Math Practice MCQs

Mathematics - Set Theory

1. $A \cup B = A \iff$

A.$A \subset B$B.$B \subset A$C.$A = B$D.$A \cap B = \emptyset$

Mathematics - Quadratic Equations

2. If the roots of the quadratic equation $x^2 - px + q = 0$ differ by 1, then which of the following is true?

A.$p^2 = 4q + 1$B.$p^2 = 4q - 1$C.$q^2 = 4p + 1$D.$q^2 = 4p - 1$

Mathematics - Definite Integrals

3. The value of $\int_{0}^{\pi/2} \frac{\sqrt{\cot x}}{1 + \sqrt{\cot x}} \, dx$ is:

A.0B.$\frac{\pi}{4}$C.$\frac{\pi}{2}$D.$\frac{\pi}{3}$

Mathematics - Integral Calculus

4. The area bounded by the curve $y = 1 - |x|$ and the x-axis is:

A.$1\text{ sq. unit}$B.$2\text{ sq. units}$C.$0.5\text{ sq. units}$D.$1.5\text{ sq. units}$

Mathematics - Complex Numbers

5. If $|z - i| = |z + i|$, then the locus of the complex number $z$ is:

A.The x-axisB.The y-axisC.The line $y = x$D.A circle

Mathematics - Trigonometry

6. In $\triangle ABC$, if $a = 3$, $b = 4$, and $c = 5$, the value of the circumradius $R$ is:

A.2B.2.5C.3D.5

Mathematics - Algebra

7. If $x^2 - 5x + 6 < 0$ and $x^2 - x - 2 > 0$, then $x$ lies in the interval:

A.$(2, 3)$B.$(-\infty, -1) \cup (2, \infty)$C.$\emptyset$ (No solution)D.$(2, \infty)$

Mathematics - Trigonometry

8. What is the value of $\sin(1920^\circ)$?

A.1/2B.-1/2C.$\frac{\sqrt{3}}{2}$D.$-\frac{\sqrt{3}}{2}$

Mathematics - Probability

9. A fair coin is tossed repeatedly until a head appears. The probability that it takes an odd number of tosses is:

A.1/2B.2/3C.1/3D.3/4

Mathematics - Number Theory

10. The digit at the unit place in the number $7^{2023} + 3^{2023}$ is:

A.0B.4C.6D.10

Mathematics - Arithmetic

11. A man sells two articles for Rs. 4000 each. On one, he gains 20% and on the other, he loses 20%. Find his total gain or loss percent.

A.0%B.4% gainC.4% lossD.2% loss

Mathematics - Coordinate Geometry

12. The acute angle between the pair of straight lines represented by $x^2 - 3xy + 2y^2 = 0$ is:

A.$\tan^{-1}(1/3)$B.$\tan^{-1}(3)$C.$45^\circ$D.$30^\circ$

Mathematics - Functions

13. The domain of the function $f(x) = \sqrt{\log_{10}(x - 1)}$ is:

A.$(1, \infty)$B.$[2, \infty)$C.$(0, \infty)$D.$[1, 2]$

Mathematics - Parabola

14. The length of the latus rectum of the parabola $y^2 - 4y + 4x = 0$ is:

A.2B.4C.8D.1

Mathematics - Sequences and Series

15. If the sum of the first $n$ odd natural numbers is 400, then $n$ is equal to:

A.10B.20C.30D.40

Mathematics - Calculus

16. The coefficient of $x^3$ in the expansion of $e^{2x}$ is:

A.4/3B.8/3C.2/3D.1/6

Mathematics - Binomial Theorem

17. The value of ${}^{20}C_0 + {}^{20}C_2 + {}^{20}C_4 + \dots + {}^{20}C_{20}$ is:

A.$2^{20}$B.$2^{19}$C.$2^{21}$D.$2^{19} - 1$

Mathematics - Matrices and Determinants

18. If $A$ is a square matrix such that $A^2 = A$, then $(I + A)^3 - 7A$ is equal to:

A.$A$B.$I - A$C.$I$D.$3A$

Mathematics - Matrices and Determinants

19. If $A$ is a square matrix of order 3 such that $|A| = 5$, then the value of $|\operatorname{adj}(A)|$ is:

A.5B.25C.125D.1/5

Mathematics - Vectors

20. The area of a parallelogram whose diagonals are represented by the vectors $2\hat{i} + \hat{j}$ and $\hat{i} - \hat{k}$ is:

A.$\sqrt{6}$B.$\frac{\sqrt{6}}{2}$C.1.5D.3

Mathematics - 3D Geometry

21. The equation of the plane passing through the point $(1, 2, 3)$ and perpendicular to the line with direction ratios $1, -1, 2$ is:

