Q1. If the HCF of two numbers is 9 and their LCM is 360. If one number is 45, what is the second number?
(यदि दो संख्याओं का HCF 9 है और उनका LCM 360 है। यदि एक संख्या 45 है, तो दूसरी संख्या क्या होगी?)
A) 36
B) 72
C) 81
D) 90
Correct Answer: B) 72
Q1 Solution
Using the formula:
$$
\text{HCF} \times \text{LCM} = \text{Product of two numbers}
$$
Given:
$$
\text{HCF} = 9
$$
$$
\text{LCM} = 360
$$
One number:
$$
45
$$
Let the second number be:
$$
x
$$
Applying the formula:
$$
9 \times 360 = 45 \times x
$$
$$
x = \frac{9 \times 360}{45}
$$
$$
x = \frac{3240}{45}
$$
$$
x = 72
$$
Correct Answer: B) 72
Q2. What is the value of $$\sin 30^\circ + \cos 60^\circ$$?
($$\sin 30^\circ + \cos 60^\circ$$ का मान क्या है?)
A) 0
B) 1/2
C) 1
D) $$\sqrt{3}$$
Correct Answer: C) 1
Q2 Solution
From trigonometric values:
$$
\sin 30^\circ = \frac{1}{2}
$$
$$
\cos 60^\circ = \frac{1}{2}
$$
Adding the values:
$$
\frac{1}{2} + \frac{1}{2}
$$
$$
= \frac{1+1}{2}
$$
$$
= \frac{2}{2}
$$
$$
= 1
$$
Correct Answer: C) 1
Q3. The roots of the quadratic equation $$x^2 – 3x – 10 = 0$$ are:
(द्विघात समीकरण $$x^2 – 3x – 10 = 0$$ के मूल (roots) क्या हैं?)
A) 5, -2
B) -5, 2
C) 5, 2
D) -5, -2
Correct Answer: A) 5, -2
Q3 Solution
Given equation:
$$
x^2 – 3x – 10 = 0
$$
Factorizing:
$$
x^2 – 5x + 2x – 10 = 0
$$
Grouping terms:
$$
x(x-5) + 2(x-5) = 0
$$
Taking common factor:
$$
(x-5)(x+2)=0
$$
Therefore:
$$
x-5=0
$$
or
$$
x+2=0
$$
So,
$$
x=5
$$
and
$$
x=-2
$$
Correct Answer: A) 5, -2
Q4. The 11th term of the AP: -3, -1/2, 2, … is:
(समान्तर श्रेणी (AP): -3, -1/2, 2, … का 11वाँ पद क्या है?)
A) 28
B) 22
C) -38
D) -48
Correct Answer: B) 22
Q4 Solution
First term:
$$
a = -3
$$
Second term:
$$
-\frac{1}{2}
$$
Common difference:
$$
d = -\frac{1}{2} – (-3)
$$
$$
d = -\frac{1}{2} + 3
$$
$$
d = \frac{5}{2}
$$
Formula for nth term:
$$
a_n = a + (n-1)d
$$
For 11th term:
$$
a_{11} = -3 + (11-1)\times\frac{5}{2}
$$
$$
= -3 + 10 \times \frac{5}{2}
$$
$$
= -3 + 25
$$
$$
= 22
$$
Correct Answer: B) 22
Q5. A tangent to a circle intersects it in how many point(s)?
(एक वृत्त की स्पर्श रेखा उसे कितने बिन्दुओं पर प्रतिच्छेद करती है?)
A) 0
B) 1
C) 2
D) Infinite (अनंत)
Correct Answer: B) 1
Q5 Solution
A tangent touches a circle at exactly one point.
Therefore:
$$
\text{Number of intersection points} = 1
$$
Correct Answer: B) 1