MCQs-Short_Questions_Math_FSc_Part2.pdf

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  1 Downloaded from http://www.MathCity.org   MathCity.org Merging man and maths  MCQs-Short Question: Maths-II   Calculus and Analytic Geometry, MATHEMATICS 12 Available online at http://www.mathcity.org, Version: 1.0.0 UNIT NO 1 (FUNCTIONS AND LIMITS) I.   CHOOSE THE CORRECT ANSWERS. 1. Domain of 1/x is …………… (a) R (b) {0} – R (c) R – {0} (d) N 2. If f(x) = 1/x then f -1  = ……….. (a) x (b) 1/x (c) 1/x 2 (d) None  ____ 3. y =   x – 1 is an ………….. function (a) Even (b) Explicit (c) Odd (d) Implicit 4.   Cosec h x = ………………. (a) e x  – e  –x  (b) 2__ (c) e x + e  –x  (d) 2__ 2 e x  – e  –x  2 e x  + e -x  5. Cos x is an …….. function. (a) Explicit (b) Implicit (c) Odd (d) even  ___ 6. If f(x) = 1/x 2  g(x) =   x then fog = ………..  ___ __ (a)   x (b) 1/   x (c) x (d) 1/x 7.   Lim a/x = …… where a € IR x !  (a) a (b) x (c) !  (d) 0 8.   Lim (1+2h) 1 / h  = …………… h 0 (a) 1 (b) 0 (c) e (d) e 2  9. Lim ( 1 + m ) 1 / m  = ……….. m !  (a) e (b) 0 (c) !  (d) e m    2 Downloaded from http://www.MathCity.org  10. Lim Sin7  = ………….  0  (a) 7 (b) 1 / 7 (c) 0 (d) !  11. Lim Cos  = ………..  0  (a) 0 (b) 1 (c) !  (d) None 12. Lim Sinx = …………. x 0 7x (a) 1 (b) 7 (c) 1/7 (d) 0 13. If x = 10 y  then y = ……… (a) ln 10 (b) ln x (c) ln 1 (d) e 14. If 4 x = 1 then x = …………. (a) 0 (b) 1 (c) 2 (d) 4 15. If 2 x + 3 y  = 13 then x + y =………… (a) 4 (b) 5 (c) 6 (d) 7 16. # x - 5 #  = x – 5 If……….. (a) x = 5 (b) x > 5 (c) x < 5 (d) x $  -5 17. Lim Sin 0  = ………………    0 (a) 0 (b) 1 (c) %  / 180 (d) 180/ %  18. Lim  __ = …………………….  0 Sin    (a) Undefined (b) 0 (c) 1 (d) None  3 Downloaded from http://www.MathCity.org  19. If 3 x  + 3 y  = 3 then x + y = ………………. (a) 0 (b) 1 (c) -1 (d) 2 20. Tan x is an ………… function. (a) Even (b) Odd (c) Explicit (d) Implicit 21. Sin h x =…………………… (a) e x + e  –x  (b) e x  + e  –x  (c) e x  – e  –x  (d) e x  – e -  2i 2 2i 2 22. Lim 1_ x - !  e  –x  (a) 0 (b) 1 (c) - !  (d) !  23. Lim (1 + 3/n)  2 n  = ………………. n !  (a) e (b) e 2  (c) e 4  (d) e 6  24. lnx is not defined at x = ………………. (a) 0 (b) 1 (c) e (d) None 25. If f(x, y) = 0 then f is called an……function. (a) Even (b) Odd (c) Explicit (d) Implicit  Written by : Mr. Parvez Khan Composed by : Momin Ali Fazaia Degree College, Peshawar.    4 Downloaded from http://www.MathCity.org   SHORT QUESTIONS 1. Show that the parametric equation x = a Cos t and y = a Sin t represent the Circle x 2  + y 2  + = a 2 . 2. Prove that Cos h 2 x – Sin h 2 x = 1 3. Determine whether f(x) = x 2/ 3 + 6 is even or odd. 4. If f(x) = ( - x + 9 ) 3  ; verify f [f -1  (x)] = f -1  [ f (x)] = x 5. Show that Limit x n  – a n  = n a n -1  x a x - a  ____ _ __ 6. Show that Limit  x + a -  a = 1/ 2  a x 0 x  __ _ 7. Evaluate Limit x – 3  / (  x -  3 )  x 3 8. Show that Limit ( 1 + 1/n) – e where 2 < e < 3 x !  9. Show that Limit a x  – 1 = lna x 0 x 10. Evaluate Limit ( 1 + 3 / n ) 2n x !  11. Evaluate Limit x n  – a n  x a x m  – a m  12. Evaluate Limit Sin x 0  x 0 x
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