List of top Mathematics Questions

Vishal purchased a machine costing Rs. 50,000. The estimated useful life of the machine is 10 years with a scrap value of Rs. 5,000. The annual depreciation using linear method is,
Face value of a bond is
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LIST-ILIST-II
A. In a binomial distribution, if n = 20, q = 0.75 then its mean isI. 25
B. An unbiased coin is tossed 4 times. The mean of the number of tails isII. 5
C. In a binomial distribution, mean is 5 and variance is 4, then the number of trials isIII. 0.5
D. In a binomial distribution, if mean is 8 and variance is 4, then the probability of success isIV. 2
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At what rate of interest per annum will the present value of a perpetuity of Rs. 500 payable at the end of every 6 months be Rs. 10,000?
Let \(X\) denote the number of hours a person drive during a randomly selected working day. The probability that \(X\) can take the value \(x_i\) has the following form, where \(k\) is some unknown constant.
\[ P(X = x_i) = \begin{cases} 0.2, & \text{if } x_i = 0 \\ kx_i, & \text{if } x_i = 1 \text{ or } 2 \\ k(4 - x_i), & \text{if } x_i = 3 \\ 0, & \text{otherwise} \end{cases} \]
Match the LIST-I with LIST-II
LIST-ILIST-II
A. The value of \(k\)I. 1
B. The probability that the person drive atleast two hours on a selected working dayII. 0.4
C. The probability that the person drive atmost three hours on a selected working dayIII. 0.2
D. The probability that the person drive atmost one hour on a selected working dayIV. 0.6
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Vatsala takes a loan of Rs. 2,00,000 at an interest rate of 10% per annum for 5 years. Her EMI using flat rate method is,
Assume an investment's starting value is Rs. 10,000 and it grows to Rs. 60,000 in 4 years, then the CAGR % of the investment is,
[given : \((6)^{1/4}=1.565\)]
The effective rate that is equivalent to a nominal rate of 6% per annum compounded semi-annually is
A letter is known to have come for 'RAVINDRA' or 'DEVINDRAN'. On the envelop just two consecutive letters 'RA' are visible. The probability that the letter has come for 'RAVINDRA' is:
A speaks truth in 80% cases and B in 90% cases. The probability that they contradict each other in stating the same fact, is:
The probability of the simultaneous occurrence of two events A and B is \(p\). If the probability that exactly one of A and B occurs is \(q\), then
A. \(P(\overline{A})+P(\overline{B})=2+2q-p\)
B. \(P(\overline{A})+P(\overline{B})=2-2p-q\)
C. \(P(\overline{A}\cap\overline{B})=1-p-q\)
D. \(P((A\cap B)|(A\cup B))=\frac{p}{p+q}\)

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If A and B are two events such that \(P(A)=\frac{1}{2}\), \(P(B)=\frac{1}{3}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P\left(\frac{A'}{B}\right)=\)
If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors such that \(\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0\) and angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{\pi}{6}\), then
If \(\alpha, \beta, \gamma\) are angles of inclinations of a line with \(x, y\) and \(z\)-axis respectively, then which of the following are correct?
A. \(\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1\)
B. \(\cos 2\alpha + \cos 2\beta + \cos 2\gamma = -1\)
C. \(\sin^2\alpha + \sin^2\beta + \sin^2\gamma = -2\)
D. \(\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 2\)
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In the linear programming problem:
Minimize \(z = x + y\), subject to the constraints:
\(x + 3y \leq 60,\ x + y \geq 10,\ x \leq y,\ x \geq 0,\ y \geq 0\)
Which of the following region in graph given below represents the feasible region of the above LPP?
Two lines \(L_1\) and \(L_2\) are given as \(L_1: \vec{r} = (\hat{i}+2\hat{j}+3\hat{k}) + \lambda(2\hat{i}+3\hat{j}+4\hat{k})\) and \(L_2: \vec{r} = (2\hat{i}+4\hat{j}+5\hat{k}) + \mu(4\hat{i}+6\hat{j}+8\hat{k})\), where \(\lambda\) and \(\mu\) are real parameters. Then which of the following statements are correct ?
A. Shortest distance between line \(L_1\) and \(L_2\) is \(\sqrt{\dfrac{5}{29}}\).
B. line \(L_1\) and \(L_2\) are parallel.
C. line \(L_1\) and \(L_2\) are concurrent lines.
D. line \(L_1\) and \(L_2\) are perpendicular.
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The lines \(x = py + q,\ z = ry + s\) and \(x = p'y + q',\ z = r'y + s'\) are perpendicular if
The objective function of a LPP is given by \(z = ax + by\), where \(a\) and \(b\) are constants. If minimum of \(z\) occurs at two points \((50, 30)\) and \((20, 40)\), then
If \(\vec{a}\) is any vector, then the value of \(|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2\) is equal to
Match the LIST-I with LIST-II
LIST-I
Differential Equations		LIST-II
Solutions[ c is an arbitrary constant]
A. \(x\,dy = y\,dx\)I. \(y = e^{x} + c\)
B. \(\log\left(\frac{dy}{dx}\right) = x\)II. \(y = c\,e^{x}\)
C. \(\frac{y\,dx - dy}{y} = 0\)III. \(xy = c\)
D. \(x\,dy + y\,dx = 0\)IV. \(y = cx\)

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The area of the region bounded by the line \(y = 3x + 2\), the \(x\)-axis and the ordinates \(x = -1\) and \(x = 1\) is:
Match the LIST-I with LIST-II
LIST-ILIST-II
A. If \(|\vec{a}| = \sqrt{26}\), \(|\vec{b}| = 7\) and \(|\vec{a} \times \vec{b}| = 35\), then \(|\vec{a} \cdot \vec{b}|\) is equal toI. 4
B. If \(2\hat{i} - 3\hat{j} + 4\hat{k}\) and \(a\hat{i} - 6\hat{j} + 8\hat{k}\) are collinear, then 'a' is equal toII. 2
C. If \(2\hat{i} + \hat{j} + \hat{k}\) and \(2\hat{i} - 4\hat{j} + \lambda\hat{k}\) are perpendicular, then \(\lambda\) is equal toIII. 7
D. \((\hat{i} \times \hat{j}) \cdot \hat{k} + (\hat{j} \times \hat{k}) \cdot \hat{i}\) is equal toIV. 0

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If \(\vec{a} = x\hat{i} + x\hat{j} + y\hat{k}\), \(\vec{b} = \hat{i} + \hat{k}\) and \(\vec{c} = y\hat{i} + y\hat{j} + z\hat{k}\) are three vectors such that \(\vec{a} \times \vec{b} \perp \vec{c}\), then
The general solution of the differential equation of the type \(\frac{dy}{dx} + py = Q\) is:
(where \(P\) and \(Q\) are functions of \(x\) only or constant)
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LIST-I
Indefinite Integral		LIST-II
Solution (where \(c\) is an arbitrary constant)
A. \(\int\sqrt{16-x^2}\,dx\)I. \(\sin^{-1}\left(\frac{x}{4}\right)+c\)
B. \(\int\frac{dx}{\sqrt{16-x^2}}\)II. \(\frac{x}{2}\sqrt{16-x^2}+8\sin^{-1}\left(\frac{x}{4}\right)+c\)
C. \(\int\frac{dx}{\sqrt{x^2-16}}\)III. \(\frac{1}{8}\log\left|\frac{4+x}{4-x}\right|+c\)
D. \(\int\frac{dx}{16-x^2}\)IV. \(\log\left|x+\sqrt{x^2-16}\right|+c\)
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