MATHS TEST PAPER
XI –: (SET – B)
TRIGONOMETRY, PMI & COMPLEX NUMBER
Max. Marks : 100
Time : 3 hrs
Each question carries 1 mark
7
1.
Convert 1 Radians into degree, minutes & seconds.
2.
Find the value of cos(17100 )
3.
4.
Convert (-35 / 2) Radians into degree measure.
Find the value of tan( / 8)
5.
Derive the formula of cos A – cos B.
6.
Express Z 
7.
For what values of x is
8.
Solve : x 2  2  0
9.
If z = a + ib is any non zero complex number, then find the value of Arg (z) + Arg (Conjugate of z)
10.
Find modulus and argument of 2 3  2i .
( 2  5)
in the form a + ib.
(1  2)
5x 2  x  5  0.
Each question carries 4 marks
11.




Evaluate : cos 2 x  cos 2  x    cos 2  x  
3
3


cos 2 33  cos 2 57
 2
2 21
2 69
sin
 sin
2
2
13. Find the value of tan ( / 8).
12.
Prove that
14.
Show that tan3x tan 2x tan x  tan 3x  tan 2x  tan x
15.
Prove that sin 3x  sin 2x  sin x  4sin x cos cos
16.
If cos (  ) sin (  )  cos ( ) sin (  ), prove that cot  cot  cot   cot .
17.
Find the modulus & Argument of the given complex no & convert it to polar form. Z 
18.
 x y  x y 
If (x  iy)1/3  (a  ib), then find the value of     
 a b  a b 
x
2
3x
2
i 1


cos  i sin
3
3
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3  2i sin 
is purely real.
1  2 i sin 
19.
Find real  such that
20.
1 1 1
1
1
Prove that 1     ...  2  2  for all n  2, n  N.
4 9 16
n
n
21.
Prove that 1.3  35  5.7  .....  (2n  1) (2n  1) 
22.
1 
1 
1 
1  n 1

Prove that 1  2 1  2 1  2  ... 1  2  
for all natural numbers, n  2.
 2  3  4   n  2n
n(4n 2  6n 1)
3
Each question carries 6 marks
sin 7x  sin 9x  sin 5x  sin 3x
23. Prove that
 tan 6x
cos 7x  cos9x  cos5x  cos3x
24.
Express cos 6x in terms of cos x only.
25.
Find the general solution of the equation : sin x  sin 3x   sin 5x.
26.
Find the modulus & Argument of the given complex no & convert it to polar form. Also write its polar
Coordinates. Z 
27.
28.
8
920
578 

(4i  4) cos
 i sin
12
51 

(i)
If a & b are different complex numbers with | b | = 1, Then find
(ii)
If x + i y =
| ba |
|1  ab |
(a  i b)
, then find the value of (x 2  y2 ).
(a  i b)
Using principle of Mathematical Induction, prove that for all natural nos n  1
n(4n 2  6n 1)
.
3
29. Using Principle of Mathematical Induction, Prove that for all natural nos n  1
1.3  3.5  5.7  .....  (2n  1) (2n  1) 
1
1
1
1
2n

 ...................... 

(1  2) (1  2  3)
(1  2  3  ......n) (n  1)
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