292
272
192
172
Correct answer is C
Using the sum of an AP, S\(_n\) = \(\fra{n}{2}\) [ 2a + (n - 1)d]
S\(_3\) = \(\fra{3}{2}\) [ 2a + (3 - 1)d]
18 = \(\fra{3}{2}\) [ 2a + 2d]
2a + 2d = 12
a = 4
2(4) + 2d = 18 --> 8 + 2d = 12
2d = 4; d = 2
a = 4: a + d
= 4 + 2 = 6
a + 2d = 4 + 2]2]
= 8
product of the terms = 4 * 6 * 8 = 192
\(\frac{48}{65}\)
\(\frac{13}{15}\)
\(\frac{-33}{65}\)
\(\frac{-48}{65}\)
Correct answer is C
From Pythagoras' theorem
when sin x = \(\frac{12}{13}\), cos x = \(\frac{5}{13}\)
Using cos (x + y) = cosx cosy - sinxsiny
\(\frac{5}{13}\) * \(\frac{3}{5}\) - \(\frac{12}{13}\) * \(\frac{4}{5}\)
= \(\frac{-33}{65}\)
If ( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\), find the value of (q - p)
-32
-16
16
32
Correct answer is D
( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\)
compared with: 1 - 8x + 24x\(^2\) - 32x\(^3\) + 16\(^4\)
q = 24 and p = -8
(q - p) = 24 - [-8] = 32
Given that F\(^1\)(x) = x\(^3\)√x, find f(x)
\( \frac{2x^{9/2}}{9} + c \)
\( 2x^{9/2} + c \)
\( \frac{2x^{5/2}}{5} + c \)
\( x^4 + c \)
Correct answer is A
F1 (x) = x\(^3\) √x = x\(^{7/2}\)
F(x) = \(\frac{x^{7/2 +1}}{7/2 + 1}\) + c
= \(\frac{x^{9/2}}{9/2}\)
= \(\frac{2x^{9/2}}{9}\) + c
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