List of practice Questions

The total cost function for x units of a commodity is given by \(C(x) = \frac{25x^3}{3}-75x^2+48x+34\). The output \(x\) at which the marginal cost is minimum is:
Match List I with List II
LIST I LIST II
A.The minimum value of \(f(x)=8x²-4x+7\) isI.48
B.The maximum value of \(f(x) = x+\frac{1}{x}, x < 0\) isII.13
C.The maximum slope of the cure \(y = -2x^3+6x^2+7x+26\) isIII.-2
D.The minimum value of \(f(x) = x² +\frac{128}{x}\) isIV.\(\frac{13}{2}\)
Choose the correct answer from the options given below:
An oil film in air of thickness 255 nm is illuminated by white light at normal incidence. As a consequence of interference, which colour will be predominantly visible in the reflected light ?
Given the refractive index of oil = 1.47
The degree of dissociation of monobasic acid is 0 3 By what percent is the observed depression in freezing point greater than the calculated depression in freezing point ?
A product costs the manufacturer ₹20 per unit. The demand function is given by p(x) = 1000-20x, then the quantity for maximum profit is:
A discrete random variable X has the following probability distribution:
X:012345
P(X):b3b5b3b4b6b
The value of b is:
A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X=1)=0.4, P(X=4)=P(X=2) and P(X=3)=2P(X=2), then P(X=0) is:
A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :
Match List I with List II
LIST I LIST II
A.In a binomial distribution, if n=10, q=0.25, then its mean isI.12
B.If the mean of a binomial distribution is 6 and its variance is 3, then p isII.7.5
C.In a binomial distribution, the probability of getting a success is 1/4 
and the standard distribution is 3, then its mean is		III.16
D.If the mean and variance of a binomial distribution are 4 and 3 respectively,
then the number of trials is		IV.½
Choose the correct answer from the options given below:
If Paasche's index number is 160 and Laspeyre's index number is 250, then Fisher's index number is:
The prices and the quantities of three commodities are given are :
Commodity

Price (₹)

Quantities

in Year
2006		in Year
2009		in Year
2006		in Year
2009
P100901210
Q80\(x\)87
R605046
The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of \(x\) is:
Consider the following data:
Year20122013201420152016
Sales (in crores)8107912
The equation of the straight line trend by the method of least squares is :
Consider the following hypothesis test:
\(Η_0: μ ≤ 20\)
\(Η_1 : μ > 20\)
A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is:
A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :
Match List I with List II
LIST I LIST II
A.A special characteristic of a population is called I.Sample Size
B.The number of statistical individuals in a sample is calledII.Statistic
C.A special characteristic of a sample is calledIII.Standard error
D.The standard deviation of the sampling distribution of a statistic is known as itsIV.Parameter
Choose the correct answer from the options given below:
The present value of a perpetual income of x paybale at the end of each 6 months is ₹ 1,80,000. If the money is worth 5% compounded semi-annually, then the value of x is ₹:
A person buys a flat for which he makes down payment of ₹7,50,000 and the balance is to be paid in 10 years by monthly instalments of ₹22,000 each. If the bank charges interest at the rate of 12% per annum, then the actual price of the flat using flat rate system is:
A car costing ₹8,00,000 has scrap value of ₹3,00,000. If the book value of car at the end of fourth year is ₹6,00,000, then the useful life of the car is:
The minimum value of z=3x+6y subject to the constraints \(2x+3y≤180\), \(x+y≥60\), \(x≥3y\), \(x≥0\), \(y≥0\) is:
A carpenter earns a profit of ₹50 and ₹80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as:
RequiredChairTableAvailable
Quantity
Wood
Labour		3
1		5
2		150
56
The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively:
Match List I with List II
LIST I LIST II
A.The common region determined by all the linear
constraints of a L.P.P. is called corner point		I.corner point
B.A point in the feasible region which is the intersection
of two boundary lines is called,		II.non-negative
C.The feasible region for an LPP is always aIII.feasible region
D.The constraints \(x, y≥0\) describes that the
variables involved in a LPP are		IV.convex polygon
Choose the correct answer from the options given below:
The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is:
If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:
In the equation of trend line \(y_t=a+bx\), a and b represent:
If Mr. Ravi borrows a sum of ₹1,50,000 at an interest rate of 10% (flat) for a tenure of 3 years, then his EMI based on above data is (approximately) ₹: