Mathematics

• Chapter 1: Algebra. Notes and past questions on Algebra for NEB Class 12 Mathematics.
• Chapter 2: Trigonometry. Notes and past questions on Trigonometry for NEB Class 12 Mathematics.
• Chapter 3: Analytic geometry. Notes and past questions on Analytic geometry for NEB Class 12 Mathematics.
• Chapter 5: Statistics and Probability. Notes and past questions on Statistics and Probability for NEB Class 12 Mathematics.
• Chapter 6: Calculus. Notes and past questions on Calculus for NEB Class 12 Mathematics.
• Chapter 7: Computational methods. Notes and past questions on Computational methods for NEB Class 12 Mathematics.
• Chapter 8: Mechanics. Notes and past questions on Mechanics for NEB Class 12 Mathematics.

• (a) In how many ways can the letters of the word "ELEMENT" be arranged? (b) Show that $\log_e 2 = \frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\fr... (2070)
• (a) Find the eccentricity and foci of the ellipse $3x^2+4y^2=36$. (b) Find the equation of the plane which makes equal intercepts on the... (2070)
• (a) Find the equation of the tangent to the curve $y=2x^3-5x^2+8$ at $(2,4)$. (b) Evaluate $\int\frac{dx}{\sqrt{(x-\alpha)(x-\beta)}},\ (... (2070)
• (a) Solve $x^2\,dy-y^2\,dx=0$. (b) If $n=10,\ \Sigma X=60,\ \Sigma Y=60,\ \Sigma X^2=400,\ \Sigma Y^2=580,\ \Sigma XY=415$, find the corr... (2070)
• From 6 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be done so as to include at least two gentlemen... (2070)
• (a) Prove that the line $3x+4y+6=0$ is tangent to the parabola $2y^2=9x$ and find its point of contact. OR: Deduce the equation of a hype... (2070)
• (a) Evaluate $\int\frac{dx}{1+2\sin x}$. (b) Solve $(1+x^2)\frac{dy}{dx}+2xy=4x^2$. OR: Solve $(x^2+y^2)\,dy=xy\,dx$. (2070)
• (a) Distribution A: mean 100, median 90, S.D. 10. Distribution B: mean 90, median 80, S.D. 10. Is A the same as B regarding degree of var... (2070)
• If $(1+x)^n=C_0+C_1x+C_2x^2+\cdots+C_nx^n$, prove that $C_0C_n+C_1C_{n-1}+\cdots+C_nC_0=\dfrac{2n!}{(n!)^2}$. (2070)
• Define scalar product of two vectors. Prove by vector method that $\cos(A-B)=\cos A\cos B+\sin A\sin B$. (2070)
• State the mean value theorem, interpret it geometrically, and verify it for $f(x)=x(x-1)^2$ on $[0,2]$. OR: Find from first principles th... (2070)
• (a) Two forces acting at $45^\circ$ have a resultant $\sqrt{10}$ N; if one force is $\sqrt2$ N, find the other. (b) Find two like paralle... (2070)
• (a) A body of weight $65$ N is suspended by two strings of lengths $5$ and $12$ m attached to two points in the same horizontal line $13$... (2070)
• A projectile thrown from a point on a horizontal plane returns to the plane in $4$ s at a distance $60$ m in front of the point of projec... (2070)
• Define moment of a force about a point. Prove that the algebraic sum of the moments of two like parallel forces about any point in their... (2070)

Frequently asked questions

Based on the official syllabus.