Mathematics NEB 2082 (MCQs) question paper

Group A

Rewrite the correct option of each question in your same answer sheet.(11 × 1 = 11)

1. 1.

   Which one is the relation between permutation and combination of '$n$' things taken '$r$' things at a time ? a) $C(n,r)=r!\times P(n,r)$ b) $C(n,r)\times r!=P(n,r)$ c) $C(n,r)\times r=P(n,r)$ d) $C(n,r)=P(n,r)\times r$

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2. 2.

   If the system of equations $p_{1}x+q_{1}y=r_1$ and $p_{2}x+q_{2}y=r_2$, what is the value of $y$ ? a) $\frac{\left|\begin{array}{cc}{p}_1& r_1\\ p_2& r_2\end{array}\right|}{\left|\begin{array}{cc}{p}_1& q_1\\ p_2& q_2\end{array}\right|}$ b) $\frac{\left|\begin{array}{cc}{p}_1& q_1\\ p_2& q_2\end{array}\right|}{\left|\begin{array}{cc}{r}_1& q_1\\ r_2& q_2\end{array}\right|}$ c) $\frac{\left|\begin{array}{cc}{r}_1& q_1\\ r_2& q_2\end{array}\right|}{\left|\begin{array}{cc}{p}_1& q_1\\ p_2& q_2\end{array}\right|}$ d) $\frac{\left|\begin{array}{cc}{r}_1& p_1\\ r_2& p_2\end{array}\right|}{\left|\begin{array}{cc}{p}_1& q_1\\ p_2& q_2\end{array}\right|}$

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3. 3.

   Which one of the following is the value of $\sec \frac{B}{2}$ ? a) $\sqrt{\frac{ca}{s-b}}$ b) $\sqrt{\frac{bc}{s(s-a)}}$ c) $\sqrt{\frac{bc}{s(s-c)}}$ d) $\sqrt{\frac{ca}{s(s-b)}}$

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4. 4.

   In which condition the line $y=mx+c$ will be tangent to the circle $x^2+y^2=a^2$ ? a) $a=c\sqrt{1+m^2}$ b) $a=\pm c\sqrt{1+m^2}$ c) $c=\pm a\sqrt{1+m^2}$ d) $c=a\sqrt{1+m^2}$

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5. 5.

   What is $\vec{a}\times \vec{b}$ if $\vec{a}=(0,0,1)$ and $\vec{b}=(0,1,0)$ ? a) (-1, 0, 0) b) (1, 0, 0) c) (0, 1, 0) d) (0, 0, -1)

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6. 6.

   If $P(A)=\frac{1}{3}$ , $P(B)=\frac{2}{3}$ and $P(A\cap B)=\frac{1}{5}$ , which one of the following is $P(B/A)$ ? a) $\frac{3}{5}$ b) $\frac{2}{5}$ c) $\frac{2}{15}$ d) $\frac{1}{15}$

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7. 7.

   Which one of the following is the slope of normal to the curve $y=3x^2-x$ at (-1, 1) ? a) -7 b) -5 c) $\frac{1}{7}$ d) $\frac{1}{5}$

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8. 8.

   What is the integral of $\int \frac{dx}{9x^2+1}$ ? a) $\frac{1}{3}{\tan }^{-1}(3x)+C$ b) $\frac{1}{27}{\tan }^{-1}(3x)+C$ c) $\frac{1}{27}{\tan }^{-1}\left(\frac{x}{3}\right)+C$ d) $\frac{1}{27}{\tan }^{-1}\left(\frac{3}{x}\right)+C$

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9. 9.

   Which one of the following is the homogeneous differential equation ? a) $\frac{dy}{dx}=\frac{x^2+y^2}{x+y}$ b) $\frac{dy}{dx}=\frac{x^2+y^2}{x-y}$ c) $\frac{dy}{dx}=\frac{x^2+y^2}{x^2-y^2}$ d) $\frac{dy}{dx}=\frac{x+y}{x^2+y^2}$

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10. 10.

    Which is the integrating factor of differential linear equation ${\cos }^{2}x\frac{dy}{dx}=1-y$ ? a) $\tan x$ b) $e^{\tan x}$ c) $e^{{\sec }^{2}x}$ d) ${\sec }^{2}x$

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11. 11.

    Two simultaneous equations are given as $3x+4y=13$ and $x-2y=1$. What is the equation after eliminating $x$ ? a) $10y=10$ b) $10y=16$ c) $y=10$ d) $2y=10$ OR What is the maximum height attained by a particle in a projectile motion if initial velocity and angle of inclination are 40m/sec and $30^{\circ }$ ? [$g=10{\text{ms}}^{-2}$] a) 20m b) 40m c) 80m d) 160m

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