1.

The period of the function f ( x )=sinnx is (2)

π 2π 3π
a) b) c) d) None of these
n n n
2. The period of the function f ( x )=sinx is (2)
a) π b)2 π c)3 π d) None of these

3. The function f ( x ) is called an even function if (2)

a) f (−x ) =−f ( x ) b) f (−x ) =f ( x )
c)Graph of f ( x ) is symmetrical about y −axis d) Both (b) and (c)

4. Which Is not an even function (1)

a) f ( x )=sin2 x b) f ( x )=x 2
c) f ( x )=x 4 d) f ( x )=co 3 x
5. If f ( x ) is an even function then (2)
π π π
a) ∫ f ( x ) dx=0 b)∫ f ( x ) dx=2∫ f ( x ) dx
−π −π 0
π π
c)∫ f ( x ) dx=∫ f ( x ) dx d) ¿
−π 0

6. If f ( x ) is an odd function then (3)

π π
a) ∫ f ( x ) dx=0 b)∫ f ( x ) cosnx dx=0
−π −π
π
c)∫ f ( x ) sinnxdx=0 d) Both ( a ) ∧(c )
−π

7. Fourier series is an infinite series representation of (3)

a) Periodic function in terms of logarithmatic functions
b) Periodic function in terms of exponential functions
c) Periodic function in terms of trigonometric functions
d) All of these
8. The Euler formula of a n for the function f ( x ) in the interval [ c , c+2 π ] is (1)
c+2 π c +2 π
1 1
a) a 0=
π
∫ f ( x ) dx b)a 0=
2π
∫ f ( x ) dx
c c
c+2 π c+2 π
2 2
c)a 0=
π
∫ f ( x ) dx d) a 0=
3π
∫ f ( x ) dx
c c

9. Fourier series expansion of an even function f ( x ) will contain

a) Sine terms only b) Cosine terms only
c) Sine and Cosine terms both d)All of these
10. The value of b n in the Fourier series expansion of the function f ( x )=x ,−π < x < π is
2 2 2 2
a) (−1 )n +2 b) (−1 )n c) (−1 )n−1 d) ) (−1 )n +1
n n n n

11. Fourier series for the function f ( x ) in the interval [ c , c+2 π ] is……………..
12. If f ( x ) is an odd function, then Fourier series of the function f ( x ) in the interval [ −π , π ] is ……
13. The value of b n in the Fourier series expansion of the function f ( x )=| x| ,−π < x <π is ………

14. The value of f ( 0 ) in the Fourier series of the function f ( x )= {−x , 0< x <π
x ,−π < x <0
is ………..

15. The Fourier Transform of a conjugate symmetric function is always

a) Imaginary b) Conjugate anti-symmetric
d) Real d) Conjugate symmetric

16. The finite fourier sine transform of

p p +1
1−(−1 ) (−1 ) p (−1 ) p+1 1−(−1 )
a) b) c) d) )
p p p p
17. Afddsfaf
18.
19. sdfgasga
Set -1 objective questions

1. The Euler formula of a n for the function f ( x ) in the interval [ c , c+2 π ] is (1)
c+2 π c +2 π
1 1
a) a 0=
π
∫ f ( x ) dx b)a 0=
2π
∫ f ( x ) dx
c c
c+2 π c+2 π
2 2
c)a 0=
π
∫ f ( x ) dx d) a 0=
3π
∫ f ( x ) dx
c c

2. The function f ( x ) is called an even function if (2)

a) f (−x ) =−f ( x ) b) f (−x ) =f ( x )
c)Graph of f ( x ) is symmetrical about y −axis d) Both (b) and (c)

−ax
e
3. The Fourier sine transform of is
x

a) tan
−1
( p2 ) b)cot ( 2p ) c) cos ( p2 ) d)sin ( 2p )
−1 −1 −1

4. The infinite fourier transform of a function f ( x ) is

∞ ∞
a) F { f ( x ) }=F ( p ) =∫ f ( x ) e b) F { f ( x ) }=F ( p ) =∫ f ( x ) e
ipx −ipx
dx dx
−∞ −∞

∞ ∞
c) F { f ( x ) }=F ( p ) =∫ f ( x ) e d) F { f ( x ) }=F ( p ) =∫ f ( x ) e
i( p−t )x i( p+ t) x
dx dx
−∞ −∞

