Show that the sequence < a_{n}> defined by
a_{n} =4n+5 is an A.P. also its common difference is
The number of committees of two or more, that can be selected from 6 people is
57.
If A, B, C be three sets such the A B = A C and A B = A C, then
B = C.
R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0), (0, 2), (0, 1)}
1/2a.
If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function described by the formula, g (x) = x + then the values of and are
α = 2, β = – 1.
The imaginary part in (3 + 2i)(1 – 4i) is _____.
(3 + 2i)(1 – 4i) = 3 – 12i + 2i – 8i^{2}
= 3 – 10i – 8(–1)
= 3 – 10i + 8
= 11 – 10i
The imaginary part in (3 + 2i)(1 – 4i) is –10.
The value of i^{9} – i^{19} is _____.
i^{9} – i^{19 }= i^{4}.i^{3} – (i^{4})^{4}i^{3}
= 1(–i) – (1)^{4}(–i) [Since i^{4} = 1 and i^{3} =  i]
= 0
The value of i^{9} – i^{19} is 0.
The derivative of x^{3}(x – 3)^{2} is ______.
Given that A = 2, B = 5, C_{1} = 7 and C_{2} = 5.
2x = 5 and x  y = 0
x = 5/2 and x = y
Thus x = y = 5/2.
Find the length of normal on the line x – y = 5.
Since the directrix is x = 2 and the focus is (2, 0), the parabola is to be of the form
y^{2}= 4ax with a = 2.
Hence the required equation is : y^{2}= 4(2)x = 8x.
Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, 8) is divided by the XZplane.
Find the distance between (2, 1, 3) and (2, 1, 3).
Find the distance of the point (5,2) from the line 7x  2y + 3 = 0.
The perpendicular distance (d) of a line Ax + By + C = 0 from a point
(x_{1} , y_{1}) is given by :
1. A' = {x : x is an odd natural number}
2. B' = {x : x N, x 2}
3. C' = {x : x N and x < 7}
4. D' = {x : x is a composite number}
If , then find the least positive integral value of m.
(a) If the 3 students join the excursion party then the number of combinations will be C_{1}= C(12, 7)
(b) If the 3 students do not join the excursion party. Then the number of combinations C_{2}= C(12, 10)
If C is the combination of choosing the excursion party, then
I (5 questions) II (7 question)
(a) 3 5
(b) 4 4
(c) 5 3
If P is the required number of ways, then
B_{1}, B_{2}, B_{3}, B_{4}, W_{1}, W_{2} and W_{3} respectively.
Case 1: When the coin shows a tail, a ball is drawn from a box containing 4 black and 3 white balls
Sample space, S_{1 }= { TB_{1}, TB_{2,} TB_{3,} TB_{4,} TW_{1,} TW_{2, } TW_{3}}
Case 2: When the coin shows a head, a die is thrown which can have any outcome between 1 and 6.
Sample space, S_{2} = { H1, H2, H3, H4, H5, H6 }
Total Sample Space, S = { TB_{1}, TB_{2,} TB_{3,} TB_{4,} TW_{1,} TW_{2, } TW_{3,} H1, H2, H3, H4, H5, H6}.
a = 4.
Focus is at (4, 0).
Equation of the directrix is : x =  4.
Length of latus rectum = 4a
= 4(4)
= 16.
x^{2}/a^{2} + y^{2}/b^{2 }=1
Since the points (2, 1) and (1, 3) lie on the ellipse, we have
Prove that
Class  010  1020  2030  3040  4050  5060 
Frequency  7  15  6  16  2  4 
Class  Frequency, f  Cumulative Frequency(c.f)  Midpoint,x 
 
010  7  7  5  20  20  140 
1020  15  22  15  10  10  150 
2030  6  28  25  0  0  0 
3040  16  44  35  10  10  160 
4050  2  46  45  20  20  40 
5060  4  50  55  30  30  120 
 50 



 =610

The classinterval containing (N/2)^{th }or 25^{th} item is 2030. Therefore, it is the
median class.
Here, l = 20, N = 50, C = 22, f= 6 and h = 10
= 20+{(50/2  22)}/6 10=25
M.D.( ) = = 610/50= 12.2
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