Mathematics is an essential subject that features in the school curriculum for all Class 11 students. It serves as a building block for advanced studies in subjects like engineering, science, economics, and more. Ranging from algebra to calculus, from geometry to trigonometry, this particular grade in mathematics encompasses significant topics. To help you strengthen your understanding and be well-prepared for exams, practicing multiple-choice questions (MCQs) is an excellent way to test knowledge and enhance problem-solving skills. In this post, we have compiled 50 MCQs covering various topics in Class 11 Maths to help you prepare and boost your confidence.
MCQs
1. Which of the following is the correct value of sin90∘\sin 90^\circsin90∘?
- A) 1
- B) 0
- C) 12\frac{1}{2}21
- D) 3\sqrt{3}3
Answer: A) 1
The sine of 90 degrees is 1.
2. The general solution of sinx=12\sin x = \frac{1}{2}sinx=21 is:
- A) x=30∘+360∘nx = 30^\circ + 360^\circ nx=30∘+360∘n
- B) x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n
- C) x=90∘+360∘nx = 90^\circ + 360^\circ nx=90∘+360∘n
- D) x=180∘+360∘nx = 180^\circ + 360^\circ nx=180∘+360∘n
Answer: B) x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n
The general solution for sinx=12\sin x = \frac{1}{2}sinx=21 is x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n, where nnn is any integer.
3. Which of the following is the solution of the quadratic equation x2−7x+12=0x^2 – 7x + 12 = 0x2−7x+12=0?
- A) x=3,4x = 3, 4x=3,4
- B) x=4,3x = 4, 3x=4,3
- C) x=1,2x = 1, 2x=1,2
- D) x=2,3x = 2, 3x=2,3
Answer: A) x=3,4x = 3, 4x=3,4
Solving the quadratic equation, we get the roots as 3 and 4.
4. The value of log232\log_2 32log232 is:
- A) 5
- B) 3
- C) 2
- D) 4
Answer: A) 5
Since 25=322^5 = 3225=32, the value of log232\log_2 32log232 is 5.
5. If α\alphaα and β\betaβ are the roots of the quadratic equation x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0, then α+β\alpha + \betaα+β is:
- A) 5
- B) 6
- C) -5
- D) -6
Answer: A) 5
The sum of the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 is −ba-\frac{b}{a}−ab. For this equation, α+β=5\alpha + \beta = 5α+β=5.
6. What is the derivative of f(x)=x2+3x+1f(x) = x^2 + 3x + 1f(x)=x2+3x+1?
- A) 2x+32x + 32x+3
- B) 2x+12x + 12x+1
- C) x+3x + 3x+3
- D) x+2x + 2x+2
Answer: A) 2x+32x + 32x+3
The derivative of x2+3x+1x^2 + 3x + 1×2+3x+1 with respect to xxx is 2x+32x + 32x+3.
7. The sum of the first 10 natural numbers is:
- A) 45
- B) 55
- C) 50
- D) 60
Answer: B) 55
The sum of the first nnn natural numbers is given by n(n+1)2\frac{n(n+1)}{2}2n(n+1). For n=10n = 10n=10, the sum is 10(10+1)2=55\frac{10(10+1)}{2} = 55210(10+1)=55.
8. What is the value of tan45∘\tan 45^\circtan45∘?
- A) 1
- B) 0
- C) 2\sqrt{2}2
- D) 12\frac{1}{\sqrt{2}}21
Answer: A) 1
The value of tan45∘\tan 45^\circtan45∘ is 1.
9. Which of the following is a solution of x2−4x+4=0x^2 – 4x + 4 = 0x2−4x+4=0?
- A) x=2x = 2x=2
- B) x=−2x = -2x=−2
- C) x=4x = 4x=4
- D) x=0x = 0x=0
Answer: A) x=2x = 2x=2
The equation x2−4x+4=0x^2 – 4x + 4 = 0x2−4x+4=0 factors as (x−2)2=0(x – 2)^2 = 0(x−2)2=0, giving the solution x=2x = 2x=2.
10. Which of the following is the correct formula for the area of a circle?
- A) πr2\pi r^2πr2
- B) 2πr22 \pi r^22πr2
- C) πd2\pi d^2πd2
- D) 2πr2 \pi r2πr
Answer: A) πr2\pi r^2πr2
The area of a circle is given by the formula A=πr2A = \pi r^2A=πr2, where rrr is the radius.
