-1/2, 1., 1/2
1/2, 1, 1/2
1/2, 1, -1/2
1/2, -1, 1/2
Correct answer is A
This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2.
Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2
Evaluate (1/2 - 1/4 + 1/8 - 1/16 + ...) - 1
2/3
zero
-2/3
-1
Correct answer is C
S = a/(1-r), where a = 1/2, r = -1/2.
S = 1/2 3/2 = 1/2 x 3/2 = 1/3.
1/3 - 1 = -2/3
p
p -1
p/(p-1)
p/(p+1)
Correct answer is C
If P-1 is the inverse of P and O is the identity, Then P-1 * P = P * P-1 = 0
i.e. P-1 + P - P-1.P = 0
P-1 - P-1.P = -P
P-1(1 - P) = -P
P-1 = -P/(P-1)
= P/(P-1)
The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.
19x - 17y
8x - 4y
x - y
2x
Correct answer is C
n = 3, U\(_3\) = 4x - 2y,
U\(_n\) = a + (n-1)d,
4x - 2y = a + 2d... (1)
U\(_9\) = 10x - 8y,
10x - 8y = a + 8d... (2)
Solving (1) and (2),
subtract eqn i from ii
a-a + 8d - 2d = 10x -4x - 8y- (-2y)
6d = 6x - 8y+ 2y.
6d= 6x - 6y
6d = 6( x-y)
d = x - y
A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a.
1, -1
1, 2
2, -2
1, -2
Correct answer is D
a * b = a\(^b\)
a * 2 = a\(^2\) = 2 - a
a\(^2\) + a - 2 = 0
a\(^2\) + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2