2nd Year Maths Past Paper

All Solved 2nd Year Maths Past Paper written by Honorable Professor Mr. Adnan Haider Suib. These notes are very helpful in the preparation of 2nd Year Maths Past Paper of all Punjab Boards (Faisalabad Board, Gujranwala Board, Lahore Board, Multan Board, Rawalpindi Board, D.G. Khan Board, Bahawalpur Board, Sargodha Board, Sahiwal Board ) for the students of the Intermediate part-I and these are according to the paper patterns of all Punjab boards.

Summary and Contents:

Topics which are discussed in the notes are given below:

Here are the detailed 2nd Year Math Past Papers to help you prepare for your exams.
1-1. If y = √1-x2, 0 < x < 1 then dy/dx =
(A) √x²-1
(B) 1/ √x²-1
(C) x/ √1-x2
(D) -x/ √1-x2
2. Integral 3^x dx =
(A) 3^x+c
(B) 3^x ln3+c
(C) 3^x/ln3 +c
(D) 3 ln3^x+c
You can also download the 2nd Year Math Past Paper for free.
3. π/2 Integral cos x dx =
(A) 0
(B) 1
(C) 2
(D) 3
4. If f(x) has second derivative at "c" such that f'(c) = 0 and f"(c) <0 then "c" is a point of:
(A) Maxima
(B) Minima
(C) Zero point
(D) Point of inflection
If you're looking for comprehensive Past Paper 2nd Year Maths, you've come to the right place.
5. If y=e^sinx, then dy/dx =
(A) e^sin x
(B) e^sin x cos x
(C) e^sinx+cosx
(D) - e^sin x cos x
6. cosh²x-sinh²x =
(A) 1
(B) -1
(C) 0
(D) 2
7. d/dx sin^-1 x =
(A) 1 /√1 + x2
(B) cos^-1 x
(C) 1 /√1 - x2
(D) 1 /√1 - x
8. Integral 1/f(x) x f'(x)dx =
(A) lnx+c
(B) ln [f'(x)+c]
(C) 1/f(x)+c
(D) In|f(x)| + c
9. The order of the differential equation d^2y/d^x2 - dy/dx +2x=0 is
(A) 2
(B) 1
(C) 0
(D) 3
This 2nd year math past papers punjab board for all students.
10. Let f(x) = x² + cosx, then f(x) is:
(A) Odd function
(C) Even function
(B) Constant function
(D) Neither even nor odd
11. The centroid of a triangle divides each median in ratio:
(A) 2:1
(B) 1:2
(C) 2:3
(D) 1:1
12. The straight line y=mx+c is tangent t to the ellipse x^2/a^2 + y^2/b^2=1 if:
(A) c²= a² m²-62
(B) c² = b² m² + a²
(C) c² = b² m²-a
(D) c² = a² m² + b²
13. The perpendicular distance of line 3x+4y-100 from the origin is:
(A) 0
(B) 1
(C) 2
(D) 2
14. Axis of the parabola x² = 4ay is:
(A) y=0
(B) x=0
(C) x=y
15. cos a sin a If a is the inclination of the line then x-x1/cosa = y-y1/sina = r (say) is called:
(A) Point slope form
(C) Symmetric form
(B) Normal form
(D) Intercept form
16. The direction cosines of y-axis are:
(A) (0,1,0)
(B) (1,0,0)
(C) (0,0,1)
(D) (0,0,0)
17. If a is the inclination of a line "l" then it must be true that:
(C) 0 ≤ α < π
(A) 0≤a< 2
(Β) α<π 2
(D) (0,0,0)
(D) 0<= α < 2π
18. The equation x^2 + y² + 2gx +2 fy + c = 0 represents a circle with centre:
(B) (-f,+g)
(A) (-g,-f)
(C) (f,g)
(D) (0,0)
19. Length of the vector 2i-j-2k is:
(A) 2
(B) 4
(C) 3
(D) 5
20. The feasible solution which maximizes or minimizes the objective function is called:
(A) Exact solution
(B) Optimal solution
(C) Final solution
(D) Objective solution
2. Write short answers to any EIGHT (8) questions:
(i) State sandwitch theorem.
(ii) Express the area " A " of a circle as a function of its circumference "C".
(iii) If f(x) = x+2, x≤-1 c+2, x>-1 , find "c" so that Lim f(x) exists x-1
(iv) Define differentiation.
(v) Differentiate (√x- 1/√x)^2 with respect to 'x'
(vi) Find dy/dx if xy + y² = 0
(vii) Find dy/dx if y=x cos y
(viii) Prove that d/dx (cos^-1 x)= -1 /√1-x2, x belongs to (-1,1)
(ix) Find dy/dx if y=x e^sinx
(x) Define power series.
(xi) Find extreme values for f(x) = x²-x-2
(xii) Find dy/dx if y = sinh^-1 (x/2)
3. Write short answers to any EIGHT (8) questions:
(i) Find dy/dx using differentials if xy - loge x = c
(ii) Evaluate the integral x/x+2 dx
(iii) Evaluate the integral 1/a^2 - x^2 dx
(iv) Evaluate the integral x sin x cos x dx
(v) Evaluate the integral x²e^ax dx
(vi) Evaluate the integral e^3x( 3sinx-cosx/sin^2x) dx
(vii) Prove that f(x).dx=-f(x).dx
(viii) Evaluate the definite integral dx/x²+9
(ix) Find the area bounded by cos function from x = -pi/2 to x = pi/2

Loading your document...

Download PDF