11. The equation of a straight line in slope-intercept form is:
- A) y=mx+by = mx + by=mx+b
- B) y=x+my = x + my=x+m
- C) y=x+by = x + by=x+b
- D) y=mx+cy = mx + cy=mx+c
Answer: A) y=mx+by = mx + by=mx+b
This is the standard form of the equation of a straight line, where mmm is the slope and bbb is the y-intercept.
12. What is the integral of ∫x2dx\int x^2 dx∫x2dx?
- A) x33+C\frac{x^3}{3} + C3x3+C
- B) x22+C\frac{x^2}{2} + C2x2+C
- C) x3+Cx^3 + Cx3+C
- D) 2×3+C2x^3 + C2x3+C
Answer: A) x33+C\frac{x^3}{3} + C3x3+C
The integral of x2x^2×2 with respect to xxx is x33+C\frac{x^3}{3} + C3x3+C.
13. If the probability of an event is 14\frac{1}{4}41, then the odds in favor of the event are:
- A) 1:4
- B) 4:1
- C) 3:1
- D) 1:3
Answer: B) 4:1
The odds in favor are the ratio of the probability of success to the probability of failure, which is 14:34=4:1\frac{1}{4} : \frac{3}{4} = 4:141:43=4:1.
14. What is the value of log101000\log_10 1000log101000?
- A) 3
- B) 2
- C) 10
- D) 100
Answer: A) 3
Since 103=100010^3 = 1000103=1000, log101000=3\log_10 1000 = 3log101000=3.
15. The slope of a line passing through the points (2,3)(2, 3)(2,3) and (5,7)(5, 7)(5,7) is:
- A) 43\frac{4}{3}34
- B) 12\frac{1}{2}21
- C) 34\frac{3}{4}43
- D) 23\frac{2}{3}32
Answer: A) 43\frac{4}{3}34
The slope of a line is calculated as y2−y1x2−x1\frac{y_2 – y_1}{x_2 – x_1}x2−x1y2−y1. Substituting the points, we get 7−35−2=43\frac{7 – 3}{5 – 2} = \frac{4}{3}5−27−3=34.
16. What is the domain of the function f(x)=1x−2f(x) = \frac{1}{x-2}f(x)=x−21?
- A) x≠2x \neq 2x=2
- B) x≥2x \geq 2x≥2
- C) x>2x > 2x>2
- D) x≤2x \leq 2x≤2
Answer: A) x≠2x \neq 2x=2
The function is undefined at x=2x = 2x=2, so the domain is x≠2x \neq 2x=2.
17. The median of the data set 3,8,1,6,23, 8, 1, 6, 23,8,1,6,2 is:
- A) 3
- B) 4
- C) 5
- D) 6
Answer: B) 4
Arrange the data in increasing order: 1,2,3,6,81, 2, 3, 6, 81,2,3,6,8. The middle value is 4.
18. If 5sinx=25 \sin x = 25sinx=2, then sinx=\sin x =sinx= is:
- A) 15\frac{1}{5}51
- B) 25\frac{2}{5}52
- C) 52\frac{5}{2}25
- D) 52\frac{5}{2}25
Answer: B) 25\frac{2}{5}52
Dividing both sides by 5, we get sinx=25\sin x = \frac{2}{5}sinx=52.
19. The value of tan60∘\tan 60^\circtan60∘ is:
- A) 3\sqrt{3}3
- B) 1
- C) 13\frac{1}{\sqrt{3}}31
- D) 0
Answer: A) 3\sqrt{3}3
The value of tan60∘\tan 60^\circtan60∘ is 3\sqrt{3}3.
20. The range of the function f(x)=x2f(x) = x^2f(x)=x2 is:
- A) x≥0x \geq 0x≥0
- B) x≤0x \leq 0x≤0
- C) x>0x > 0x>0
- D) x2≥0x^2 \geq 0x2≥0
Answer: D) x2≥0x^2 \geq 0x2≥0
The square of any real number is always non-negative, so the range of f(x)=x2f(x) = x^2f(x)=x2 is x2≥0x^2 \geq 0x2≥0.
