Mathematics NEB 2081 (old course) question paper

Group A

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1. 1.
   • a) How many numbers of three different digits less than 500 can be formed with digits 1, 2, 3, 4, 5, 6? [2]
   • b) Find the co-efficient of $x^6$ in the expansion of ${\left(3x-\frac{1}{3x}\right)}^9$. [2]
   • c) Let $G=\{0,1,2\}$ form a composition table for G under the multiplication modulo 3. Find the inverse element of 1. [2]

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2. 2.
   • a) Find the equation of the hyperbola having focus at $(5,0)$ and vertex at $(3,0)$. [2]
   • b) Find the equation of a plane which makes equal intercepts on the axes and passes through the point $(2,3,4)$. [2]
   • c) Prove vectorically that $b=c\cos A+a\cos C$. [2]

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3. 3.
   • a) If $\vec{a}=3\vec{i}-\vec{j}-4\vec{k}$, $\vec{b}=4\vec{j}-2\vec{i}-3\vec{k}$ and $\vec{c}=7\vec{j}-\vec{k}-5\vec{i}$, find $\left|\vec{a}-2\vec{b}+\vec{c}\right|$. [2]
   • b) Evaluate : $\int \frac{dx}{5x^2-4}$ . [2]
   • c) Evaluate, using L'Hospital rule : ${\lim }_{x\to 0}\frac{\tan x-x}{x-\sin x}$ . [2]

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4. 4.
   • a) Solve: $\sin x\cdot \cos xdx+\sin y\cdot \cos ydy=0$. [2]
   • b) If $\sum X^2=600$, $\sum X=150$, $Mode(M_o)=1.75$, find Pearsonian co-efficient of skewness for the group of 50 items. [2]
   • c) An urn contains 8 white and 4 red balls. If two balls are drawn at random, find the probability that they are of different colour. [2]

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