Multiplication of a two digit number with Eleven

Its very easy to multiply any two digit number by eleven once you know the secret. Consider the following problem.

                                                                   12 x 11

To solve this simple add the digits, 1+2 = 3, put the 3 between 1 and 2, and there is your answer:
                                                                      132
Consider another problem:

                                                                   35 x 11

Since 3+5=8, your answer is simply

                                                                      385

Now do this in you mind. 
                                                                   45 x 11

Now let us move to a bit complex problem. Suppose the problem is

                                                                  76 x 11

Although 7+6 = 13, the answer is NOT 7136!
As before, the 3 goes in between the numbers, but the 1 needs to be added to the 7 to get the correct answer i.e 1 will be moved as carry to the next digit. So the answer will be
                                                                     836
Similarly , 
                                                                  88 x 11 
will give ans  
                                                                     968

Take a moment to practice this skill a few times. You have to practice these tricks otherwise you will forget them very soon. Whenever you find some free time take a pen and a paper and make problems by your own and solve them. This first lesson is much easier while the problems will become complex after a few days so for that you need practice. The more you will practice the better you will be at mental calculations.

The answer to the problem 45 x 11 is 495.

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Papers of Math

1 ) Bahawalpur Board Math 2010-Part 2
2) Bahawalpur Board Math 2009-Part 2 (Group 1)
3) Bahawalpur Board Math 2009-Part 2 (Group 2)

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Bahawalpur Board 2009 maths Part 2 Group 2

1) ( e2x - 1 )/ 2ex equals a) Sin x b) Sinh x c) Cos x d) Cosh x 2) Limn→∞ (1 - 1/n)n equals: a) e b) e2 c) e-1 d) e-2 3) d/dx [x(x-3)] equals: a) 2x - 3 b) 3x - 2 c) 2x + 3 d) 3x - 2 4) (d/dx(Sin x))2 + (d/dx(Cos x))2 equals: a) -1 b) 1 c) 0 d) 2 5) If y=Cos(π/2 - x) , then y2 equals: a) -Sin x b) Sin x c) Cos2x d) -Cos x 6) ∫ cosec2x equals: a) Cot x + c b) -Cot x + c c) -2Cosec x + c d) 2Cosec x + c 7) ∫ esin x . Cos x equals: a) esin x + c b) ecos x + c c) -esin x + c d) - ecos x + c 8) ∫ Sec2 dx with limits 0 to π/4 equals: a) 0 b) -1 c) 1 d) 2 9) ∫ 1/√(1-x2) dx with limits 0 to 1 is equal to a) π/6 b) π/4 c) π/3 d) π/2 10) The solution of differential equation dy/dx = 1/1+x2 is: a) y = Sin-1x + c b) y = Sec-1x + c c) y = Tan-1x + c d) y = Cot-1x + c 11) The midpoint of the line through two points (-1,-4) and (-1.0) is : a) (-1,-2) b) (-2,-2) c) (-1,2) d) (-1,0) 12) The slope of the line parallel to 2x - 7y + 4 = 0 is: a) -7/2 b) 7/2 c) 2/7 d) -2/7 13) The angle between two lines represented by x2 - 2xy + y2 = 0 is: a) π/2 b) 0 c) π/4 d) π/3 14) The radius of the circle x2 + y2 = 5 equals: a) 5 b) 25 c) 5/2 d) √5 15) The length of the tangent from point (0,1) to circle x2 + y2 + 8 = 0 equals a) 3 b) 8 c) 4 d) √3 16) The focus of the parabola x2 = 4(y-1) equals : a) (0,0) b) (0,2) c) (0,-2) d) (2,0) 17) The center of the ellipse (x+1)2/9 + (y-1)2/5=1 is: a) (-1,1) b) (1,-1) c) (1,1) d) (-1,-1) 18) Transverse axis of y2/a2 - x2/b2 = 1 is : a) y=0 b) y=a c) x=0 d) x=b 19) If | xi - j + k | = √6 , then x equals: a) ±2 b) ±3 c) ±1 d) 0 20) The value of (i x j) . k is a) 0 b) -1 c) 1 d) 2

