Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},...\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term.
پاسخ دهید
(C)
\(81\sqrt{2}\)
5
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.
A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.
پاسخ دهید
(D)
-4
16
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.
پاسخ دهید
(B)
5.50
17
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
پاسخ دهید
(A)
8.25
18
If r denotes the correlation coefficient between two variables, which of the following is always true?
پاسخ دهید
(D)
\(-1 \leq r \leq 1\)
19
A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)
پاسخ دهید
(A)
3.0 seconds
20
Differentiate \(\frac{x}{x + 1}\) with respect to x.
پاسخ دهید
(B)
\(\frac{1}{(x + 1)^{2}}\)
21
Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.
پاسخ دهید
(A)
\(5\sqrt{3} - 3\)
22
Find the unit vector in the direction of the vector \(-12i + 5j\).
پاسخ دهید
(C)
\(\frac{-12i}{13} + \frac{5j}{13}\)
23
In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean
پاسخ دهید
(B)
21
24
Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
پاسخ دهید
(B)
3
25
Which of the following is nor a measure of central tendency?
پاسخ دهید
(B)
Variance
26
A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.
پاسخ دهید
(D)
\(\frac{1}{36}\)
27
If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).
پاسخ دهید
(C)
2
28
Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x - 3\) and the lines \(y + x = 1\).
پاسخ دهید
(D)
(1, -4)
29
Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).
پاسخ دهید
(A)
90720
30
A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.
پاسخ دهید
(D)
-2x + 3y - 6 =0
31
Find the number of different arrangements of the word IKOTITINA.
پاسخ دهید
(A)
30240
32
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
پاسخ دهید
(C)
45°
33
A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.
پاسخ دهید
(A)
\(\frac{4}{7}\)
34
The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.
پاسخ دهید
(C)
\(3 ms^{-2}\)
35
The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.
