Question 1

Which term is NOT used in a circle?

Accepted Answer

Correct Answer: Diagonal

Explanation: The term 'Diagonal' is used for polygons (like squares, rectangles) to describe a line connecting non-adjacent vertices. Circles do not have vertices, so they don't have diagonals. The equivalent line passing through the center of a circle is called the Diameter.

Question 2

If a coin is tossed twice, probability of getting 2 Heads is:

Accepted Answer

Correct Answer: 1/4

Explanation: Possible outcomes are {HH, HT, TH, TT}. Total outcomes = 4. Favorable outcome is only {HH}, which is 1. Probability = 1/4. Alternatively, P(Head) = 1/2. Since tosses are independent, P(Head and Head) = 1/2 × 1/2 = 1/4.

Question 3

Integration of 1/x dx is:

Accepted Answer

Correct Answer: ln(x)

Explanation: The derivative of ln(x) is 1/x. Therefore, the integral (anti-derivative) of 1/x is the natural logarithm ln|x| + C. This is a special case of the power rule for integration, which applies to x^n for all n except n = -1.

Question 4

Which of the following is a scalar quantity?

Accepted Answer

Correct Answer: Speed

Explanation: A Scalar quantity has only magnitude but no direction. Speed tells you how fast you are going (e.g., 50 km/h) but not where. Velocity, Force, and Displacement are Vectors because they require both magnitude and direction to be fully described.

Question 5

The binary number 1010 is equal to decimal:

Accepted Answer

Correct Answer: 10

Explanation: Convert 1010 (binary) to decimal using place values (8, 4, 2, 1). 1×8 + 0×4 + 1×2 + 0×1. This simplifies to 8 + 0 + 2 + 0 = 10. Understanding binary conversion is essential for computer science related math problems.

Question 6

The domain of Sin(x) is:

Accepted Answer

Correct Answer: (-∞, ∞)

Explanation: The Domain is the set of all possible input values (x-values). For the Sine function, you can input any real number (angle) from negative infinity to positive infinity. So the domain is all real numbers (-∞, ∞). The Range (output) is restricted to [-1, 1].

Question 7

The value of 0! (zero factorial) is:

Accepted Answer

Correct Answer: 1

Explanation: By convention and definition in combinatorics, 0! is equal to 1. This ensures that formulas like nCr work correctly (e.g., choosing n items from n should be 1 way). It also fits the pattern n! = (n+1)! / (n+1). So 0! = 1! / 1 = 1.

Question 8

What is the arithmetic mean of first n natural numbers?

Accepted Answer

Correct Answer: (n+1)/2

Explanation: The sum of first n natural numbers is n(n+1)/2. To find the mean (average), we divide the sum by n. So, Mean = [n(n+1)/2] / n. The 'n' cancels out, leaving (n+1)/2. Example: Mean of 1,2,3 (n=3) is (3+1)/2 = 2.

Question 9

If f(x) = x³, is the function Even or Odd?

Accepted Answer

Correct Answer: Odd

Explanation: A function is Odd if f(-x) = -f(x). Let's test x³: f(-x) = (-x)³ = -x³. Since this equals -f(x), the function is Odd. Graphically, odd functions are symmetric about the origin (like sin x or x³), while even functions are symmetric about the y-axis (like cos x or x²).

Question 10

A line touching a circle at only one point is called:

Accepted Answer

Correct Answer: Tangent

Explanation: A Tangent is a line that touches the circle at exactly one point, known as the point of tangency. A key property is that the tangent is always perpendicular to the radius at that point. A Secant cuts the circle at two points, and a Chord is a segment inside the circle.

Question 11

Solve: log(1000) base 10

Accepted Answer

Correct Answer: 3

Explanation: Logarithm asks: 10 raised to what power equals 1000? Since 10 × 10 × 10 = 1000, it means 10³ = 1000. Therefore, the log of 1000 with base 10 is 3. The number of zeros in powers of 10 usually gives the answer directly.