5. Example for Transcendental equation is (b)

a) x 2−logx−12=0 b) x 3 +2 x 2 + x +1=0

c) x 3−3 x−5=0 d) x 3−5 x+ 1=0

6. The Newton- Raphson method fails when (b)

 a) f ' ( x ) is negative b) f ' ( x ) is zero c) c) f ' ( x ) is toolarge d) Never fails

7. The relation between E∧∆ is (3)

a) ∆=E+1 b) E=∆−1c) c) ∆=E−1 d) E=1−∆

8. The following formula is used for unequal intervals of x values (b)

a) Newtons farward foumula b) Lagranges formula c) Gauass formula d) Newtons backward fomula
10
dx
9. The value of ∫ by trapezoidal rule (taking n=4) is (1)
1 x

a)2.3788 b)2.2221 c)2.2988 d)1.9999

1 rd
dx 1
10. The value of ∫ by by simpson’s rule (taking n=4) is (d)
0 1+ x 3

a)0.999 b)0.6123 c)0.7145 d)0.6931

11. Fourier series for the function f ( x ) in the interval [ c , c+2 π ] is……………..
12. If f ( x ) is an odd function, then Fourier series of the function f ( x ) in the interval [ −π , π ] is ……
13. State the Infinite Fourier Sine transform is ………
14. Write the function of finite Fourier cosine transform is………………..
15. The real root of the equation 5 x−2 cosx−1=0 (upto two decimal accuracy) is …….
2
16. Evaluate ∆ y 0 … … . .
17. State the Newton’s Forward Interpolation Formula……
18. State the Lagranges Interpolation Formula……
rd b
1
19. By Simpson’s Rule ∫ f ( x ) dx=… … ..
3 a
4
20. The value of ∫ logxdx calculated using the Trapezoidal rule with five subintervals is 1.7533
2.5

Set 2 objective questions

1. The period of the function f ( x )=sinx is (2)

a) π b)2 π c)3 π d) None of these

2. The function f ( x ) is called an odd function if (1)

 a) f (−x ) =−f ( x ) b) f (−x ) =f ( x )
c)Graph of f ( x ) is symmetrical about y −axis d) Both (b) and (c)

3. The finite fourier sine transform of (c)

p p +1
1−(−1 ) (−1 ) p (−1 ) p+1 1−(−1 )
a) b) c) d) )
p p p p

4. Fourier sine Transform of f ( x )=x is ….

a) 2 b)0 c)1 d) 3

5. If first two approximations x 0 and x 1 are 0 and 1 by bisection method then x 2 is

a)0.5 b)0.25 c) 0.125 d) 1

6. ∆ is called

a)Displacement Operator b)Forward Difference operator

c) Backward differenc e operator d) A veraging operator

7. ∆ [ f ( x ) ] =¿

a) f ( x )−f ( x−h ) b) f ( x +h ) c) f ( x−h )−f ( x ) d) f ( x−h )

8. A linear version of the Lagrange’s Interpolation for f ( x )

a)
( x−x 0
x 0−x 1)f ( x 0 )−
(
x−x 0
x 0 −x1 )
f ( x 1 ) b)
(
x−x 0
x 0−x 1 )
f ( x0)+
x −x 0
x 0−x 1(f ( x1)
)
c)
( x−x 0
x 0−x 1 )
f ( x 0 )−
( )
x −x0
x−x1
f ( x1 ) d)
x−x 0
x 0−x 1(f ( x0)+
)x −x 0
x 1−x 0 (
f ( x1)
)
1
9. The value of ∫ x dx by trapezoidal rule (taking n=4) is
3

a)0.26 b)0.78 c)0.453 d)0.69

2 rd
1 1
10. The value of ∫ dx by Simpson’s Rule (taking n=4) is
1 x 3

a)0.364 b)0.693 c)0.347 d)0.259

1. Half Range Fourier Sine series for the function f ( x ) in the interval [ 0 , π ] is……………..
2. If f ( x ) is an Even function, then Fourier series of the function f ( x ) in the interval [ −π , π ] is ……
3. Write the fuction of Infinite Fourier Cosine transform is ………
4. Write the function of Inverse finite Fourier cosine transform is………………..
5. The real root of the equation 3 x=cosx+1 by bisection method(in two decimal places)…….
3
6. Evaluate ∆ y 0 … … . .
7. State the Newton’s Backward Interpolation Formula……
8. State the Gauss Forward Interpolation Formula…..
b
9. By Trapezoidal Rule ∫ f ( x ) dx=… … ..
a
th
3
10. Simpson’s Rule States…..
8