21. The length of the median of a triangle is given by the formula m=2b2+2c2−a24m = \sqrt{\frac{2b^2 + 2c^2 – a^2}{4}}m=42b2+2c2−a2. In this, the median is represented by:
- A) mmm
- B) bbb
- C) aaa
- D) ccc
Answer: A) mmm
The formula represents the length of the median of a triangle.
22. What is the sum of the first 50 natural numbers?
- A) 1275
- B) 1225
- C) 1300
- D) 1375
Answer: A) 1275
The sum of the first nnn natural numbers is n(n+1)2\frac{n(n+1)}{2}2n(n+1). For n=50n = 50n=50, the sum is 50(50+1)2=1275\frac{50(50+1)}{2} = 1275250(50+1)=1275.
23. If a line divides two angles of a triangle in the same ratio, then it divides the third side in the same ratio. This is known as:
- A) Angle Bisector Theorem
- B) Pythagorean Theorem
- C) Mid-point Theorem
- D) Theorem of Proportions
Answer: A) Angle Bisector Theorem
This is the Angle Bisector Theorem, which states that the angle bisector divides the opposite side into segments proportional to the adjacent sides.
24. The value of cos0∘\cos 0^\circcos0∘ is:
- A) 1
- B) 0
- C) 12\frac{1}{2}21
- D) 3\sqrt{3}3
Answer: A) 1
The value of cos0∘\cos 0^\circcos0∘ is 1.
25. The sum of the interior angles of a polygon with 8 sides is:
- A) 1440°
- B) 1080°
- C) 900°
- D) 720°
Answer: A) 1440°
The sum of interior angles of a polygon with nnn sides is (n−2)×180°(n – 2) \times 180°(n−2)×180°. For an octagon (n=8n = 8n=8), the sum is (8−2)×180°=1440°(8 – 2) \times 180° = 1440°(8−2)×180°=1440°.
26. If f(x)=3x+4f(x) = 3x + 4f(x)=3x+4, then f(2)f(2)f(2) is:
- A) 10
- B) 6
- C) 5
- D) 12
Answer: A) 10
Substitute x=2x = 2x=2 into the function: f(2)=3(2)+4=10f(2) = 3(2) + 4 = 10f(2)=3(2)+4=10.
27. The value of log101\log_10 1log101 is:
- A) 1
- B) 0
- C) ∞\infty∞
- D) -1
Answer: B) 0
By the definition of logarithms, logb1=0\log_b 1 = 0logb1=0 for any base bbb.
28. The general solution of cosx=12\cos x = \frac{1}{2}cosx=21 is:
- A) x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n
- B) x=90∘+360∘nx = 90^\circ + 360^\circ nx=90∘+360∘n
- C) x=120∘+360∘nx = 120^\circ + 360^\circ nx=120∘+360∘n
- D) x=180∘+360∘nx = 180^\circ + 360^\circ nx=180∘+360∘n
Answer: A) x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n
The general solution of cosx=12\cos x = \frac{1}{2}cosx=21 is x=60∘+360∘nx = 60^\circ + 360^\circ nx=60∘+360∘n, where nnn is any integer.
29. The equation of a circle with center (0,0)(0, 0)(0,0) and radius rrr is:
- A) x2+y2=r2x^2 + y^2 = r^2×2+y2=r2
- B) x2+y2=rx^2 + y^2 = rx2+y2=r
- C) x+y=rx + y = rx+y=r
- D) x2−y2=r2x^2 – y^2 = r^2×2−y2=r2
Answer: A) x2+y2=r2x^2 + y^2 = r^2×2+y2=r2
This is the standard equation of a circle with center at (0,0)(0, 0)(0,0) and radius rrr.
30. The value of cot45∘\cot 45^\circcot45∘ is:
- A) 1
- B) 0
- C) 2\sqrt{2}2
- D) 12\frac{1}{\sqrt{2}}21
Answer: A) 1
The value of cot45∘\cot 45^\circcot45∘ is 1, as cotθ=1tanθ\cot \theta = \frac{1}{\tan \theta}cotθ=tanθ1.
31. The solution of the equation 2x+3=72x + 3 = 72x+3=7 is:
- A) x=2x = 2x=2
- B) x=1x = 1x=1
- C) x=−2x = -2x=−2
- D) x=3x = 3x=3
Answer: B) x=1x = 1x=1
Solving for xxx, we get 2x=42x = 42x=4, so x=1x = 1x=1.
