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Q1. The value of $$\sin 30^\circ$$ is:
A) $$0$$
B) $$\frac{1}{2}$$
C) $$\frac{\sqrt{3}}{2}$$
D) $$1$$
Answer: $$\frac{1}{2}$$
Solution:
We know that:
$$\sin 30^\circ = \frac{1}{2}$$
Therefore, the correct answer is:
$$\frac{1}{2}$$
Q2. Solve the quadratic equation:
$$x^2 – 9 = 0$$
A) $$3, -3$$
B) $$9, -9$$
C) $$1, -1$$
D) $$0, -9$$
Answer: $$3, -3$$
Solution:
Given:
$$x^2 – 9 = 0$$
Add $$9$$ to both sides:
$$x^2 = 9$$
Taking square root:
$$x = \pm 3$$
Therefore, the roots are:
$$3, -3$$
Q3. The common difference of the AP
$$2, 5, 8, 11$$
is:
A) $$2$$
B) $$3$$
C) $$5$$
D) $$8$$
Answer: $$3$$
Solution:
Common difference is:
$$5 – 2 = 3$$
Checking next terms:
$$8 – 5 = 3$$
$$11 – 8 = 3$$
Therefore, the common difference is:
$$3$$
Q4. The value of $$\tan 45^\circ$$ is:
A) $$0$$
B) $$1$$
C) $$\sqrt{3}$$
D) $$\frac{1}{2}$$
Answer: $$1$$
Solution:
We know that:
$$\tan 45^\circ = 1$$
Therefore, the correct answer is:
$$1$$
Q5. Factorize:
$$x^2 – 25$$
A) $$(x+5)(x-5)$$
B) $$(x+25)(x-1)$$
C) $$(x-25)(x+1)$$
D) $$(x+5)^2$$
Answer: $$(x+5)(x-5)$$
Solution:
We know the identity:
$$a^2 – b^2 = (a+b)(a-b)$$
Here:
$$a=x,\ b=5$$
Therefore:
$$x^2 – 25 = x^2 – 5^2$$
$$= (x+5)(x-5)$$
Hence, the correct answer is:
$$(x+5)(x-5)$$
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