The sum to infinity of a GP is 100, find its first term if the common ratio is -\(\frac{1}{2}\)
პასუხი
(A)
150
15
PQR is a triangle such that |PQ| = |QR| = 8cm and QPR = 60º. Find the area of \(\angle\) PQR
პასუხი
(A)
16\(\sqrt{3}cm^2\)
16
The Venn diagram above shows the number of students offering physics and chemistry in a class of 65. What is the probability that a student selected from the class offers physics and chemistry if every students offers at least one subject?
პასუხი
(A)
\(\frac{2}{13}\)
17
From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building and the tree.
პასუხი
(A)
15\(\sqrt{3}\)m
18
A boy bought Oranges at the rate of #24.00 for 5 and sold it at the rate of # 30.00 for 4 Oranges. Find the profit made of the ones sold
პასუხი
(C)
# 10.80
19
Differentiate y = (5x + 1)\(^4\)
პასუხი
(A)
20 (5x + 1)\(^3\)
20
Simplify \(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
პასუხი
(B)
4 - \(\sqrt{7}\)
21
Find the perimeter of a triangle whose vertices pass through ( 3, 2), (4, 5) and (6, 2) in surd form.
პასუხი
(C)
3 + \(\sqrt{10} + \sqrt{13}\)
22
Find the 7\(^{th}\) term of the sequence -10, 50, -250 ...........
პასუხი
(C)
-156250
23
The scores of students in a test are recorded as follows: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, and 5. Find the mode of the mark.
პასუხი
(B)
3
24
P(x, 4) and Q( 10, 8) are two points joined by a straight line in a plane. If the midpoint of the line is (9, 6), find the value of x.
პასუხი
(C)
8
25
Find x if \(\frac{16^{2 + x}}{4} = 64^x\)
პასუხი
(A)
3
26
Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0 and 10. Find the union of elements in P that are not in Q and the elements in Q that are not in P.
პასუხი
(D)
{1, 2, 9}
27
In the diagram above, T represents the construction of angle .....
პასუხი
(B)
30\(^0\)
28
Convert the number 10111.11\(_{two}\) to a mixed number.
პასუხი
(B)
23\(\frac{3}{4}\)
29
Subtract 14256\(_{seven}\) from 20045\(_{seven}\)
პასუხი
(B)
2456\(_{seven}\)
30
The average age of the four female teachers in a school is 40 and the average age of eight male teachers in the school is 25. Calculate the average age of the teachers in the school.
პასუხი
(D)
30
31
How many proper and improper subsets are there in the set K = { a, b, c, d, e}?
პასუხი
(C)
32
32
Differentiate Cos25º - Sin 25º
პასუხი
(A)
- ( Sin25º + Cos25º)
33
The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
პასუხი
(B)
17
34
Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.
პასუხი
(C)
152
35
Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8
პასუხი
(A)
\(\sqrt{2}\)
36
From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?
პასუხი
(A)
350 ways
37
In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?
პასუხი
(A)
105ways
38
A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.
პასუხი
(B)
\(\frac{65}{121}\)
39
U varies directly as the square root of V when U = 24, V = 9, find the value of V when U = 16.
პასუხი
(B)
4
40
If B varies inversely as c\(^{\frac{1}{3}}\) and C = 27 when B = 2, find the value of the constant of proportionality K.
პასუხი
(B)
6
41
Find the roots of x\(^3\) - 19x - 30=0
პასუხი
(C)
5, -3 and -2
42
If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y
პასუხი
(B)
x = \(\frac{36}{y}\)
43
Given P = \(\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\), find P\(^2\) - 4P - I where I is the identity matrix
პასუხი
(B)
\(\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}\)
44
If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)
