Applied-Mathematics PYQ — Page 7

A company intends to create a sinking fund to replace at the end of 20$^{th}$ year assets costing Rs. 2,50,000. Then the value of the amount to be retained out of profits every year if the interest rate is 5% is : [Given $(1.05)^{20} = 2.6532$]

The effective rate that is equivalent to a nominal rate of 16% compounded semi-annually is :

The digit in the unit's place of $13^{37}$ is :

If Paasche's index number is 160 and Laspeyre's index number is 250, then Fisher's index number is :

A shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below: | Sale of cars (Units) | 0 | 1 | 2 | 3 | |---|---|---|---|---| | Probabilities | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{3}{10}$ | $\frac{1}{30}$ | The expected number of cars sold is :

The price relatives and weights of a set of commodities are given as: | Commodity | A | B | C | |---|---|---|---| | Price Relative | 150 | 130 | 180 | | Weight | $x$ | $3x$ | $y$ | If the sum of weights is 30 and the index for the set is 144, then the values of $x$ and $y$ are:

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

If the life expectancy of an asset is 10 years, scrap value Rs.5,000 and annual depreciation of Rs.3000 per annum, then original cost of the asset is:

Which constraints correctly represent the situation 'mixture of x and y must be at least 8 units' ?

A container contains 50 litres of milk. From this container 10 litres of milk was taken out and replaced by water. This process is repeated two more times. How much milk is now left in the container ?

Consider the following hypothesis test : $H_0 : \mu \leq 20$ $H_1 : \mu > 20$ A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is :

If $f(x) = a \log x + \frac{b}{x} + x$ has its extreme values at $x = -1$ and $x = 3$, then $(a, b)$ is equal to:

The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :

Rahul can run 34.4 m in the given time as Amit runs 50 m. By how much distance Rahul is away from Amit at the winning point, in a two km race ?

Match List I with List II | LIST I | LIST II | |---|---| | A. The variance of a Poisson distribution with mean $\lambda$ is | I. $\sqrt{\lambda}$ | | B. The standard deviation of a Poisson distribution with mean $\lambda$ is | II. 4 | | C. In a Poisson distribution, if mean is 4, then the standard deviation is | III. $\lambda$ | | D. In a Poisson distribution, if mean is 4, then the variance is | IV. 2 | Choose the correct answer from the options given below:

Match List I with List II | LIST I | LIST II | |---|---| | A. A special characteristic of a population is known as a: | I. statistic | | B. A special characteristic of a sample is known as a: | II. Confidence interval | | C. The uncertainty of a sampling process is expressed by: | III. Estimation | | D. The process by which one makes the inferences about a population based on the information obtained from a sample is known as: | IV. Parameter | Choose the correct answer from the options given below:

If the probability distribution of a discrete random variable $X$ is given as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.5 | 2k | 3k | 3k | 2k | Then the value of $k$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. A matrix that has unequal number of rows and columns is called | I. Non-singular matrix | | B. A matrix whose determinant is non-zero is called | II. Null matrix | | C. A diagonal matrix whose diagonal elements are equal is called | III. Rectangular matrix | | D. A matrix that is both symmetric and skew-symmetric is | IV. Scalar matrix | Choose the correct answer from the options given below:

A, B and C entered in a partnership business. They invested their capitals in the ratio of $\frac{4}{3} : \frac{5}{2} : \frac{6}{5}$. After 5 months, B invested 40% more than what he had invested earlier. If the total profit at the end of one year was Rs 50,550, then how much profit did A earn?

If the cost function $C(x)$ of producing $x$ units of a commodity is given as $C(x) = x^3 - 60x^2 + 13x + 50$, then the level of output for which the marginal cost is minimum is

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$, then $P(X \leq 9)$ is :