Kathmandu BernHardt HS School
Balkhu, Kathmandu
First Terminal Examination- 2069
Set:A
Faculty: Management
Class XII
Subject: Basic Maths(216)
Time: 3hrs
7.
FM: 100
PM: 35
2.
Find how many even numbers of four different digits can be formed
from 2, 3, 4, 5, 6, 7.
b) In how many ways can a student choose 5 subjects out of 7 subjects, if
two subjects are compulsory?
c) Expand 1 + x up to 4 terms using binomial theorem.
dy
a) Find if xy = yx.
dx
8.
a)
b) Evaluate: 
2x + 3
x2 + 4x + 8
4.
2
(x  x‾ ) (y  y‾ ) = 5.86, (x  x‾ )
5.
[2]
9.
[2]
[2]
[2]
[2]
dx
dx = log (x + x2 + a2) + c
 x + a2
a) Find the equation of the parabola with the vertex (0,0) and focus (0, 3).
b) Find the mean deviation from the median of: 20, 30, 40, 50, 60, 70
c) Calculate the arithmetic mean of the data with coefficient of variation
40% and variance 16.
a) The lower and upper quartiles of a set of data are 10 and 15
respectively. Test whether the data set is symmetrical or not if the
median is 12.
b) Calculate the coefficient of correlation from the given information:
c)
3.
Prove that 
dx
= 7.71, (y  y‾ ) = 31.43.
c) The two regression equation between x and y are
1
y = 2x – 1 and x = y + 2
3
Find means of x and y.
a) If 5 persons are selected from a group of 6 men and 7 women, find the
probability that there are 2 men and 3 women.
b) A person has got Rs. 10,000 to invest in two types of noodles R and W.
Noodles R costs Rs 300 per carton and W, Rs 350 per carton. He can
make a profit of Rs 150 by selling R and Rs 175 by selling W. If the
storage capacity is for 250 cartons only, formulate this problem as LPP
to maximize the profit.
c) Convert 1234510 to hexadecimal number system.
2
a)
Find in how many ways can the letters of the word COLLEGE be
arranged so that L’s do not come together.
1 1+3 1+3+5
b) Prove that +
+
+ … = 2e .
1!
2!
3!
a)
Differentiate (sinh x)cosh
-1 x
with respect to x.
dx
b) Evaluate: 
(a > b).
a + b cos x
Attempt all the questions. The figures in the margin indicate full marks.
1.
6.
[2]
[2]
[2]
[2]
[2]
2
[2]
[2]
[2]
[2]
[2]
[4]
19
1
[4]
[4]

b) Given a = (1, 2) and b = (3, 4), find the unit vector in the direction of

[4]
[4]
[4]
a) Derive the equation of a parabola in the form y2 = 4ax.
b) Calculate the Karl Pearson’s coefficient of skewness.
Variable
10
12
13
14
16
Frequency
2
5
8
7
6
a) State and prove the “Addition Theorem” of probability.

[4]

3a  b .
Past records show that a factory produces 10% defective items. If a
sample of 5 items is selected at random, what is the probability that at
least 3 items are defective? (Assume binomial distribution)
b) Solve the following LPP by graphical method.
Minimize Z = 120x + 60y
Subject to: 3x + y  15, x + 5y  20, 3x + 2y  24,
and x, y  0.
11. If C0, C1, …, Cn are binomial coefficients in the expansion of (1 + x)n, show
that C0 + C1 + … + Cn = 2n. Also prove that
(2n)!
C0C2 + C1C3 + … + Cn – 2Cn =
.
(n – 2)! (n + 2)!
x
12. Find the derivative of x from the first principle.
[4]
10. a)
13. Following are the marks obtained by two students A and B in 10 different
tests. Find who is more consistent.
Student A 80
87
78
79 83
84
90
75
77 89
Student B 78
80
81
80 79
84
85
84
86 77
14. Using appropriate linear regression equation, estimate the value of Y when
X = 17.
X
12
14
16
18
20
25
30
35
Y
112 115 118 117 119 120 127 133
15. Solve the following LPP using simplex method.
Max Z = 14x1 + 4x2
Subject to: 2x1 + x2  3, x1 – x2  1, and x1, x2  0

