\{1,2,3,4\}\) is given by \(R=\{(1,1),(2,2),(1,2),(2,3),(3,4),(4,4),(1,3),(2,4),(1,4)\}\) is

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

A problem in mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}\) and \(\frac{1}{4}\) respectively, the probability that the problem is solved is ______________.

If \(A\) is a square matrix and \(I\) is an identity matrix of same order such that \(A^2=A\), then \((2 I+A)^2-5 A\) is :

Which of the following statements are correct?
A. Dispersion is the splitting of light into it's constituent colours.
B. The unit for power of a lens is m¯¹.
C. Optical fibres consist of glass fibres coated with a thin layer of material of higher refractive index.
D. Cassegrain telescope has the advantages of a large focal length in a short telescope.
E. Glass is a dispersive medium.
Choose the correct answer from the options given below:

Which of the following statements are correct:
A. In semiconductor diodes carriers are generated by photo-excitation.
B. When the photo diode is illuminated with light with energy (E) > Energy gap (Eg) of the semiconductor, then electron-holepairs are generated.
C. Photovoltaic devices convert electricity into optical radiation.
D. Photodiode can be used as a photodetector to detect optical signal.
E. Zener diode specification should be taken as per the required output voltage.
Choose the correct answer from the following options given below:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
How is the osmotic pressure of a concentrated solution related to the osmotic pressure of a dilute solution of the same substance at a given temperature?

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

The area (in square units) bounded by the curve \(y=\cos x\) between \(x=0\) and \(x=2 \pi\) in first quadrant is equal to :

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4: 5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.