Question 1. 1x10= 10
i) (i¹⁸ + (1/i)²⁵)³ is
A) 1 B) -1 C) 1 + i D) 2(1- i)
ii) If one root of 2x² - 5x + k= 0 be double the other, find the value of k
A) 2 B) 7 C) 9 D) 25/9
iii) Which term of the series 5, 8, 11, ....is 320 ?
A) 106 B) 110 B) 100 D) 98
iv) How many 9-digits numbers of different digits can be formed?
A) 3298760 B) 3456890
C) 3265920 D) 345690
v) 2³ˣ -1 is divisible by
A) 5 B) 6 C) 7 D) 8
vi) Cos 83 - cos 17 =
A) sin 50 B) sin 33 C) sin 50 sin 33 D) - sin 50 sin 33
vii) If (x+3, y -5) = (5,0) then x and y are
A) 2,5 B) -2,5 C) 2, -5 D) - 2, -5
viii) If f(x)= √x , then the value of f(125)/{f(16)+ f(1)} is
A) 0 B) 1 C) 2 D) none
ix) lim ₓ→₁ {(x²-1)/(x-1)} is
A) 1 B) -1 C) 0 D) 2
x) dy/dx of 1/√x³ is
A) x B) x³ C) 2x³ D) none
Question 2 (2x10)= 20
i) Which term of the progression 19, 91/5, 87/5,......is the first negative term?
ii) Find the coefficient of x⁴ in the expansion of (x/2 - 3/x²)¹⁰
iii) Find the value of cos (15/2)°
iv) There are 3 copies each of 4 different books. Find the number of ways of arranging them on a shelf
v) Value of (cos 10+ sin 20)/(cos 20+ sin 10)
vi) Prove by Induction: 1+5+12+22 +35+....+ n/2 (3n-1)= n²(n +1)/2
Or
Solve: tanx + sec x =√3
vii) Find the domain and range of (4- x)/(x -4)
viii) lim ₓ→π/2 cotx/(π/2 - x).
ix) Find dy/dx with the help of 1st principal sin x
OR
Find dy/dx of cos(sin x²)
x) The angle between the lines whose slopes are -3 and -1/2
OR
Find the centre and radius of the circle of 2x² + 2y²= 3x - 5y +7.
Question 3 10x3 = 30
i) Solve: | 1 - i|ˣ = 2ˣ.
OR
If x be real, Prove that the value of (2x² - 2x +4)/(x² - 4x +3) can not lie between -7 and 1.
ii) The product of first three terms of a GP is 1000. If we add 6 to its second term and 7 to its third term, the resulting three terms form an AP. Find the terms of the GP.
iii) Find the number of words which can be formed by taking two alike and two different letters from the word COMBINATION.
iv) 2 cos a = x + 1/x , Prove 2 cos 2a = x³ + 1/x³
Or
v) Express cos 6x in terms of cos 3x
vi) Solve 3 - 2 cosx - 4 sinx - cos2x + sin2x = 0
vii) If f(x)= log {(1-x)/(1+ x)}, show that f(a) + f(b)= f{(a+ b)/(1+ ab)}.
OR
vii) If y = 1/(a - z) show that dz/dy = (z - a)²
ix) Find the equation of the line joining the origin to the point of intersection of 4x + 3y = 8 and x+ y = 1.
OR
Find the equation of the straight line which passes through the point (4,5) and is perpendicular to the line 3x - 2y +5= 0.
x) Find the Cartesian equation of the curve whose parametric equations is x= t, y= t².
OR
The point diametrically opposite to the point P(1,0) on the circle x² + y² + 2x + 4y - 3= 0 is
A) (3,-4) B) (-3,4) C) (-3,-4) A) (3,4)
Question 4. 4x 5 = 20
i) Two samples of sizes 50 and 100 are given. The mean of these samples are respectively 56 and 50. Find the mean of size 150 by combining.
ii) Find the standard deviations of
Class: 0-4 4-8 8-12 12-16
F: 4 8 2 1
iii) In Two factories A and B engaged in the same industrial area, the average weekly wages (in rupee) and the standard deviations are as follows:
Factory Average S.D workers
A 34.5 5 476
B 28.5 4.5 524
a) Which factory, A or B, pays out a larger amounts as weekly wages?
b) which factory, A or B, has greater variability in individual wages?
iv) Find the value of 8th decile and 75th percentile from the following:
Class. Frequency
10-14 3
15-19 7
20-24 16
25-29 12
30-34 9
35-39 5
OR
Determine the mode:
Marks No. Of students
00-10 5
10-20 12
29-30 14
30-40 10
40-50 8
50-60. 6
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