Business Mathematics NEB 2080 (old course) question paper

Group A

?(10x2x3=60)

1. 1.
   • a) Rewrite $|2x-5|\le 3$ without absolute value sign. [3]
   • b) Find the domain and the range of the following relation $R=\{(1,1),(2,4),(3,9),(4,16)\}$ [3]

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2. 2.
   • a) A parent places in the saving bank Rs. 500 on his child's first birth, Rs. 1000 on his second, Rs. 1500 on his third and so on increasing the amount by Rs. 500 on each birthday. How much will he save up when the child reaches the sixteenth birthday, the latter inclusive ? [3]
   • b) Insert 4 geometric means between $\frac{2}{3}$ and $5\frac{1}{16}$ [3]

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3. 3.
   • a) How many license plates consisting of 3 different numbers of digits can be made out of given digits 1,2,3,4,5,6 ? [3]
   • b) If $A=\left(\begin{array}{cc}-3& -2\\ 5& 3\end{array}\right)$ and $B=\left(\begin{array}{cc}3& 2\\ -5& 3\end{array}\right)$, find $|AB|$. [3]

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4. 4.
   • a) The middle point of a line is (2, 3) and one end of the same line is (3,4). Find the co-ordinates of the other end. [3]
   • b) Find the equation of a straight line making 9 and 15 as x-intercept and y-intercept respectively. [3]

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5. 5.
   • a) Using log-table, evaluate $\frac{(3.678{)}^4}{\sqrt[3]{42.75}}$ [3]
   • b) Evaluate : ${\lim }_{x\to 3}\frac{x^3-27}{x^2-5x+6}$ [3]

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6. 6.
   • a) Examine the continuity or discontinuity of the function $f(x)=\frac{x^2-16}{x-4}$ at x = 4 [3]
   • b) Find $\frac{dy}{dx}$ if $x=2a(t+3)$ and $y=a(t^2+7)$ [3]

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7. 7.
   • a) Evaluate: $\int \frac{x^2-4}{x+2}.dx$ [3]
   • b) If for 2 units of production, total revenue is Rs. 200, find the total revenue function given that $MR=10+20x-3x^2$. [3]

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8. 8.
   • a) Find the standard deviation from the following data : 158, 166, 164, 160, 172, 170, [3]
   • b) For two events A and B of $P(A)=0.40$, $P(B)=0.75$ and $P(A\cap B)=0.61$, find $P(A\cup B)$. [3]

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9. 9.
   • a) A contractor has to the complete the work of a road in 16 days. He employed 30 persons for 12 days and completes $\frac{5}{7}$ of the work. How many more persons should be employed now in order to complete the work in time ? [3]
   • b) Mohan bought 100 kg of oranges at Rs 72 per kg. If 10 kg orange are rotten and are of no use to sell, at what rate must the remaining oranges be sold so as to gain 15% on the whole outlay ? [3]

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10. 10.
    • a) If 90 dollars = 75 Euro, 60 Euro = 89.10 Swiss francs, 56 Swiss francs = $25 and $1 = Rs. 134.40, how many rupee are equivalent to 500 dollars ? [3]
    • b) Find the amount of an immediate annuity of Rs. 700 a year for 4 years at 5 percent per annum. [3]

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