At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000 ?

The solution set of the linear inequation \(|4 x-3| \leq \frac{3}{4}\) is :

The points on the curve \(\frac{x^2}{16}+\frac{y^2}{25}=1\) at which tangents are parallel to \(x\)-axis are:

Which of the following inequalities holds true?
(A) \(\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}\).
(B) If \(a>b\) and \(c<0\), then \(\frac{a}{c}<\frac{b}{c}\).
(C) \(\frac{1}{x^2}>\frac{1}{x}>1\), if \(0<x<1\).
(D) If \(a\) and \(b\) are positive integers and \(\frac{a-b}{6.25}=\frac{4}{2.5}\), then \(b>a\).
Choose the correct answer from the options given below:

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

\(\int_{\pi / 6}^{\pi / 3} \frac{1}{1+\sqrt{\cot x}} d x\) is :

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

The least distance of distinct vision of a person is 50 cm. He wants to read a book placed at 25 cm. The focal length of the spectacles would be :

Which one of the given assisted reproductive technologies (ART) involves transfer of fertilized egg into the fallopian tube?

Which of the following is not a natural method of birth control?

Choose the correct match. '+' for beneficial interaction '-' for detrimental and 'O' for neutral effect.

LIst - I		LIst - II
Species A	Species B	Name of Interaction
(A) +	+	(I) Competition
(B) +	-	(II) Mutualism
(C) -	-	(III) Amensalism
(D) -	0	(IV) Predation

Choose the correct answer from the options given below:

Express 16 mg mass into equivalent energy in Ev

Use of biofertilizers as a nutrient source is a practised in __________.