At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

Let \(f(x)=x^2+\frac{250}{x}\) be any function defined on \(R -\{0\}\), where \(R\) is the set of real numbers. Then which of the following are FALSE?

Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to :

A random variable has the following probability distribution:\(\begin{array}{llllll}X= x_{-} i & 2 & 3 & 4 & 5 \\P\left(X=x \_i\right) & 4 k & k & 5 k & 2 k\end{array}\)The value of \(P(X<3)\) is

If \(f(x)=\left|\begin{array}{ccc}0 & x-1 & x-2 \\ x+1 & 0 & x-3 \\ x+2 & x+3 & 0\end{array}\right|\), then the value of f(0) is equal to:

The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If \(x\) and \(y\) represent the length and breadth of rectangular region, then the area A of the window in terms of \(x\) is :

If the points \(A, B, C\) with position vectors \(20 \hat{i}+\lambda \hat{j}, 5 \hat{i}-\hat{j}\) and \(10 \hat{i}-13 \hat{j}\) respectively are collinear, then the value of \(\lambda\) is:

If \(y=x^4-10\) and if x changes from 2 to 1.99, then the changed value of y is approximately :

The correct increasing order of reactivity of alkyl halides with \(CH _3 NH _2\) is
(A) \(C _2 H _5- Br\)
(B) \(C _2 H _5- I\)
(C) \(C _2 H _5- F\)
(D) \(C _2 H _5- Cl\)
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Propionibacterium sharmanii is used for the production of-

If \(C(x)=a x^ 2-bx-c\) represents the total cost function then the slope of the tangent to the marginal cost curve at the point \((x, y)\) is:

If the molar conductivities at infinite dilution for \(\mathrm{CH}_3 \mathrm{COOK}, \mathrm{K}_2 \mathrm{SO}_4\) and \(\mathrm{H}_2 \mathrm{SO}_4\) are respectively, \(\mathrm{z}, \mathrm{y}\) and \(\times\left(\mathrm{S} \mathrm{cm}^2 \mathrm{~mol}^{-1}\right)\), the molar conductivity of \(\mathrm{CH}_3 \mathrm{COOH}\) at infinite dilution will be:

Which of the following is NOT an Intra Uterine Device ?