Bahawalpur Board 2009 maths Part 2

1) If |AB x AC| = 9 , then the area of triangle ABC equals: a) 18 b) 9 c) 9/2 d) 27 2) A unit vector in direction of [3 , -4] is: a) [1/5 , 2/5] b) [-3/5 , 4/5] c) [-1/5 , 4/5] d) [3/5 , -4/5] 3) Vertices of hyperbola x2/16 - y2/4=1 are: a) (±2,0) b) (0,±2) c) (±4,0) d) (0,±4) 4) For an ellipse eccentricity is a) one b) less than one c) greater than one d) zero 5) Focus of parabola y2 = 8x is: a) (0,-2) b) (8,0) c) (2,0) d) (-8,0) 6) The length of tangent drawn from (1,2) to the circle x2 + y2 + 2x + 4y - 14 = 0 is: a) 1 b) √6 c) 4 d) 12 7) The center of the circle x2 + y2 + 12x -10y = 0 a) (6,5) b) (-6,5) c) (-6,-5) d) (6,-5) 8) if f(tx , ty) = tnf(x,y) then f(x,y) is a homogeneous function of degree: a) n-1 b) t c) n d) n + 2 9) Slope of line parallel to x axis is a) π/3 b) 1 c) 0 d) undefined 10) Distance of the point (1,2) from y axis is a) -2 b) 1 c) -1 d) 2 11) Order of differential equation y dy/dx + 2x = 0 is a) 3 b) 2 c) 1 d) 4 12) ∫ sec2x dx with limits 0 to π/4 is equal to: a) 0 b) 1/2 c) 1/4 d) 1 13) ∫ 1/x dx with limits 0 to 1 is equal to: a) 0 b) 1 c) ∞ d) -1 14) ∫ 1/xlnx dx equals: a) ln(lnx) + c b) lnx + c c) -lnx + c d) -ln(lnx) + c 15) ∫ tanx dx equals: a) ln|Cosx| + c b) -ln|Cosx| + c c) -ln|Secx| + c d) ln|Sinx| + c 16) f(x) decreases if: a) f'(x) = 0 b) f'(x) > 0 c) f'(x) ≥ 0 d) f'(x) < 0 17) d/dx ( Sin 1/x) is equal to a) 1/x Cos 1/x b) -1/x2Cos 1/x c) 1/x2Cos 1/x d) -1/x Cos 1/x 18) dy/dx for 3x + 4y + 7 = 0 is a) 1/4 b) 4/3 c) -4/3 d) -3/4 19) Limx→0 (ex - 1)/x equals: a) 0 b) 1 c) -2 d) 2 20) If f(x)=e2lnx, then f(0) is a) 0 b) 2 c) ∞ d) 1

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Bahawalpur Board Math 2010-Part 2

1) The volume of parallelepiped is equal to: a) ( u x v ) . w b) ( u x v ) x w c) u x ( v x w ) d) u x ( v x v ) 2) Two non- zero vectors u and v are parallel if a) u . v = 1 b) |u . v| = 1 c) u . v = 0 d) u . v ≠ 0 3) Which one is focus of parabola y2= 4ax a) (a,0) b) (-a,0) c) (0,0) d) (0,-a) 4) x2 + y2 + 2gx + 2fy = 0 represents : a)circle b) ellipse c) hyperbola d) parabola 5) eccentricity of ellipse x2 / a2 + y2 / b2 = 1 , a > b is a) a / c >1 b) ac < 1 c) c / a < 1 d) a / c2 > 1 6) the variables used in system of linear equalities are also known as a) constants b) constraints c) solutions d) corners 7) second degree homogenous equation is equal to a) ax2 + bx + c = 0 b) ax3 + bx2 + cx +d=0 c) ax+by+c=0 d) ax2 + 2hxy + by2 = 0 8) if line is parallel to x-axis then "α" is equal to a) 0o b) 90o c) 120o d) 150o 9) ∫ 1/√(1-x2) dx with limits 0 to 1 is equal to a) π/6 b) π/4 c) π/3 d) π/2 10) d3y/dx3 + 2d2y/dx2 + d/dx + y = 0 is the differential equation of the order a) 2 b) 3 c) 4 d) 5 11) ∫ e^x [ cosx + sinx ]dx is equal to: a) ex cosx + c b) ex sinx + c c) ex tanx + c d) ex cotx + c 12) ∫ sec2x / tanx dx is : a) ln tanx b) ln cotx + c c) cotx + c d) tanx + c 13) ∫ x^n dx where n ≠-1 is equal to: a) xn-1 / n-1 + c b) xn+1 / n+1 + c c) xn /n + c d) xn+2 / n+2 + c 14) the function f(x) = ax2 + bx + c = 0 has the minimum value if a) a > 0 b) a < 0 c) a > 1 d) a > 2 15) 1 – 1/2 +1/3 -1/4 + …… is the expansion of a) ln2 b) ln3 c) ln4 d) ln5 16) d/dx cos-1x is equal to a) 1 / √(1-x2) b) -1 / √(1-x2) c) 1 / √(x2-1) d) -1 / √(x2-1) 17) d/dx ( x + 1/x) is equal to a) 1 + 1/x b) 1 – 1/x2 c) x – 1/x2 d) x + 1/x2 18) ∫ cosx dx with limits 0 to π is : a) -2 b) -1 c) 0 d) 2 19) Area, surface area, volume etc deal with a) integral calculus b) differential calculus c) complex numbers d) infinite numbers 20) sinhx is equal to: a) [ ex + e-x ] / 2 b) [ ex – e-x ] / 2 c) [ ex - e-x ] / [ex + e-x] d) [ ex + e-x ] / [ex - e-x]

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