-3x2 - 17
-3x2 + 9x - 1
3x2 + 17
3x2 - 9x + 5
Correct answer is B
\(\begin{vmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4\end{vmatrix}\) = x\(\begin{vmatrix}2 & 3 \\ 1+x & 4\end{vmatrix}\) - \(\begin{vmatrix}1-x & 3 \\ 1 & 4\end{vmatrix}\) = 0
= x[8 - 3(1 + x)] - [4(1 - x)-3] - 0 = x[5 - 3x] - [1 - 4x]
= 5x - 3x2 -1 + 4x
= -3x2 + 9X - 1
-1
4
1
5
Correct answer is C
x \(\ast\) y = xy - y - x, x \(\ast\) 3 = 3x - 3 - x = 2x - 3
2 \(\ast\) x = 2x - x - 2 = x - 2
∴ 2x - 3 = x - 2
x = -2 + 3
= 1
p
q
r
s
Correct answer is B
The identity element (e) under an operation, say \(\otimes\), is the element such that for any given element under the operation, say a,
\(a \otimes e = e \otimes a = a\)
From the table, q is the identity element.
\(p \otimes q = q \otimes p = p\)
Same as all through.
\(\frac{1}{4}\)
\(\sqrt{\frac{3}{2}}\)
\(\frac{1}{\sqrt{3}}\)
\(\frac{1}{\sqrt{2}}\)
Correct answer is B
Let the G.p be a, ar, ar2, S3 = \(\frac{1}{2}\)S
a + ar + ar2 = \(\frac{1}{2}\)(\(\frac{a}{1 - r}\))
2(1 + r + r)(r - 1) = 1
= 2r3 = 3
= r3 = \(\frac{3}{2}\)
r(\(\frac{3}{2}\))\(\frac{1}{3}\) = \(\sqrt{\frac{3}{2}}\)
-4, 2
-3, \(\frac{4}{11}\)
-\(\frac{4}{11}\), 2
5, -3
Correct answer is C
2p - 10 = \(\frac{p + 1 + 1 - 4P^2}{2}\) (Arithmetic mean)
= 2(2p - 100 = p + 2 - 4P2)
= 4p - 20 = p + 2 - 4p2
= 4p2 + 3p - 22 = 0
= (p - 2)(4p + 11) = 0
∴ p = 2 or -\(\frac{4}{11}\)