A simple random sample of 100 items from a population with \(\sigma=8\) has a standard error of mean :

A company has been producing steel tubes of mean inner diameter 2 cm.
A sample of 10 tubes gives a mean inner diameter of 2.01 cm and a variance of \(0.0004 cm^2\).
The value of the test statistic is :

Area of the region enclosed by the curves \(y=\sqrt{x}\) and \(y=x^2\) is :

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{x^2+2 x+3}} d x\) is :

The value of the integral \(\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x\) is equal to:

The area bounded by the curve \(y=x^2\) between \(x=0\) and \(x=\pi\), in the first quadrant is :

A lot of \(50\) watches is known to have \(10\) defective watches. If \(8\) watches are selected one by one with replacement at random, then the probability that there will be at least one defective watch is:

A total of \(5.0 \times 10^{16}\) electrons per second go through a conductor of area \(2 mm^2\). The current density will be:

Match List-I with List-II:

List-I (AC Circuit)	List-II (Phase Angle)
(A) Phase Difference between current and voltage in a pure inductive ac circuit	(I) zero
(B) Phase Difference between current and voltage in a pure resistive ac circuit	(II) \(\pi/2\), current lags voltage
(C) Phase Difference between current and voltage in a pure capacitive ac circuit	(III) \(\tan^{-1}(\frac{X_L - X_C}{R})\)
(D) Phase Difference between current and voltage in a series LCR circuit	(IV) \(\pi/2\), current leads voltage

Choose the correct answer from the options given below

A mark placed on the surface of a sphere is viewed through glass from a position directly opposite. If the diameter of the sphere is 10 cm and refractive index of glass is 1.5, the image would be at

Enthalpy of atomisation of transition elements can be arranged in increasing order as:
A. \(V\)
B. \(Cr\)
C. \(Mn\)
D. \(Fe\)
E. \(Co\)
Choose the correct answer from the options given below:

Read the paragraph and answer the question.
Broadly, genetic disorders may be grouped into two categories - Mendelian disorders and Chromosomal disorders. Mendelian disorders are mainly determined by alteration or mutation in the single gene. These disorders are transmitted to the offspring on the same lines as we have studied in the principle of inheritance. The trait may also be linked to the sex chromosome as in case of haemophilia. It is evident that this X-linked recessive trait shows transmission from carrier female of male progeny.
What is the probability of having a haemophilic child to a carrier mother and a normal father ?