Algebra MCQs PDF

Algebra MCQs

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If f(x) = x³ - x² + x + 1 then f(2) = ____?

5
7
3
None of these

(0)

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Explanation

Let's evaluate $f (2)$ for the function $f (x) = x^{3} - x^{2} + x + 1$ .

Substitute $x = 2$ into the function:

$f (2) = (2)^{3} - (2)^{2} + (2) + 1$

Calculate step by step:

$2^{3} = 8$
$2^{2} = 4$
So, $8 - 4 = 4$
Then, $4 + 2 = 6$
Finally, $6 + 1 = 7$

Therefore, $f (2) = 7$ .

Cos2θ/Cos⁴θ-Sin⁴θ = _____?

-1
0
1
None of these

(0)

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Explanation

Let's simplify the expression:

$\frac{\cos 2 θ}{\cos^{4} θ - \sin^{4} θ}$

Step 1: Simplify the denominator
Note that:

$\cos^{4} θ - \sin^{4} θ = (\cos^{2} θ)^{2} - (\sin^{2} θ)^{2} = (\cos^{2} θ - \sin^{2} θ) (\cos^{2} θ + \sin^{2} θ)$

Since $\cos^{2} θ + \sin^{2} θ = 1$ , we have:

$\cos^{4} θ - \sin^{4} θ = (\cos^{2} θ - \sin^{2} θ) \cdot 1 = \cos 2 θ$

(because $\cos 2 θ = \cos^{2} θ - \sin^{2} θ$ ).

Step 2: Substitute back into the expression

$\frac{\cos 2 θ}{\cos^{4} θ - \sin^{4} θ} = \frac{\cos 2 θ}{\cos 2 θ} = 1$

Therefore, the expression simplifies to 1.

What is the nth term of A.P 1, 3, 5, 7, _____?

n
n²
2n - 1
None of these

(0)

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Explanation

The given sequence is an arithmetic progression (AP) of odd numbers:

$1 comma 3 comma 5 comma 7 comma point point point$
.
The formula for the $n$th term (
$a sub n$
) of an AP is
$a sub n equals a plus open paren n minus 1 close paren d$
.

Identify the first term (
$a$
):
$a equals 1$
.
Identify the common difference (
$d$
): The difference between consecutive terms is constant.
$3 minus 1 equals 2$
,
$5 minus 3 equals 2$
, etc. So,
$d equals 2$
.
Substitute the values into the formula:
$a sub n equals 1 plus open paren n minus 1 close paren 2$
Simplify the expression:
a_n=1+2n-2
a_n=2n-1

√-98 = _____?

7√2i
4√7i
49i
None of these

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Explanation

Let's simplify $\sqrt{- 98}$ step by step.

Express under the square root as a product of a positive number and $- 1$ :
$\sqrt{- 98} = \sqrt{98 \cdot (- 1)} = \sqrt{98} \cdot \sqrt{- 1}$
Simplify $\sqrt{98}$ :
Factor 98:
$98 = 49 \times 2 = 7^{2} \times 2$
So,
$\sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \cdot \sqrt{2} = 7 \sqrt{2}$
Recall that $\sqrt{- 1} = i$ :
So,
$\sqrt{- 98} = 7 \sqrt{2} \cdot i = 7 \sqrt{2} i$

If z = i then (z bar)² = ____?

-1
-i
i
None of these

(0)

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Explanation

Let's solve the problem step by step.

Given:

$z = i$
We need to find $(\overset{ˉ}{z})^{2}$ , where $\overset{ˉ}{z}$ is the complex conjugate of $z$ .

Step 1: Find the conjugate of $z$ .
Since $z = i$ , its conjugate is $\overset{ˉ}{z} = - i$ .

Step 2: Square the conjugate.
So, $(\overset{ˉ}{z})^{2} = (- i)^{2} = (- i) \times (- i) = i^{2}$ .

Recall that $i^{2} = - 1$ .

Therefore, $(\overset{ˉ}{z})^{2} = - 1$ .

i²¹ + i²⁷ + i³⁰ = ____?

-i
i
-1
None of these

(0)

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Explanation

$i^{21} = i$ (since 21 mod 4 = 1)
$i^{27} = - i$ (since 27 mod 4 = 3)
$i^{30} = - 1$ (since 30 mod 4 = 2)
Adding: $i + (- i) + (- 1) = - 1$

For any two sets A and B if A∩B= B∪A then?

A = B
A ≠ B
A
None of these

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The solution of 2x² - 6x = 0 when?

x∈0{3}
x∈0{0}
x∈W is {0, 3}
All of these

(0)

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Explanation

Step 1: Factor the equation

$2 x squared minus 6 x equals 0$

Factor out
$2 x$
from both terms to get:
$2 x open paren x minus 3 close paren equals 0$

Step 2: Solve for x
Set each factor equal to zero to find the solutions:
$2 x equals 0$
leads to
$x equals 0$

$x minus 3 equals 0$
leads to
$x equals 3$

Step 3: Check the options
The solutions are
$x equals 0$
and
$x equals 3$
. The notationx∈W is {0, 3}means that the solutions are 0 and 3, and they are elements of the set of whole numbers (W), which is true.

If, f has a relative maximum at x = c then?

f'(c) < 0
f'(c) = 0
f'(c) > 0
None of these

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If A and B are two non-empty disjoint sets then (A-B)∩B = ____?

A∩B
AUB
∅
None of these

(0)

ALGEBRA MCQS

If f(x) = x³ - x² + x + 1 then f(2) = ____?

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Explanation

Cos2θ/Cos⁴θ-Sin⁴θ = _____?

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Explanation

What is the nth term of A.P 1, 3, 5, 7, _____?

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Explanation

√-98 = _____?

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Explanation

If z = i then (z bar)² = ____?

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Explanation

i²¹ + i²⁷ + i³⁰ = ____?

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Explanation

For any two sets A and B if A∩B= B∪A then?

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Explanation

The solution of 2x² - 6x = 0 when?

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Explanation

If, f has a relative maximum at x = c then?

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Explanation

If A and B are two non-empty disjoint sets then (A-B)∩B = ____?

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Explanation

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