Miscallenous Test -02

Group A ( 12*1=12)

[ Q. No. 1] If A & B are only subsets of U, which of the following is the correct set symbol for “at least one” ?
i. n(A ᑎ B)
ii. n(A ᑌ B)
iii. n(only A) + n(only B)
iv. None of the above

[ Q. No. 2 ] If n(A)=40, n(B)=60 & n(A ᑌ B)=80, the value of n(A ᑎ B) is :
i. 10
ii. 20
iii. 30
iv. 40

[ Q. No. 3 ] If n(A)=10, n(B)=30,n(C)=50 and if set A, B, C are pairwise disjoint then which of the following is correct ?
i. n(A U B)=0
ii. n(B U C)=0
iii. n(A U B U C)=90
iv. All of the above

[ Q. No. 4 ] If n(A)=30%, n(B)=40% and n(A ᑎ B) = 10%, the value of n(A-B) is :
i. 20%
ii. 30%
iii. 40%
iv. 50%

[ Q. No. 5 ] If the principal is twice the compound interest, which of the following is the correct relation between CI & CA ?
i.CI = CA
ii. 2CI = CA
iii. 3CI = CA
iv. 4CI = CA

[ Q. No. 6 ] : The compound amount of a certain sum of money in 2 yrs and 3 yrs are Rs. 8820 and Rs. 9261. The rate of interest per annum is : (*No need to solve)
i. 4%
ii. 5%
iii. 6%
iv. 7%

[ Q. No. 7 ] In a continuous series, mean (x̅) = 50 and the ∑fx = 1000, the total number of term is :
i. 10
ii. 20
iii. 30
iv. 4

[ Q. No. 8 ] If f(x)=a & g(x)=b, the value of fog(x) is:
i. 0
ii. a
iii. b
iv. ab

[ Q. No. 9 ] Which of the following holds true when f(x) is divided by a Divisor D such that the quotient is Q and Remainder R ?
i. f(x)=Q×D×R
ii. f(x)=Q+D×R
iii. f(x)=Q×D+R
iv. f(x)=Q×(D+R)

[ Q. No. 10 ] Which of the following is the correct order to complete the compound formula sin(A+B)=sinA.____+____sinB ?
i) sinA , cosB
ii) cosB , sinA
iii) sinB , cosA
iv) cosB , cosA

[ Q. No. 11 ] If î is a unit vector along X-axis, the value of î² is :
i. 0
ii. 1
iii. -1
iv. Doesn’t exist

[ Q. No. 12 ] If I be the identity matrix, the correct value of |I|⁵⁰ is :
i. 0
ii. 1
iii. -1
iv. Doesn’t exist

Group B ( 4×12=48)

[ Q. No. 13 ] In a survey of some students, it was found that 60% of the students studied Commerce and 40% studied Science. Also, 40 students studied both the subjects and 10% didn’t study any of the subjects.
a) Show the information in Venn-Diagram. [1]
b) Find the percentage of students who studied both the subjects. [1]
c) Find the total number of students. [1]
d) Find the number of students who studied science only. [ 1 ]

[ Q. No. 14 ] Out of 250 tourists arriving to visit Nepal, 40% of them have already visited Pokhara and 30% visited Lumbini. Also, 10% of them have already visited both the places. Then
a) Show the above information in Venn-Diagram. [1]
b) How many tourists had not visited both places? [1]
c) Find the ratio of tourists who visited Pokhara to Lumbini. [2]

[ Q. No. 15 ]
a) The annual compound interest on a certain sum of money P in T years at R% rate of interest is CI. Write the relation between P, T, R & CI. [ 1 ]
b) If the annual compound interest of Rs. 1,000 for 1 year is Rs. 100, find the rate of interest. [ 1 ]
c) At what rate percent per annum compound interest will the sum of Rs. 700 amounts to Rs. 847 in 2 years ? Find it. [ 2 ]

[ Q. No. 17 ]
If a polynomial f(x) of degree ‘n’ is divided by (x-a), the remainder is f(a).
a) Name the theorem. [ 1 ]
b) What change would occur in the remainder f(a) when (x-a) is replaced by (ax-b) ?[ 1 ]
c) Write the degree of the quotient in the above case. [ 1 ]
d) Use the theorem to find the remainder when (x³-1) is divided by (x-2). [ 1 ]

[ Q. No. 18 ]
a) State factor theroem. [ 1 ]
b) Use it to check whether x³+6x²+7x+2 is a factor of (x+1). [ 1 ]
c) Using synthetic division method, divide (x³-21x-20) by (x+1) and hence obtain the quotient and the remainder. [ 1+1 ]

[ Q. No. 19 ] The concept of sequence and series is very useful when it comes to deal with huge numbers repeated in same manner either increasing or decreasing.
a) By observing common difference (d), how can you decide whether the sequence is increasing or decreasing ? [1]
b) Write the sum of first ‘n’ natural numbers. [1]
c) Write the sum of first ‘n’ even natural numbers.[1]
d) Write the sum of first ‘n’ odd natural numbers. [1]

[ Q. No. 20 ] The general term of an arithmetic series is given by tn=a+(n-1)d.
a) State the meaning of each term in the above formula. [ 1 ]
b) Find the fifteenth term of the sequence 3, 6, 9, 12, …….. [ 1 ]
c) Which term of the series 3 + 6 + 9 + 12 + …….. is 96 ? Find it. [ 1 ]
d) If 25, m+1, 35 is in arithmetic sequence, find the value of m. [ 1 ]

[ Q. No. 21 ]
a) Define the terms : [ 0.5 + 0.5 ]
i. Inverse Matrix. ii. Singular Matrix
b) Evaluate the determinant of a 2 × 2 identity matrix. [ 1 ]
c) Construct a 2×2 matrix whose elements are given by aij=3i-2j and hence find its inverse. [ 2 ]

[ Q. No. 23 ] The marks obtained by 60 students in a test of 80 full marks is given below :
6, 78, 68, 25, 36, 38, 10, 17, 48, 35, 38, 39, 58, 60, 35, 40, 35, 45, 56, 50, 31, 46, 33, 48, 60, 35, 41, 42, 46, 50, 25, 38, 23, 45, 28, 28, 32, 30, 23, 25, 31, 29, 35, 10, 50, 60, 35, 31, 35, 48, 72, 41, 42, 55, 09, 05, 19, 35, 46, 30.
a) Construct a frequency table of class interval 10. [ 2 ]
b) Calculate the mean marks obtained by the students. [ 2 ]

[ Q. No. 24 ]

Group C ( 5 × 3 = 15 )

[ Q. No. 25] In a survey organized by an institution regarding the causes of HIV, 110 said it is transferred by unprotected sex, 75 said it is by infected syringes and 60 said it is by infected father and mother can infect their babies. Similarly 25 said it is by unprotected sex and infected syringes, 10 said it is by infected syringes and infected father and mother and 10 said it is by unprotected sex and infected father and mother and 5 said it is by all the three causes. If each of them said at least one answer:
a) Show the above information in a Venn-diagram. [1]
b) How many people were surveyed?[2]
c) How many people said that it is caused by infected syringes only ? [2]

[ Q. No. 26 ] Prativa deposited Rs.1,50,000 in a bank at the rate of 10% p.a. Pramila deposited same sum in another bank at the rate of 12% p.a. If Prativa received semi annual compound interest and Pramila received annual compound interest, which interest is more and by how much in 3 years ? Find it. [ 5 ]

[ Q. No. 27 ] Two simulateous equations are given by 2x + 3y – 3 = 0 and x – 4y – 7 = 0.
a) Express in matrix form. [ 1 ]
b) Does the system of simultaneous equation has unique solution ? Clarify with reason. [ 1 ]
c) Solve by matrix method. [ 3 ]

* Best Of Luck *