[4]
[4]
[6]
[6]
[6]
[6]
[6]
Kathmandu BernHardt HS School
Balkhu, Kathmandu
First Terminal Examination- 2069
Set: B
Faculty: Management
Class XII
Subject: Basic Maths(216)
Time: 3hrs
7.
FM: 100
PM: 35
2.
Find how many odd numbers of four different digits can be formed
from 2, 3, 4, 5, 6, 7.
b) From 10 persons, in how many ways can you select 4 persons if a
particular person is never included?
1
c) Expand
up to 4 terms using binomial theorem.
1+x
dy
a) Find if xx = yx.
dx
8.
a)
b) Evaluate: 
2x + 3
dx
x2 + 4x + 3
dx
c) Prove that  2
dx = log (x + x2  a2) + c
 x  a2
3.
4.
5.
a) Find the equation of the parabola with the vertex (0,0) and focus (4, 0).
b) Find the mean deviation from the median of: 12, 13, 14, 15, 16, 17
c) Calculate the arithmetic mean of the data with coefficient of variation
50% and variance 64.
a) The lower and upper quartiles of a set of data are 20 and 30
respectively. Test the symmetry if the median is 25.
b) Calculate the coefficient of correlation from the given information:
Cov (X, Y) = 12.34, Var (X) = 30, Var (Y) = 20.
c) The two regression equation between x and y are
2x = y + 1 and 3x = y + 6
Find means of x and y.
a) If 5 persons are selected from a group of 7 men and 6 women, find the
probability that there are 3 men and 2 women.
b) A person has got Rs. 20,000 to invest in two varieties A and B of same
product. A costs Rs 400 per unit and B, Rs 600 per unit. He can make a
profit of Rs 200 by selling A and Rs 300 by selling B. If the storage
capacity is for 500 units only, formulate this problem as LPP to
maximize the profit.
c) Convert 5432110 to hexadecimal number system.
a)
Find in how many ways can the letters of the word MANAGEMENT
be arranged so that M’s do not come together.
1 1+2 1+2+3
3e
b) Prove that +
+
+…= .
1!
2!
3!
2
a)
Differentiate (cosh x)sinh
-1 x
with respect to x.
dx
b) Evaluate: 
(a < b).
a + b cos x
Attempt all the questions. The figures in the margin indicate full marks.
1.
6.
[2]
9.
[2]
[2]
[4]
39
2
[4]
[4]

b) Given a = (2, 1) and b = (1, 4), find the unit vector in the direction of

[4]
[4]
[4]
a) Derive the equation of a parabola in the form y2 = 4ax.
b) Calculate the Karl Pearson’s coefficient of skewness.
Variable
30
32
33
34
36
Frequency
1
6
7
8
5
a) State and prove the “Multiplication Theorem” of probability.

[4]

a  2b .
10. a)
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
Past records show that a factory produces 5% defective items. If a
sample of 6 items is selected at random, what is the probability that at
least 4 items are defective? (Assume binomial distribution)
b) Solve the following LPP by graphical method.
Maximize F = 9x + 40y
Subject to: y – x  1, y – x  3, 2  x  5.
11. If C0, C1, …, Cn are binomial coefficients in the expansion of (1 + x)n, show
that C0 + C1 + … + Cn = 2n. Also prove that
(2n)!
C02 + C12 + C22 + … + Cn 2 =
.
n! n!
2
12. Find the derivative of 2x from the first principle.
[4]
13. Following are the marks obtained by two students A and B in 10 different
tests. Find who is more consistent.
Student A 80
81
85
89
83
84
90
85
87 89
Student B 78
80
81
90
79
94
85
84
86 77
14. Using appropriate linear regression equation, estimate the value of Y when
X = 17.
X
112 114 116 118 120 125 130 135
Y
12
15
18
17
19
20
27
33
15. Solve the following LPP using simplex method.
Max Z = 25x1 + 45x2
Subject to: x1 + 3x2  21, 2x1 + 3x2  24, and x1, x2  0
[2]
[2]

[4]
[4]
[6]
[6]
[6]
[6]
[6]