What sum of money is needed to invest now so as to get Rs. 5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

The slope of the normal to the curve \(y=2 x^2\) at \(x=1\) is:

The particular solution of the differential equation \(x d y=\left(2 x^2+1\right) d x, x \neq 0\), given that \(y=1\) when \(x=1\) is:

If \(\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|\), then \(x\) is equal to:

A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

The function, \(f(x)=x+\frac{a^2}{x}, a>0, x \neq 0\) has a local maxima at

Area of the region bounded by the curve \(y=\cos x\) between \(x=0, x=\pi\) and \(x\)-axis is :

If \(\hat{i}, \hat{j}, \hat{k}\) are unit vectors along X, Y, Z axes then,
(A) \(\hat{i} \times \hat{i}=1\)
(B) \(\hat{j} \cdot \hat{j}=0\)
(C) \(\hat{i} \times \hat{j}=\hat{k}\)
(D) \(\hat{k} \times \hat{i}=\hat{j}\)
(E) \(\hat{i} \cdot \hat{j}=0\)
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Answer the question on basis of passage given below :
Lyophobic sols like those of metals (Au, Ag, etc) are unstable and are easily precipitated by addition of electrolytes. However, it is observed that the addition of certain lyophilic colloids like gums, soaps, gelatine, etc. to lyophobic colloids (like a metal sol) render lyophobic colloids difficult to coagulate by the addition of electrolytes. The process is known as 'protection' and the lyophilic colloid. colloids are termed as Protective colloids. It is believed that the protective action of the lyophilic colloids is due to the covering up of the particles of the lyophobic colloid by those of the lyophilic Evidenty, smaller the gold number of a protective colloid, the greater is its protective action.
Critical micelle concentration of soap solutions lie in the range of :

To remove an electron from the first orbit to infinity of hydrogen atom, the amount of energy required will be :

A system has two charges, \( q_A = 5 \times 10^{-7} \, \text{C} \) and \( q_B = -5 \times 10^{-7} \, \text{C} \), located at points \( A : (0, 0, -10 \, \text{cm}) \) and \( B : (0, 0, +10 \, \text{cm}) \), respectively. Which of the following are true?
(A) The electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^6 \, \text{NC}^{-1} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment \( (p) = 5 \times 10^{-8} \, \text{C-m} \)
(D) direction of the dipole moment is along the negative z- axis
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A storage battery of EMF 10 V and internal resistance 1 \( \Omega \) is being charged by a 120 V dc supply using a series resistor of 21 \( \Omega \). What is the terminal voltage of the battery during charging ?

The steam distillation method is used for the separation of 1 : 1 mixture of p-nitrophenol and o-nitrophenols because