NEB Class 12 Mathematics Question Paper 2082 (Set R)

Which one is the relation between permutation and combination of $n$ things taken $r$ things at a time?

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 $y$?

Which one of the following is the value of $\\sec\\dfrac{B}{2}$?

In which condition the line $y = mx + c$ will be tangent to the circle $x^2 + y^2 = a^2$?

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

If $P(A) = \\dfrac{1}{3}$, $P(B) = \\dfrac{2}{3}$ and $P(A \\cap B) = \\dfrac{1}{5}$, which one of the following is $P(B/A)$?

Which one of the following is the slope of normal to the curve $y = 3x^2 - x$ at $(-1, 1)$?

What is the integral of $\\displaystyle\\int \\dfrac{dx}{9x^2 + 1}$?

Which one of the following is the homogeneous differential equation?

Which is the integrating factor of differential linear equation $\\cos^2 x\\dfrac{dy}{dx} = 1 - y$?

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 $40\\,\\text{m/sec}$ and 30^\\circ? $[g = 10\\,\\text{ms}^{-2}]$

A) $20\\,\\text{m}$  B) $40\\,\\text{m}$  C) $80\\,\\text{m}$  D) $160\\,\\text{m}$

Write the expansion of $\\log_e(1-x)$; $|x| < 1$.

Write the total number of permutations of a set having $n$ elements.

State De-Moivre's theorem.

Write the sum of cubes of first $n$ natural numbers.

Write the augmented matrix of the system of equation $3x + 2y - 1 = 0$ and $4x + y = 3$.

A committee is to be chosen from $a$ boys and 6 girls and is to consist 2 boys and 3 girls. If 120 committees are formed, what is the number of boys represented by $a$?

The square roots of any complex number are $(\\sqrt{3} + i)$ and $(-\\sqrt{3} - i)$. Write the complex number in polar form.

In any triangle PQR, if $p\\sin^2\\dfrac{R}{2} + r\\sin^2\\dfrac{P}{2} = \\dfrac{q}{2}$, prove that the sides are in A.P.

If $\\vec{a} = 4\\hat{i} - 3\\hat{j} + 2\\hat{k}$ and $\\vec{b} = 3\\hat{i} - 2\\hat{j} + 4\\hat{k}$ are two vectors, find the projection $\\vec{b}$ on $\\vec{a}$.

Find the eccentricity of conic $3x^2 - 4y^2 - 6x = 0$.

Find the eccentricity of ellipse whose major axis is four times its minor axis and passes through the point $(4, 2)$.

Consider the following data for supply $(X)$ and the price $(Y)$ of a commodity for last six years.

Find the correlation coefficient between X and Y.

Calculate the supply when the price of commodity is Rs. 150. (Using the data of Q16: X = supply, Y = price.)

Write the derivative of $\\text{cosech}^{-1}(x)$.

Define L-Hospital's rule.

Write the condition where the curve $y = f(x)$ has tangent parallel to y-axis.

Write the integral of $\\displaystyle\\int \\dfrac{1}{x^2 - a^2}\\,dx$.

Write the standard form of first order linear differential equation.

Find the derivative of $\\coth^{-1}(\\sin 2x)$.

Integrate: $\\displaystyle\\int \\dfrac{dx}{x^3 - x^2 - 2x}$.

Using simplex method, maximize $P(x, y) = 10x + 3y$ subject to constraint $6x + 7y \\le 42$, $x + 3y \\le 42$, $x + 3y \\le 9$, $x \\ge 0$, $y \\ge 0$.

Or

Two forces A and B acting parallel to the length and base of an inclined plane respectively, would each of them singly support a weight $R$ on the plane, prove that $\\dfrac{1}{A^2} = \\dfrac{1}{B^2} + \\dfrac{1}{R^2}$.

If the middle term in the expansion $\\left(\\dfrac{a}{2} + 2\\right)^8$ is 1120, find the value of $a$.

Using mathematical induction, prove that $1 + 7 + 13 + 19 + \\cdots + (6n - 5) = n(3n - 2)$.

Solve the following linear equations by using matrix method: $7x - 2y = 18$, $3x + 7z = 33$, $x + y + z = 12$.

The scalar product of two vectors and cross product of two vectors are interrelated. Explain.

If the cosines of two angles of a triangle are proportional to the opposite sides, show that it is an isosceles triangle.

Establish the condition that the line $ax + by + c = 0$ may be normal to the parabola $x^2 = 4ay$.

Find the rate of change of volume of a sphere with respect to its surface area when radius is 7 cm.

Integrate: $\\displaystyle\\int \\dfrac{dx}{5 - 3\\cos x}$.

Solve: $(1 + x^2)dy - (1 + y^2)dx = 0$.