The area (in sq. units) of the region bounded by the curve \(x^2 = 250y, y = 0\) and \(x = 50\) is

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

The curve \(y = f ( x )\) is normal probability curve, then which of the following statements are correct?
(A) mean, median and mode of the distribution coincide.
(B) the area bounded by the curve \(y = f ( x )\) and \(x\)-axis is one unit.
(C) The curve is symmetrical about the line \(x =\mu\), where \(\mu\) is the mean.
(D) y -axis is an asymptote to the curve.
Choose the correct answer from the options given below :

The value of \(\sin \left(2 \sin ^{-1} \frac{4}{5}\right)\) is given by :

If \(A=\left[\begin{array}{cc}2-x & 1 \\ 3 & y+2\end{array}\right]\) and \(B=\left[\begin{array}{cc}y & 1 \\ 3 & 2 x+1\end{array}\right]\) are such that A = B, then values of z and y are respectively :

The system of linear equations \(k x+5 y=5,2 x+3 y=5\) will be consistent if

A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is

The area of the region bounded by the parabola \(y^2=4 a x\) and its latus rectum is:

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^x[B]^y\)
Here \(k\) is the rate constant
\(z+y\) gives the overall order of a reaction, whereas \(z\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The order of a reaction which does not exist is:

The angle of dip at a location in Southern India is about 18°. Which of the following is correct for dip angle in Britain ?
(A) Dip angle will be greater in Britain than in India.
(B) Dip angle will be smaller in Britain than in India.
(C) Nearer the place to the poles, lesser is the dip angle.
(D) Nearer the place to the poles, more is the dip angle.
(E) Dip angle is also called the angle of declination.

Out of all isomers of \(\text{C}_4\text{H}_{11}\text{N}\), how many are primary amines?

Arrange the steps of DNA Fingerprinting in a correct sequence:
(A) Digestion of DNA by restriction endonucleases
(B) Hybridisation using labelled VNTR probe and detection of hybridized DNA by autoradiography
(C) Isolation of DNA
(D) Separation of DNA fragments by electrophoresis and blotting
Choose the correct answer from the options given below: