Below Questions are very basic questions. These are more to test your concepts so you might not find complexity. More questions with higher difficulty level will be put up. But do not ignore below questions by assuming easy ones.
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q1. which of the following is equal to 5.35828282.... ?
A. 53582 / 100
B. 53047 / 9900
C. 535.828282 / 99
D. None of above
Ans 1 :- B
5.35828282.. = 535.828282.. / 100
= (53582 - 535 ) / 9900 click here for concept
= 53047 / 9900
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q2 . Which of following is true about 29^12 ?
A. Result is a even number.
B. Result is a odd number.
C. Result is a perfect Square.
D. Both B& C
E. Nothing can be said.
Ans 2 :- D
odd raise to any integer will be a odd number. Hence option A is eliminated and option 2 is true.
Any number raise to a even power is a perfect square. (29^6)^2. Hence option C is true.
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q3. If A is an odd number and B is an even number, then what can be said about following statements ?
I. AB is an odd number.
II. A/B is a fraction.
III. |AB| = A*B
IV. A= B+1 or B = A+1
A. I & II are true.
B. II & III are true.
C. If III is true then IV is definitely true.
D. Only II is true.
Ans 3:- D
If A is an odd number and B is an even
AB is an even number. (Even * any integer = even ) hence I is false.
A/B is a fraction. As an odd can not be divided completely by an even. Hence II is true.
|AB| not equal to A*B as even or odd numbers can be negative. hence III is false.
Fourth statement is just an weird option.Hence answer option D.
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q4. Which of following is not twin prime numbers?
A. (3,5)
B. (5,7)
C. (17,19)
D. (37,39)
Ans 4:- D
Twin Prime Numbers:- a pair of prime numbers with difference of 2 are called twin prime numbers. In option 4 , 39 is not a prime number.
You can list all twin prime numbers less than 100.
{3, 5}, {5, 7}, {11, 13}, {17, 19}, {29, 31}, {41, 43}, {59, 61}, {71, 73}
_________________________________________________________________q5. Which of following is/are perfect numbers ?
A. 6
B. 28
C. Both
D. None
Ans 5: C
Perfect Number:- A number is a perfect number when all its factors excluding number itself add up to number.
A. 6 -> 1 + 2 + 3 = 6 hence a perfect number.
B. 28 -> 1 + 2 + 4 + 7 + 14 = 28 hence a perfect number. so answer option C.
Some other perfect numbers are 496 & 8128.
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q6. Simplify (8+2i) / (8-2i) in form of a+bi
A. 15/17 + 8i/17
B. 15/17 + 15i/17
C. 8/17 + 15i/17
D. 8/17 - 15i/17
Ans 6 :- A
This is asking of rationalization of imaginary number. that is making denominator independent of imaginary number. This is done by multiplying and divide the number by complex conjugate of Denominator.
= (8+2i) / (8-2i)
= (8+2i) (8+2i) / (8-2i) (8+2i)
= (64 + 32i + 4(i^2 ) / (64 - 4(i^2 ))
=( 60 + 32i) / (68) as i^2 = -1
= 15/17 + 8i/17
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q7. Find the largest value of n, for which (18 n^2 + 4n + 7) / n would be a natural number.
A. 18
B. 1
C. 7
D. 9
E. 4
Ans :- C
First two terms of numerator are divided by n. Third term should be 1 or 7 so that complete expression is a natural number. Max of both is answer i.e. 7.
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