A.$x - y + 2z = 5$B.$x + y + z = 6$C.$x - y + 2z = 0$D.$x - y - 2z = -7$

Mathematics - Statistics

22. What is the variance of the first 5 natural numbers?

A.2B.2.5C.3D.4

Mathematics - Inverse Trigonometry

23. The value of $\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right)$ is equal to:

A.$\frac{\pi}{2}$B.$\frac{\pi}{3}$C.$\frac{\pi}{4}$D.$\frac{\pi}{6}$

Mathematics - Circles

24. A chord of a circle is equal in length to its radius. The angle subtended by this chord at a point on the minor arc is:

A.$60^\circ$B.$120^\circ$C.$150^\circ$D.$30^\circ$

Mathematics - Ellipse

25. The eccentricity of the ellipse $16x^2 + 25y^2 = 400$ is:

A.3/5B.4/5C.3/4D.1/5

Mathematics - Calculus

26. The value of $\lim_{x \to 0} \frac{e^x - 1 - x}{x^2}$ is:

A.0B.1/2C.1D.2

Mathematics - Calculus

27. The derivative of $\ln(\sin x)$ with respect to $x$ is:

A.$\tan x$B.$\cot x$C.$-\cot x$D.$\sec x$

Mathematics - Calculus

28. What is the slope of the normal to the curve $y = 2x^2 - 3x + 1$ at $x = 1$?

A.1B.-1C.2D.-1/2

Mathematics - Integral Calculus

29. The integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is equal to:

A.$\frac{e^x}{x} + C$B.$\frac{e^x}{x^2} + C$C.$e^x \ln x + C$D.$-\frac{e^x}{x} + C$

Mathematics - Differential Equations

30. The order and degree of the differential equation $\sqrt{1 + \left(\frac{dy}{dx}\right)^2} = \frac{d^2y}{dx^2}$ are respectively:

A.1, 2B.2, 1C.2, 2D.1, 1

1. $A \cup B = A \iff$

2. If the roots of the quadratic equation $x^2 - px + q = 0$ differ by 1, then which of the following is true?

3. The value of $\int_{0}^{\pi/2} \frac{\sqrt{\cot x}}{1 + \sqrt{\cot x}} \, dx$ is:

4. The area bounded by the curve $y = 1 - |x|$ and the x-axis is:

5. If $|z - i| = |z + i|$, then the locus of the complex number $z$ is:

6. In $\triangle ABC$, if $a = 3$, $b = 4$, and $c = 5$, the value of the circumradius $R$ is:

7. If $x^2 - 5x + 6 < 0$ and $x^2 - x - 2 > 0$, then $x$ lies in the interval:

8. What is the value of $\sin(1920^\circ)$?

9. A fair coin is tossed repeatedly until a head appears. The probability that it takes an odd number of tosses is:

10. The digit at the unit place in the number $7^{2023} + 3^{2023}$ is:

11. A man sells two articles for Rs. 4000 each. On one, he gains 20% and on the other, he loses 20%. Find his total gain or loss percent.

12. The acute angle between the pair of straight lines represented by $x^2 - 3xy + 2y^2 = 0$ is:

13. The domain of the function $f(x) = \sqrt{\log_{10}(x - 1)}$ is:

14. The length of the latus rectum of the parabola $y^2 - 4y + 4x = 0$ is:

15. If the sum of the first $n$ odd natural numbers is 400, then $n$ is equal to:

16. The coefficient of $x^3$ in the expansion of $e^{2x}$ is:

17. The value of ${}^{20}C_0 + {}^{20}C_2 + {}^{20}C_4 + \dots + {}^{20}C_{20}$ is:

18. If $A$ is a square matrix such that $A^2 = A$, then $(I + A)^3 - 7A$ is equal to:

19. If $A$ is a square matrix of order 3 such that $|A| = 5$, then the value of $|\operatorname{adj}(A)|$ is:

20. The area of a parallelogram whose diagonals are represented by the vectors $2\hat{i} + \hat{j}$ and $\hat{i} - \hat{k}$ is:

21. The equation of the plane passing through the point $(1, 2, 3)$ and perpendicular to the line with direction ratios $1, -1, 2$ is:

22. What is the variance of the first 5 natural numbers?

23. The value of $\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right)$ is equal to:

24. A chord of a circle is equal in length to its radius. The angle subtended by this chord at a point on the minor arc is:

25. The eccentricity of the ellipse $16x^2 + 25y^2 = 400$ is:

26. The value of $\lim_{x \to 0} \frac{e^x - 1 - x}{x^2}$ is:

27. The derivative of $\ln(\sin x)$ with respect to $x$ is:

28. What is the slope of the normal to the curve $y = 2x^2 - 3x + 1$ at $x = 1$?

29. The integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is equal to:

30. The order and degree of the differential equation $\sqrt{1 + \left(\frac{dy}{dx}\right)^2} = \frac{d^2y}{dx^2}$ are respectively:

Test Result