List of top Mathematics Questions

A tin container contains 50 litres of cow milk. From this container 5 litres cow milk was taken out and replaced with soya milk. This process was repeated further two more times. How much cow milk is there in the container now?
The sum of two skew-symmetric matrices of the same order is a
Which of the following properties are not correct for three real numbers a, b and c?

A. If \(a > b\) and \(b > c\), then \(a < c\)
B. If \(a > b\), and \(c < 0\), then \(ac < bc\)
C. If \(a > b\), and \(c < 0\), then \(a \div c < b \div c\)
D. If \(a > b\) and \(c > 0\), then \(a \div c < b \div c\)

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Match the LIST-I with LIST-II
LIST-ILIST-II
A.Row matrixI.\(\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix}\)
B.Scalar matrixII.\(\begin{bmatrix}1\\2\\3\end{bmatrix}\)
C.Column matrixIII.\(\begin{bmatrix}1 & 2 & 3\end{bmatrix}\)
D.Diagonal matrixIV.\(\begin{bmatrix}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix}\)

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A man can row a boat in still water at the rate of 17 km/hr. He finds that it takes him thrice as long to row upstream of a river as to row downstream of the same river. The speed of of the stream is,
If \(53 \equiv y \pmod 6\), then the possible values of \(y\) are:-
Match the LIST-I with LIST-II
LIST-I
Matrix \(A\)		LIST-II
\(|\text{adj}\,A|\)
A. \(A=\begin{bmatrix}2&4\\1&3\end{bmatrix}\)I. 1
B. \(A=\begin{bmatrix}5&2\\7&4\end{bmatrix}\)II. 7
C. \(A=\begin{bmatrix}1&0\\0&1\end{bmatrix}\)III. 2
D. \(A=\begin{bmatrix}6&1\\5&2\end{bmatrix}\)IV. 6
Choose the correct answer from the options given below:
Match the LIST-I with LIST-II
LIST-ILIST-II
A.If A is a square matrix of order 3 such that \(|A| = 3\), then \(|adj (adj A)| =\)I.16
B.If A is a non-singular matrix and \(|A| = \frac{1}{16}\), then \(|A^{-1}| =\)II.512
C.If A is a square matrix of order 4 such that \(|A| = 2\), then \(|adj (adj A)| =\)III.9
D.If A is a square matrix of order 2 such that \(|A| = 9\), then \(|adj (adj A)| =\)IV.81

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For a given square matrix \(A\) of order n, if there exists another square matrix \(B\) of the same order n, such that \(AB = BA = I\), then \(A\) is said to be invertible and \(B\) is called the inverse matrix of \(A\).

Which of the following statements are not TRUE ?

A. Inverse of a matrix, if it exists, is unique.
B. For two invertible matrices of same order, say \(A\) and \(B\) , then \((AB)^{-1} = A^{-1}B^{-1}\)
C. For an invertible matrix \(A\), \((A^{-1})^{-1} = A\)
D. For an invertible matrix \(A\), \((A^{T})^{-1} = A^{T}\)

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The number of wedding cards, in thousands, distributed in a certain city on each day for a week is given as follows:-
21, 35, 19, 27, 32, 22, 12.
The three days moving averages will be:
The patterns and behavior of the data in any time series are based on which of the following components.
A. Seasonal component
B. Secular trend component
C. Irregular component
D. Cyclical component
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The following data are from a simple random sample: 3 , 7 , 4 , 12 , 4 , 12. The point estimate of the population mean is,
Particular solution of the differential equation \((x-1)\frac{dy}{dx}=2xy\), when \(y(2)=1\) is:- (consider \(\log_e x=\log x\))
Consider a LPP given by
Maximize \(Z=38x+19y\)
Subject to \(3x+5y\le 15,\ 5x+2y\le 10,\) and \(x,y\ge 0\)
The optimum value of \(Z\) is,
\(\int (x+1)e^x\,dx\) is equal to
[ \(C\) is an arbitrary constant]
Let R be the feasible region for a linear programming problem, and Let \(z=ax+by\) be the objective function. If the feasible region R is bounded then which of the following are true ?
A. The maximum or minimum value of objective function may not exist.
B. The objective function \(z\) has both a maximum and a minimum value on R.
C. Maximum and minimum values lie in the unbounded region
D. The objective function \(z=ax+by\) has both a maximum value and a minimum value and each of these values occurs at a corner point of R.
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Which of the following is/are true about parameter ?
A. It is a characteristic of a sample.
B. It is a characterstic of a population.
C. It is a numerical value that is taken from the entire population, such as the population mean.
D. It is the numerical value taken from a sample and calculated from the sample observations alone.
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Consider a office having seating capacity of 58 employees and all of them are to be seated in such a way that an employee can sit on any available vacant seat . What will be the degree of freedom?
If \(X\) is a Poisson variate such that \(4P(X = 2) = 3P(X = 1)\), then the mean of the distribution is equal to:
The demand function for a certain product is represented by the equation \(p=150+12x-x^2\), where \(x\) is the number of units demanded and \(p\) is the price per unit. The marginal revenue when 5 units are sold is
The order and degree of the following differential equation:
\(y=px+\sqrt{a^2p^2+b^2}\), where \(p=\frac{dy}{dx}\), are
In a math aptitude test, students scores are found to be normally distributed having mean as 45 and standard deviation 5. What percent of students scored more than the mean score?
The function \(f(x)=4x^3-18x^2+27x-7\) has:-
If \(y=e^{4x}(92)^x\); then \(\frac{dy}{dx}\) is equal to
(\(\log_e x=\log x\))
The function \(f(x)=\frac{2}{x}+5,\ x\ne 0\) is