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E - TEST
CLASS: XI A
SUB: MATHEMATICS
Instructions:
1.All questions are compulsory.
2 Question numbers 1 to 4 are of 1 marks each.
3.Question numbers 5 to 10 are of 4 marks each.
4.Question numbers 11and 12 are of 6 marks each.
TIME: 90 Minutes
Max.Marks:40
SECTION - I
1. Find the principal solution of cosecx = -2
2. Find tan 750 .
3. Find the value of
i99 + i100 + i101 + i102.
4. If
n
c3  n c 2
then find n.
SECTION - II
5. Find the general solution of Cos 3x + cos x – cos 2x = 0
6. Prove by induction that 3 4n+1 + 2 2n+2 + 2 is divisible by 7.
4n 2  1
2
2
2
2
7. 1 +3 + 5 + ---+ (2n-1) = n (
)
3
1  7i
8. Convert the following in the polar form
(2  i) 2
9. Solve the following system of in equations graphically.
x + 2y  3 3x + 4y  12, x  0, y  0
10. (a). How many words, with or without meaning, each of 2 vowels and 3
consonants can be formed from the letters of the word DAUGHTER.
(b). How many natural numbers less than 1000 can be formed with the
digits1,2,3,4,5
If no digit is repeated.
SECTION - III
21
and  lies in the second quadrant,
29
5
show that sec  + tan  = - .
2
x y
(b). (Cosx – cos y)2 + (sinx – sin y)2 = 4 sin2 (
)
2
12. (a). In how many ways can one select a cricket team of 11 from 17 players in
which
only 5 players can bowl if each cricket team of 11 must incluye exactly 4
bowlers.
(b). A bag contains 5 black and 6 red balls. Determine the number of ways in
which 2 black and 3 red balls can be selected.
11. (a) . If sin  =