Show that the sequence < an> defined by
an =4n+5 is an A.P. also its common difference is
In the Venn diagram shown below, (A B C)' =
{}.
R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0), (0, 2), (0, 1)}
1/2a.
The value of 0! × 2! × 3! is ____.
0! × 2! × 3! = 1× (2 × 1) × (3 × 2× 1)
= 12
The value of 0! × 2! × 3! is 12.
There are 4 elements in a set A and 5 elements in the set B, then there will be ___ elements in A × B.
It is given that n(A) = 4
and n(B) = 5
Therefore, n(A × B) = 4 × 5
= 20
There are 4 elements in a set A and 5 elements in the set B, then there will be 20 elements in A × B.
The imaginary part in (3 + 2i)(1 – 4i) is _____.
(3 + 2i)(1 – 4i) = 3 – 12i + 2i – 8i2
= 3 – 10i – 8(–1)
= 3 – 10i + 8
= 11 – 10i
The imaginary part in (3 + 2i)(1 – 4i) is –10.
The value of i9 – i19 is _____.
i9 – i19 = i4.i3 – (i4)4i3
= 1(–i) – (1)4(–i) [Since i4 = 1 and i3 =  i]
= 0
The value of i9 – i19 is 0.
The derivative of x3(x – 3)2 is ______.
Here,
where n is any integer.
Here,
where n is any integer.
Given that A = 2, B = 5, C1 = 7 and C2 = 5.
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
(x1 , y1) 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 C1= C(12, 7)
(b) If the 3 students do not join the excursion party. Then the number of combinations C2= 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
B1, B2, B3, B4, W1, W2 and W3 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, S1 = { TB1, TB2, TB3, TB4, TW1, TW2, TW3}
Case 2: When the coin shows a head, a die is thrown which can have any outcome between 1 and 6.
Sample space, S2 = { H1, H2, H3, H4, H5, H6 }
Total Sample Space, S = { TB1, TB2, TB3, TB4, TW1, TW2, TW3, 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.
x2/a2 + y2/b2 =1
Since the points (2, 1) and (1, 3) lie on the ellipse, we have
Prove that
The sum and sum of squares corresponding to height x (in cm) and weight y (in gram) of 50 plant products are given below:
Which is more varying, the height or weight?
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 25th 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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