A-AS Level (CIE) Mathematics Paper-5: Specimen Questions with Answers 6 - 9 of 20

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Question 6

Question

MCQ▾

If the system of equations has non-trivial solution, then

Choices

Choice (4)

a.

b.

c.

d.

Answer

d.

Explanation

A nonhomogeneous system of linear equations has a unique non-trivial solution if and only if its determinant is non-zero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

Writing given equations in determinant form.

Putting value of in given equations

Question 7

Question

MCQ▾

If and then

Choices

Choice (4)

a.

1

b.

c.

2

d.

Answer

d.

Explanation

For any non-zero complex number , there exists a complex number such that , i.e.. , multiplicative inverse of .

and

Or

Comparing both sides we get,

and

Now,

[Using (1) ]

Question 8

Question

MCQ▾

The remainder, when is divided by , is________

Choices

Choice (4)

a.

10

b.

6

c.

8

d.

9

Answer

c.

Explanation

i.e.. , is divisible by

is divisible by for all odd

is divisible by and hence it is divisible by

Also, is divisible by

i.e.. ,

… Multiplying by

… put

Hence remainder is .

Question 9

Question

MCQ▾

It be a complex number and . Then the value of lies in________

Choices

Choice (4)

a.

b.

c.

d.

Answer

d.

Explanation

Complex Numbers

When we combine a Real Number and an Imaginary Number, we get a Complex Number:

Complex Numbers

We know

Hence,

Now,

But

and

Least value of is

From (1) and (2)

Hence, the value of lies in

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