16m
26m
36m
46m
Correct answer is C
from the equation of motion
u = 5m/s, a = 2m/s\(^2\), t = 4s
s = ut + \(\frac{1}{2} at^2\)
s = 5*4 + \(\frac{1}{2} 2*4^2\)
s = 20 + 16
s = 36m
{20, 21, 25, 30, 33}
{21, 25, 27, 33, 35}
{20, 21, 25, 27, 33, 35}
{21, 25, 27, 30, 33, 35}
Correct answer is B
P = { 20, 25, 30, 35}, Q = {21, 24, 27, 30, 33}, R = {21, 23, 25, 27, 29, 31, 33, 35}
(P⋃Q)∩R = {20, 21, 24, 25, 27, 30, 33, 35} ∩ {21, 23, 25, 27, 29, 31, 33, 35}
= {21, 25, 27, 33, 35}
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
10
40
32
80
Correct answer is A
\((x + \frac{2}{x^2})^5\)
n = 5, r = 4, p = x and q = \(\frac{2}{x^2}\)
5C\(_4\)x\(^4\) (\(\frac{2}{x^2}\))1 = 5C\(_4\) \(\frac{2x^4}{x^2}\)
5C\(_4\) 2x\(^2\) = \(\frac{5!}{[5-4]!4!}\) * 2x\(^2\)
\(\frac{5*4!}{4!} * 2x^2\) = 5 * 2x\(^2\) = 10x\(^2\)
The coefficient is 10.
Evaluate \(4p_2 + 4C_2 - 4p_3\)
18
6
-6
-18
Correct answer is C
\(4p_2 + 4C_2 - 4p_3\)
\(np_r = \frac{n!}{[n-r]!} and nC_r = \frac{n!}{[n-r]!r!} \)
= \(\frac{4!}{[4-2]!} + \frac{4!}{[4-2]!2!} - \frac{4!}{[4-3]!} = \frac{4!}{2!} + \frac{4!}{2!2!} - \frac{4!}{1!}\)
= \(\frac{4*3*2!}{2!} + \frac{4*3*2!}{2!2!} - \frac{4*3*2*1}{1!}\)
12 + 6 - 24 = -6
(7, -2)
(5, -2)
(-2, 7)
(-7, 2)
Correct answer is A
Let (x1, y1) be the image of the point (x, y) under the given transformations.
x1 = 3x - y
y1 = x + 4y
\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} x \\ y = \end{vmatrix} \begin{vmatrix} x_1 \\ y_1 \end{vmatrix}\)
\(\begin{vmatrix} 3 & -1 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} 2 \\ 1 = \end{vmatrix} \begin{vmatrix} 7 \\ -2 \end{vmatrix}\)