Mathematics NEB 2076 (old course) question paper

Group A

Very short answer questions(5 × 3 × 2 = 30)

1. 1.

   a. Find the truth value of the biconditional statement of p and q where p represents '2 is an even number' and q represents '4 is an even number'. b. If $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=2x-3$, find $f^{-1}$. c. Test the even or odd nature and symmetricity of the function $y=8x^2$.

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2. 2.

   a. Express ${\tan }^{-1}x$ in terms of inverse of sin function. b. Prove by mathematical induction: $1+3+5+...+(2n-1)=n^2$ c. Find the adjoint of the matrix $\left(\begin{array}{cc}2& 5\\ 3& -7\end{array}\right)$

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3. 3.

   a. Using Cramer's rule, solve: $3x+2y+9=0$, $2x-3y+6=0$ b. Express $\sqrt{3}+i$ in polar form. c. If one root of the equation $a{x}^2+bx+c=0$ be twice the other, show that $2b^2=9ac$.

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4. 4.

   a. Find the equation of the straight line that has $y$-intercept '2' and is parallel to $4x-8y+3=0$. b. Find the equation of the circle which passes through origin and makes equal intercepts on both axes. c. Evaluate: ${\lim }_{x\to 0}\frac{1-\cos mx}{1-\cos nx}$

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5. 5.

   a. Find $\frac{dy}{dx}$ when $x=2at$ and $y=2a{t}^2$ b. Evaluate: $\int \sin 2x\cdot \sin 3xdx$ c. Determine the interval in which the function $f(x)=\frac{1}{2}{x}^2-x$ is increasing or decreasing.

   GROUP: B | Short answer questions | 5 × 2 × 4 = 40

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