Download Practice Paper - 2 1. Simplify, , Or Show that tan 70 = 2 tan 50 +

Practice Paper - 2
1.
2.
3.
4.
5.
6.
7.
8.
 3

cos     sec2 
   tan  2   
 2

Simplify,
, Or Show that tan 70 = 2 tan 50 + tan 20
 3

sin     cot 
 
 2

Using principle of mathematical induction, prove that 23n – 1 is divisible by 7, for all n  N.
If r1, r2 are the roots of the equation x2 + px + q = 0 such that r1 – r2 = 1, prove that p2 = 1 + 4q.
If 16Cr = 16Cr+2, find rC3
In how many ways can 4 men and 4 women sit together so that women do not sit together ?
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and
nth terms is (2m – 1) : (2n – 1)
The girder of a railway bridge is a parabola with its vertex at the highest point, 10m above the
ends. If the span is 100 m, find the height at 20 m from the mid point.
Find the left hand limit of the function defined by f  x   5  x as x  5. Does the right hand
ax  tan x
x 0 b sin x
100
99
x
x
x2
For the function, f  x  

 ...... 
 x  1 , show that f′(1) = 100 f′(0)
100 99
2
If is known that person A is rich and person B is poor, assign the truth values to the following
statements :
(i) person A is poor
(ii) Person B is rich
(iii) person A is poor or person B is poor
(iv) person A is rich and person B is rich
An urn contains 5 blue and an unknown number x of red balls. Two balls are drawn at random. If
the probability of both of them being blue is 5/14. Find x.
Given two real numbers x and y, such that 0 ≤ x, y ≤ 2. Find the probability that x2 + y2 ≤ 1.
Write all the possible subsets of A = {a, b, c}
Show that the following four conditions are equivalent
(i) A  B
(ii) A – B = 
(iii) A  B = A (iv) A  B = B
If A = {a, b}, B = {b, c} and C = {0}, form the set A  B  C
For the functions f(x) = ax + b, f(-1) = -5 and f(3) = 3, find a and b. Or
4 x
Find the domain and range of the function, f  x  
x4
Prove that, cos2 A + cos2 (A + 120) + cos2 (A – 120) = 3/2
Show that z1  z2  z1 z2 , for z1, z2  C. Or
i 1
Write the complex number z 
in polar form.


cos  i sin
3
3
Solve, 4x – y > 0, graphically.
5 men and 4 women are to be seated in a row so that women occupy even places. How many
such arrangements are possible ?
If the sum of two arithmetic progressive are in the ratio 14 – 4n; 3n + 5, find the ratio of their 8th
terms.
ABCD is a parallelogram. The coordinates of A, B, C are (2, 3), (1, 4) and (0, -2) respectively. Find
the coordinates of D.
Solve for  : tan  + tan 2 + tan 3 = tan  tan 2 tan 3.
limit exists as x  5. Or Evaluate, lim
9.
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23.
FTM-02
Page 1
9
24.
25.
26.
x 5 
Find the 4 tem from the end, in the expansion of   2 
5 x 
Or
Find the coefficient of a5b7 in (a – 2b)12.
Find the distance of origin from the line 3x  y  2  0
Or
Show that the line 3x + 3y + k = 0 passes through the point of intersection of 3x + 4y = -6 and
6x + 5y – 9 = 0, if k = -1
Find mean derivative about median for the following data :
C.I
31-35
36-40
41-45
46-50
51-55
56-60
61-65
66-70
f
2
3
8
12
16
5
2
2
th
ANSWERS
1. cot  cosec 
4. 35
7. 8.4 m
a 1
8. 0; does not exists Or
b
2
10. (i) False
(ii) False
(iii) True
5. 2880
(iv) False
11. 3
12.

16
13. , {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}
15. {(a, b, 0), (a, c, 0), (b, b, 0),(b, c, 0)}
16. a = 2, b = -3 or Domain : R – {4}; Range : {-1}.
5 
23
 5
18. Or 2  cos
20. 2880
21. 
 i sin 
12
12 
25

10500
22. (1, -3)
23.  = n/3, n  I
24.
Or  10,1376
x9
25. 1
26. 14.7
FTM-02
Page 2