Mcq
### 1. **Which of the following is the correct formula for the area of a circle?**
A) \( \pi r^2 \)
B) \( 2\pi r \)
C) \( \pi d \)
D) \( 2r \)
**Answer:** A) \( \pi r^2 \)
---
### 2. **If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and distinct, then the discriminant \( \Delta \) is:**
A) \( \Delta = b^2 - 4ac \)
B) \( \Delta = b^2 + 4ac \)
C) \( \Delta = 0 \)
D) \( \Delta = a^2 + b^2 + c^2 \)
**Answer:** A) \( \Delta = b^2 - 4ac \)
---
### 3. **The product of the zeroes of the quadratic equation \( 3x^2 - 7x + 2 = 0 \) is:**
A) \( \frac{2}{3} \)
B) \( \frac{3}{2} \)
C) \( \frac{7}{3} \)
D) \( \frac{1}{3} \)
**Answer:** A) \( \frac{2}{3} \)
**Explanation:** The product of the zeroes of \( ax^2 + bx + c = 0 \) is given by \( \frac{c}{a} \). Here, \( a = 3 \) and \( c = 2 \), so the product of the zeroes is \( \frac{2}{3} \).
---
### 4. **In a right-angled triangle, the length of the hypotenuse is 13 cm and one of the legs is 5 cm. What is the length of the other leg?**
A) 8 cm
B) 12 cm
C) 10 cm
D) 15 cm
**Answer:** A) 8 cm
**Explanation:** By Pythagoras’ theorem, \( c^2 = a^2 + b^2 \). Here, \( c = 13 \) and \( a = 5 \). Thus,
\[
13^2 = 5^2 + b^2 \\
169 = 25 + b^2 \\
b^2 = 169 - 25 = 144 \\
b = \sqrt{144} = 12 \, \text{cm}
\]
Therefore, the other leg is 12 cm.
---
### 5. **Which of the following is a solution to the equation \( 2x - 3 = 9 \)?**
A) \( x = 6 \)
B) \( x = 3 \)
C) \( x = 5 \)
D) \( x = 7 \)
**Answer:** A) \( x = 6 \)
**Explanation:** Solve for \( x \):
\[
2x - 3 = 9 \\
2x = 9 + 3 = 12 \\
x = \frac{12}{2} = 6
\]
---
### 6. **The value of \( \cos 90^\circ \) is:**
A) 1
B) 0
C) \( \frac{1}{2} \)
D) Undefined
**Answer:** B) 0
---
### 7. **What is the value of \( \sqrt{49} + \sqrt{64} \)?**
A) 13
B) 14
C) 15
D) 16
**Answer:** A) 13
**Explanation:**
\[
\sqrt{49} = 7, \quad \sqrt{64} = 8 \\
\text{So, } 7 + 8 = 13
\]
---
### 8. **What is the sum of the zeroes of the quadratic equation \( x^2 - 5x + 6 = 0 \)?**
A) 5
B) 6
C) -5
D) -6
**Answer:** A) 5
**Explanation:** The sum of the zeroes of \( ax^2 + bx + c = 0 \) is given by \( -\frac{b}{a} \). For the equation \( x^2 - 5x + 6 = 0 \), \( a = 1 \), \( b = -5 \), so the sum is \( -\frac{-5}{1} = 5 \).
---
### 9. **What is the length of the diagonal of a square whose side length is 6 cm?**
A) 6 cm
B) \( 6\sqrt{2} \) cm
C) \( 12 \) cm
D) 9 cm
**Answer:** B) \( 6\sqrt{2} \) cm
**Explanation:** The diagonal of a square is given by \( \text{diagonal} = \text{side} \times \sqrt{2} \). Here, side = 6 cm, so the diagonal is \( 6\sqrt{2} \).
---
### 10. **Which of the following is a solution to the equation \( x^2 - 4x - 12 = 0 \)?**
A) \( x = 6 \)
B) \( x = -6 \)
C) \( x = 3 \)
D) \( x = -3 \)
**Answer:** D) \( x = -3 \)
**Explanation:** Solving the quadratic equation \( x^2 - 4x - 12 = 0 \) using factorization:
\[
(x - 6)(x + 2) = 0 \\
x = 6, \, x = -2
These are some sample MCQs that might appear in the UP Board Class 10 Mathematics exam. The questions cover topics such as algebra, trigonometry, geometry, and quadratic equations, which are part of the standard curriculum. Let me know if you need more questions or explanations!
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