32. The inverse of the function f(x)=2x+3f(x) = 2x + 3f(x)=2x+3 is:
- A) f−1(x)=x−32f^{-1}(x) = \frac{x – 3}{2}f−1(x)=2x−3
- B) f−1(x)=2x−3f^{-1}(x) = 2x – 3f−1(x)=2x−3
- C) f−1(x)=x+32f^{-1}(x) = \frac{x + 3}{2}f−1(x)=2x+3
- D) f−1(x)=x2f^{-1}(x) = \frac{x}{2}f−1(x)=2x
Answer: A) f−1(x)=x−32f^{-1}(x) = \frac{x – 3}{2}f−1(x)=2x−3
To find the inverse, solve for xxx in terms of yyy: y=2x+3y = 2x + 3y=2x+3. Hence, f−1(x)=x−32f^{-1}(x) = \frac{x – 3}{2}f−1(x)=2x−3.
33. The sum of the angles in a quadrilateral is:
- A) 360°
- B) 180°
- C) 90°
- D) 270°
Answer: A) 360°
The sum of the interior angles of any quadrilateral is always 360°.
34. The area of a triangle with base 5 cm and height 8 cm is:
- A) 13 cm²
- B) 40 cm²
- C) 20 cm²
- D) 18 cm²
Answer: C) 20 cm²
The area of a triangle is given by 12×base×height=12×5×8=20\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 8 = 2021×base×height=21×5×8=20.
35. The expression (x+2)(x−3)(x + 2)(x – 3)(x+2)(x−3) simplifies to:
- A) x2+5x−6x^2 + 5x – 6×2+5x−6
- B) x2−x−6x^2 – x – 6×2−x−6
- C) x2−5x−6x^2 – 5x – 6×2−5x−6
- D) x2+x−6x^2 + x – 6×2+x−6
Answer: C) x2−5x−6x^2 – 5x – 6×2−5x−6
Using the distributive property, (x+2)(x−3)=x2−3x+2x−6=x2−5x−6(x + 2)(x – 3) = x^2 – 3x + 2x – 6 = x^2 – 5x – 6(x+2)(x−3)=x2−3x+2x−6=x2−5x−6.
36. What is the derivative of f(x)=x3−5xf(x) = x^3 – 5xf(x)=x3−5x?
- A) 3×2−53x^2 – 53×2−5
- B) 3×2+53x^2 + 53×2+5
- C) x2−5x^2 – 5×2−5
- D) 5×2−35x^2 – 35×2−3
Answer: A) 3×2−53x^2 – 53×2−5
The derivative of x3x^3×3 is 3x23x^23×2 and the derivative of −5x-5x−5x is −5-5−5, so the derivative is 3×2−53x^2 – 53×2−5.
37. If tanx=1\tan x = 1tanx=1, then x=x =x= is:
- A) 45°
- B) 90°
- C) 30°
- D) 60°
Answer: A) 45°
The value of tan45∘=1\tan 45^\circ = 1tan45∘=1, so x=45∘x = 45^\circx=45∘.
38. The product of roots of the quadratic equation x2−6x+8=0x^2 – 6x + 8 = 0x2−6x+8=0 is:
- A) 8
- B) 6
- C) -6
- D) -8
Answer: A) 8
For the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, the product of the roots is ca\frac{c}{a}ac. Here, the product is 81=8\frac{8}{1} = 818=8.
39. The perimeter of a rectangle is given by:
- A) 2l+2b2l + 2b2l+2b
- B) l+bl + bl+b
- C) 2l+b2l + b2l+b
- D) 2l+2b22l + 2b^22l+2b2
Answer: A) 2l+2b2l + 2b2l+2b
The perimeter of a rectangle is calculated as 2×(length+breadth)2 \times (\text{length} + \text{breadth})2×(length+breadth).
40. What is the solution of the system of equations x+y=5x + y = 5x+y=5 and x−y=1x – y = 1x−y=1?
- A) x=3,y=2x = 3, y = 2x=3,y=2
- B) x=4,y=1x = 4, y = 1x=4,y=1
- C) x=2,y=3x = 2, y = 3x=2,y=3
- D) x=5,y=0x = 5, y = 0x=5,y=0
Answer: A) x=3,y=2x = 3, y = 2x=3,y=2
Solving the system of equations, we find that x=3x = 3x=3 and y=2y = 2y=2.
