For what value of x is the tangent to the curve y = x2 - 4x + 3 parallel to the x-axis?
A
3
B
2
C
1
D
6
CORRECT OPTION:
b
32
Two variables x and y are such that \(\frac{dy}{dx}\) = 4x - 3 and y = 5 when x = 2. Find y in terms of x
A
2x2 - 3x + 5
B
2x2 - 3x + 3
C
2x2 - 3x
D
4
CORRECT OPTION:
b
∫dy = ∫(4x - 3)dx, y = 2x2 - 3x + C
when y = 5, x = 2, C = 3
y = 2x2 - 3x + 3
33
Find the area bounded by the curve y = 3x2 - 2x + 1, the ordinates x = 1 and x = 3 and the a-axix
A
24
B
22
C
21
D
20
CORRECT OPTION:
b
\(\pi\) = \(\int^{3}_{1}(3x^2 - 2x + 1)\)
dx = [x3 - 3x + x + C]
= 22
34
\(\begin{array}{c|c} \text{Age in years} & 13 & 14 & 15 & 16 & 17 \ \hline \text{No. of students} & 3 & 10 & 30 & 42 & 15\end{array}\)
The frequency distribution above shows the ages of students in a secondary school. In a pie chart constructed to represent the data, the angles corresponding to the 15 years old is
A
27o
B
30o
C
54o
D
108o
CORRECT OPTION:
d
35
The pie chart shows the distribution of students in a secondary school class. If 30 students offered French, how many offered C.R.K?
A
25
B
15
C
10
D
8
CORRECT OPTION:
c
\(\frac{30}{90}\) x 30o
= 10
36
\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\ \hline Frequency & 5 & 8 & 5\end{array}\)
Find the standard deviation of the data using the table above
Median = \(\frac{a + b}{fm}\) (\(\frac{1}{2} \sum f - CF_b\))
= 2.95 + \(\frac{0.5}{15}\)(2.-7)
= 2.95 + \(\frac{0.5}{15}\) x 13
= 2.95 + 0. 43
= 3.38
= 3.4
40
Let p be a probability function on set S, where S = (a1, a2, a3, a4). Find P(a1) if P(a2) = \(\frac{1}{3}\), p(a3) = \(\frac{1}{6}\) and p(a4) = \(\frac{1}{5}\)
A
\(\frac{7}{3}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{3}\)
D
\(\frac{3}{10}\)
CORRECT OPTION:
d
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