Mathematics NEB 2082 question paper

Group A

?(11 × 1 = 11)

1. 1.

   What is the number of combinations of n object taken r at a time ? a) $\frac{n!}{(n-r)!}$ b) $\frac{n!}{(n-r)!r!}$ c) $\frac{n!}{r!}$ d) $\frac{n!}{n!r!}$

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2. 2.

   Which one of following is the argument of a complex number $z=-1+\sqrt{-3}$ ? a) $\frac{\pi }{3}$ b) $\frac{\pi }{6}$ c) $\frac{2\pi }{3}$ d) $\frac{3\pi }{2}$

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3. 3.

   In a triangle ABC, $2\cos \mathrm{A}=\sin \mathrm{B}:\sin \mathrm{C}$, what type of triangle is ABC ? a) Isosceles b) Scalene c) Right angled d) Equilateral

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4. 4.

   What is the length of the tangent to the circle $x^2+y^2=25$ from a point $(3,5)$ ? a) 8 units b) 5 units c) 4 units d) 3 units

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5. 5.

   If $|\vec{a}|=5$, and $|\vec{b}|=6$ and $\vec{a}.\vec{b}=15$, which of the following is the angle between $\vec{a}$ and $\vec{b}$? a) $\frac{\pi }{6}$ b) $\frac{\pi }{4}$ c) $\frac{\pi }{3}$ d) $\frac{\pi }{2}$

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6. 6.

   For two events A and B, $P(B)=0.32$, $P(A\cap B)=0.2$ and $P(B/A)=0.5$, then what is the probability of P(A) ? a) 0.40 b) 0.20 c) 0.15 d) 0.10

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7. 7.

   Which one of the following is the derivative of $cothx$ ? a) ${\tanh }^{2}x$ b) $-cot{h}^{2}x$ c) $-cosec{h}^{2}x$ d) $-cosechxcothx$

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8. 8.

   What is the slope of the curve of the function $f(x)=x^2-2x$ at $x=5$ ? a) 2 b) 4 c) 8 d) 10

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9. 9.

   Which one of the following is equal to ${\lim }_{x\to 0}\frac{1-\cos x}{6x^2}$ ? a) 0 b) $\frac{1}{6}$ c) $\frac{1}{8}$ d) $\frac{1}{12}$

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10. 10.

    A circular copper plate is heated so that its radius increases from 5 cm to 5.06 cm then what is approximate increase in area ? a) $0.6036\pi {\mathrm{cm}}^2$ b) $0.6\pi {\mathrm{cm}}^2$ c) $0.675\pi {\mathrm{cm}}^2$ d) $0.634\pi {\mathrm{cm}}^2$

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11. 11.

    Which one of the following system of linear equation is diagonally dominant ? a) $12x_1+3x_2-5x_3=1$, $x_1+5x_2+3x_3=28$, $3x_1+7x_2+13x_3=1$ b) $3x_1+12x_2-5x_3=1$, $x_1+5x_2+3x_3=28$, $2x_1+7x_2+13x_3=1$ c) $12x_1-5x_2+3x_3=1$, $x_1+2x_2+4x_3=2$, $5x_1+3x_2+x_3=28$ d) $x_1+2x_2+4x_3=2$, $5x_1+3x_2-4x_3=28$, $2x_1+4x_2-x_3=1$ OR A particle starts from rest and moves with a uniform acceleration of $10cm/se{\mathrm{c}}^2$. What will be its velocity at the end of 20 seconds ? a) $200cm/sec$ b) $100cm/sec$ c) $2cm/sec$ d) $0.5cm/sec$ GROUP: B | ? | 8 × 5 = 40

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