When flipping a fair coin, the probability of any single outcome equals the number of favorable outcomes divided by total possible outcomes.
A coin has exactly 2 possible outcomes: Head or Tail.
Number of ways to get a Head = 1
Therefore, the probability of getting a head in a coin toss is \(\frac{1}{2}\) or 0.5 or 50%.
The answer is C) 1/2
Square root is the inverse operation of squaring, and asks: what number multiplied by itself equals 144?
We need to find a number that when multiplied by itself gives 144.
We test the options by squaring them:
- 11² = 11 × 11 = 121 (not 144)
- 12² = 12 × 12 = 144 (matches!)
- 13² = 13 × 13 = 169 (not 144)
- 14² = 14 × 14 = 196 (not 144)
Since 12 × 12 = 144, we have √144 = 12
Therefore, the answer is (B) 12
Differentiation is finding the rate of change of a function with respect to a variable.
We have y = 3x² and we need to use the Power Rule of differentiation.
The Power Rule states: If y = ax^n, then \(\frac{dy}{dx} = n \cdot a \cdot x^{n-1}\)
Here, a = 3 and n = 2
Therefore, the derivative of y = 3x² is 6x
Answer: A) 6x
To find f(2), substitute x = 2 into the given function and calculate the result.
Therefore, f(2) = 12
The answer is B) 12
To find the median, we must first arrange all numbers in ascending order, then locate the middle value.
We have 7 numbers: 5, 8, 3, 9, 1, 7, 6
1, 3, 5, 6, 7, 8, 9
Since n = 7 (odd number), median position = \(\frac{n+1}{2} = \frac{7+1}{2} = 4\)
Counting from left: 1st is 1, 2nd is 3, 3rd is 5, 4th is 6
Therefore, the median is 6.
The answer is (A) 6
Logarithm is the inverse operation of exponentiation; \(\log_b(x) = y\) means \(b^y = x\).
We need to find the value of \(\log_{10}(1000)\). This asks: "10 raised to what power equals 1000?"
Since \(10^3 = 1000\), we have:
Therefore, \(\log_{10}(1000) = 3\)
The answer is (B) 3
The sum of all three interior angles of any triangle is always constant, regardless of the triangle's shape or size.
Every triangle has exactly 3 interior angles. These angles are formed where two sides of the triangle meet.
The angle sum property of a triangle states:
- Equilateral triangle: 60° + 60° + 60° = 180°
- Right triangle: 90° + 45° + 45° = 180°
- Isosceles triangle: 70° + 70° + 40° = 180°
This property holds for all triangles without exception. It's a basic axiom in Euclidean geometry.
Therefore, the sum of angles in a triangle = 180°
Answer: B) 180°
To find the area of a circle, we use the formula Area = πr², where r is the radius.
- Radius r = 7 cm
- π = 22/7
Therefore, the area of the circle is 154 sq cm.
The answer is (A) 154 sq cm.
This is a linear equation problem where we need to isolate the variable x on one side.
\[2(5) + 5 = 10 + 5 = 15\] ✓
Therefore, x = 5
The answer is B) x = 5
This question tests your knowledge of standard trigonometric ratios for common angles.
Therefore, sin 30° = 0.5
Answer: B) 0.5