Question 12

In a pie chart, the total angle at the center is:

Accepted Answer

Correct Answer: 360°

Explanation: A pie chart represents data as slices of a circle. Since a complete circle corresponds to one full rotation, the total angle at the center is always 360 degrees. To calculate the angle for a specific sector: (Value / Total Value) × 360°.

Question 13

What is the differentiation of a constant?

Accepted Answer

Correct Answer: 0

Explanation: The derivative of any constant number (like 5, 100, π) is always 0. This is because the derivative represents the rate of change. A constant value does not change, so its rate of change is zero. Graphically, it's a horizontal line with a slope of 0.

Question 14

The determinant of a singular matrix is:

Accepted Answer

Correct Answer: 0

Explanation: A square matrix is called a Singular Matrix if its determinant is equal to zero (|A| = 0). A singular matrix does not have an inverse (A⁻¹ does not exist) because calculating the inverse involves dividing by the determinant. Non-singular matrices have non-zero determinants.

Question 15

Cos(90° - θ) is equal to:

Accepted Answer

Correct Answer: Sin θ

Explanation: This is a co-function identity. Sine and Cosine are co-functions, meaning Sin(θ) = Cos(90°-θ) and Cos(90°-θ) = Sin(θ). In a right triangle, the two acute angles sum to 90°. The sine of one acute angle is always equal to the cosine of the other.

Question 16

The sum of roots of the equation x² - 5x + 6 = 0 is:

Accepted Answer

Correct Answer: 5

Explanation: For a quadratic equation ax² + bx + c = 0, the sum of roots = -b/a. Here, a=1, b=-5, c=6. Sum = -(-5)/1 = 5. The product of roots is c/a = 6/1 = 6. The actual roots are 2 and 3, and indeed 2+3=5.

Question 17

Which logic gate gives output 1 only if both inputs are 1?

Accepted Answer

Correct Answer: AND

Explanation: The AND gate is a basic digital logic gate that implements logical conjunction. It produces a HIGH output (1) only if all the inputs to the AND gate are HIGH (1). If any input is LOW (0), the output is LOW. It works like series switches.

Question 18

Find the distance of point (3, 4) from the origin (0, 0).

Accepted Answer

Correct Answer: 5

Explanation: Using the distance formula d = √(x² + y²), since the second point is the origin (0,0). Distance = √(3² + 4²) = √(9 + 16) = √25 = 5. This is a classic application of the Pythagorean theorem where the distance is the hypotenuse.

Question 19

The area of a triangle with base b and height h is:

Accepted Answer

Correct Answer: 0.5 × b × h

Explanation: The area of a triangle is half the product of its base and its height. Formula: Area = (1/2)bh. This is derived from the fact that a triangle is essentially half of a rectangle (or parallelogram) with the same base and height. This formula applies to all types of triangles.

Question 20

The degree of a differential equation is the power of the:

Accepted Answer

Correct Answer: Highest Derivative

Explanation: The degree of a differential equation is the power (exponent) of the highest order derivative present in the equation, provided the equation is a polynomial in derivatives. For example, in (d²y/dx²)³ + dy/dx = 0, the order is 2 and the degree is 3.

Mathematics MCQs

Which term is NOT used in a circle?

If a coin is tossed twice, probability of getting 2 Heads is:

Integration of 1/x dx is:

Which of the following is a scalar quantity?

The binary number 1010 is equal to decimal:

The domain of Sin(x) is:

The value of 0! (zero factorial) is:

What is the arithmetic mean of first n natural numbers?

If f(x) = x³, is the function Even or Odd?

A line touching a circle at only one point is called:

Solve: log(1000) base 10

In a pie chart, the total angle at the center is:

What is the differentiation of a constant?

The determinant of a singular matrix is:

Cos(90° - θ) is equal to:

The sum of roots of the equation x² - 5x + 6 = 0 is:

Which logic gate gives output 1 only if both inputs are 1?

Find the distance of point (3, 4) from the origin (0, 0).

The area of a triangle with base b and height h is:

The degree of a differential equation is the power of the: