List of practice Questions

If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:

The value of \(sin^{-1}\frac{12}{13} +cos^{-1}\frac45+tan^{-1}\frac{63}{16}\) is :

The coordinates of the foot of the perpendicular drawn from origin to the plane \(2x - 3y + 4z - 6 = 0\) is :

The probability distribution of a discrete random variable \(X\) is given below :

\(X\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(X)\)	\(\frac5k\)	\(\frac7k\)	\(\frac9k\)	\(\frac{11}{k}\)

then the value of k is:

The maximum value of\( z=2.5x+y\) subject to the constraints \( x+3y\leq12, 3x+y\leq12, x, y\geq0, \) is: 

If \(A=\begin{bmatrix} -2&6\\-5&-1\end{bmatrix}\) then \(A^{-1}\) is:

A discrete random variable X has the following probability distribution:

The value of b is:

A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :

The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:

The corner points of feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy where p, q > 0. The condition on p and q so that, minimum of Z occurs at (3, 0) and (1, 1) is :

For fencing of flower bed with 100 cm long wire in the form of circular sector, the maximum area of the flower bed is :

Consider the following statements :
A. Cost of living at two different cities can be compared with volume index.
B. When the prices of rice are to be compared we use price index.
C. In Laspeyre's price index number weight is considered as price in current year.
D. Purchasing power of money can be assessed through consumer price index.
E. Fisher Index number is called ideal index number.
Choose the correct answer from the options given below :

Arun covers first 28 kms of his journey in 45 minutes and the remaining 32 kms in 35 minutes. What is his average speed in m/s ?

A and B started a business by investing ₹10,000 and ₹18,000 respectively. After 4 months C joined the business with a capital of ₹12,000. After two more months B left the business his capital. At the end of the year A got a share of ₹7,500 in the profit. What is the total profit earned ?

The maximum value of the function \(f(x)=x+\sqrt{1-x}\) on the interval [0,1] is, 

If a random variable X follows poison distribution such that 3P(X=1)=P(X=2), then P(X=4) is,

What is the value of ⁸¹P₂-⁸¹C₂?

Which of the following is called 'Trapezium'?

From the given statements, what conclusion can be made?
Statements: Some men are wise
                    All wise are professors
Conclusion I: Some men are professors.
                    II: All professors are wise

If the mean of 5 observations x, x+2, x+4, x+6 and x+8 is 11, then value of x

A solution of CuSO4 is electrolysed for 10 min with a current of 1.5 A. What is the mass of copper deposited at the cathode (molar mass of Cu= 63 g) (1F = 96487c).

Which of the following relationships are not correct ?
(A) \(E\degree=\frac{0.0591}{nF}\log Kc\)
(B) \(\lambda_m\degree Na_2SO_4=\lambda_m\degree (Na^+)+\lambda_m\degree (SO_4^{2-})\)
(C) Cell constant = \(\frac{Conductivity}{Conductance}\)
(D)\(\Delta G\degree = nF\;E\degree_{Cell}\)
(E) \(Zn_{(s)}|Zn^{2+}_{(aq)}||Cu^{2+}_{(aq)}|Cu\)
Choose the correct answer from the options given below:

Given:
\(E\degree_{K^+/K}=-2.93V,\)
\(E\degree_{Ag^+/Ag}=0.80V,\)
\(E\degree_{Hg^{2+}/Hg}=0.79V,\)
\(E\degree_{Mg^{2+}/Mg}=-2.37V,\)
\(E\degree_{Cr^{3+}/Cr}=-0.74V,\)
Choose the correct order :
(A) Ag <Hg< Cr <Mg <K (increasing reducing power)
(B) Ag <Hg< Cr <Mg <K (decreasing oxidising power)
(C) Ag > Hg > Cr > Mg > K (decreasing oxidising power)
(D) Hg > Cr > Ag > K > Mg (increasing reactivity)
(E) K > Mg > Cr > Hg > Ag (decreasing reactivity order)
Choose the correct answer from the options given below:

The standard reduction potential for Sn$^{4+}$/Sn$^{2+}$ is +0.15 V and for Cr$^{3+}$/Cr is -0.74 V. These two half-cells, coupled in their standard states, are connected to make a cell. The galvanic cell can be correctly represented by: