Using binomial expansion of ( 1 + x)\(^6\) = 1 + 6x + 15x\(^2\) + 20x\(^3\) + 6x\(^5\) + x)\(^6\), find, correct to three decimal places, the value of (1.998))\(^6\)
Answer
(B)
63.167
8
In how many ways can 8 persons be seated on a bench if only three seats are available?
Answer
(C)
336
9
If α and β are the roots of 3x\(^2\) - 7x + 6 = 0, find \(\frac{1}{α}\) + \(\frac{1}{β}\)
Answer
(A)
\(\frac{7}{6}\)
10
If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p
Answer
(B)
-8.0
11
For what value of k is 4x\(^2\) - 12x + k, a perfect square?
Answer
(D)
9
12
A binary operation * is defined on the set of real numbers, R, by
P * q = \(\frac{q^2 - p^2}{2pq}\). Find 3 * 2
Answer
(C)
-\(\frac{5}{12}\)
13
Find the inverse of \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)
Given that P = { x: 0 ≤ x ≤ 36, x is a factor of 36 divisible by 3} and Q = { x: 0 ≤ x ≤ 36, x is an even number and a perfect square}, find P n Q.
Answer
(D)
{36}
15
A body of mass 15kg is placed on a smooth plane which is inclined at 60° to the horizontal. If the box is at rest,
calculate the normal reaction to the plane. [ Take g = 10m/s\(^2\) ]
Answer
(B)
75N
16
A fair die is tossed 60 times and the results are recorded in the table
Number of die
1
2
3
4
5
6
Frequency
15
10
14
2
8
11
Find the probability of obtaining a prime number.
Answer
(D)
\(\frac{8}{15}\)
17
If 2y\(^2\) + 7 = 3y - xy, find \(\frac{dy}{dx}\)
Answer
(D)
\(\frac{ -y}{4y+ x -3}\)
18
Three forces, F\(_1\) (8N, 030°), F\(_2\) (10N, 150° ) and F\(_3\) ( KN, 240° )are in equilibrium. Find the value of N
Answer
(C)
6√3
19
In △PQR, \(\overline{PQ}\) = 5i - 2j and \(\overline{QR}\) = 4i + 3j. Find \(\overline{RP}\).
Answer
(A)
-i - 5j
20
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).
Calculate the maximum height reached.
Answer
(C)
31.5m
21
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).
Calculate the distance travelled in the third second.
Answer
(A)
5.5m
22
Given that F\(^1\)(x) = x\(^3\) √x, find f(x)
Answer
(A)
\(\frac{2x^{9/2}}{9}\) + c
23
If ( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\), find the value of (q - p)
Answer
(D)
32
24
If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are acute angles, find cos (x + y)
Answer
(C)
\(\frac{-33}{65}\)
25
The first term of an AP is 4 and the sum of the first three terms is 18. Find the product of the first three terms
Answer
(C)
192
26
A committee consists of 6 boys and 4 girls. In how many ways can a sub-committee consisting of 3 boys and 2 girls be formed if one particular boy and one particular girl must be on the sub-committee?
Answer
(D)
30
27
If √5 cosx + √15sinx = 0, for 0° < x < 360°, find the values of x.
Answer
(C)
150° and 330°
28
If 2i +pj and 4i -2j are perpendicular, find the value of p.
Answer
(C)
4
29
Consider the following statements:
X: Benita is polite
y: Benita is neat
z: Benita is intelligent
Which of the following symbolizes the statement: "Benita is neat if and only if she is neither polite nor intelligent"?
Answer
(C)
y⟺ ~x ^ ~z
30
A bag contains 8 red, 4 blue and 2 green identical balls. Two balls are drawn randomly from the bag without replacement. Find the probability that the balls drawn are red and blue.
A. 12/91 B. C. D.
Answer
(D)
32/91
31
The gradient ofy= 3x\(^2\) + 11x + 7 at P(x.y) is -1. Find the coordinates of P.
Answer
(B)
(-2,-3)
32
Find the equation of the normal to the curve y= 2x\(^2\) - 5x + 10 at P(1, 7).
Answer
(C)
y - x - 6=0
33
Find the value of the derivative of y = 3x\(^2\) (2x +1) with respect to x at the point x = 2.
Answer
(B)
84
34
Find the radius of the circle 2x\(^2\) - 4x + 2y\(^2\) - 6y -2 = 0.
Answer
(D)
\(\frac{\sqrt{17}}{2}\)
35
Given that f: x --> x\(^2\) - x + 1 is defined on the Set Q = { x : 0 ≤ x < 20, x is a multiple of 5}. find the set of range of F.