41. The standard equation of a parabola opening upwards is:
- A) y2=4axy^2 = 4axy2=4ax
- B) x2=4ayx^2 = 4ayx2=4ay
- C) y=x2y = x^2y=x2
- D) x=y2x = y^2x=y2
Answer: B) x2=4ayx^2 = 4ayx2=4ay
This is the standard form of the equation for a parabola opening upwards.
42. The inverse of the matrix [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}[1324] is:
- A) [−211.5−0.5]\begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix}[−21.51−0.5]
- B) [−10.50.75−0.25]\begin{bmatrix} -1 & 0.5 \\ 0.75 & -0.25 \end{bmatrix}[−10.750.5−0.25]
- C) [−211−0.5]\begin{bmatrix} -2 & 1 \\ 1 & -0.5 \end{bmatrix}[−211−0.5]
- D) [2−1−1.50.5]\begin{bmatrix} 2 & -1 \\ -1.5 & 0.5 \end{bmatrix}[2−1.5−10.5]
Answer: A) [−211.5−0.5]\begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix}[−21.51−0.5]
The inverse of a 2×2 matrix is given by 1ad−bc×[d−b−ca]\frac{1}{ad – bc} \times \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}ad−bc1×[d−c−ba]. For the given matrix, the inverse is [−211.5−0.5]\begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix}[−21.51−0.5].
43. The value of 2log2162 \log_2 162log216 is:
- A) 4
- B) 8
- C) 10
- D) 16
Answer: B) 8
log216=4\log_2 16 = 4log216=4 because 24=162^4 = 1624=16. Therefore, 2log216=2×4=82 \log_2 16 = 2 \times 4 = 82log216=2×4=8.
44. The sum of squares of the first 10 natural numbers is:
- A) 385
- B) 400
- C) 450
- D) 460
Answer: A) 385
The sum of squares of the first nnn natural numbers is n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}6n(n+1)(2n+1). For n=10n = 10n=10, the sum is 385385385.
45. The area of a rhombus is given by:
- A) base×height\text{base} \times \text{height}base×height
- B) 12×product of diagonals\frac{1}{2} \times \text{product of diagonals}21×product of diagonals
- C) side2\text{side}^2side2
- D) 12×side2\frac{1}{2} \times \text{side}^221×side2
Answer: B) 12×product of diagonals\frac{1}{2} \times \text{product of diagonals}21×product of diagonals
The area of a rhombus is given by 12×d1×d2\frac{1}{2} \times d_1 \times d_221×d1×d2, where d1d_1d1 and d2d_2d2 are the lengths of the diagonals.
46. The equation of a line passing through the points (1,2)(1, 2)(1,2) and (4,6)(4, 6)(4,6) is:
- A) y=x+1y = x + 1y=x+1
- B) y=2x+1y = 2x + 1y=2x+1
- C) y=43x+23y = \frac{4}{3}x + \frac{2}{3}y=34x+32
- D) y=x+1y = x + 1y=x+1
Answer: C) y=43x+23y = \frac{4}{3}x + \frac{2}{3}y=34x+32
The slope of the line is 6−24−1=43\frac{6 – 2}{4 – 1} = \frac{4}{3}4−16−2=34, and using point-slope form, the equation is y=43x+23y = \frac{4}{3}x + \frac{2}{3}y=34x+32.
47. The function f(x)=x2f(x) = x^2f(x)=x2 is:
- A) Increasing
- B) Decreasing
- C) Constant
- D) Neither increasing nor decreasing
Answer: A) Increasing
For x>0x > 0x>0, the function f(x)=x2f(x) = x^2f(x)=x2 is increasing.
48. If x=3x = 3x=3, then the value of 2×2+5x2x^2 + 5x2x2+5x is:
- A) 30
- B) 40
- C) 50
- D) 60
Answer: B) 40
Substituting x=3x = 3x=3, we get 2(3)2+5(3)=18+15=402(3)^2 + 5(3) = 18 + 15 = 402(3)2+5(3)=18+15=40.
49. What is the perimeter of a triangle with sides 7 cm, 9 cm, and 12 cm?
- A) 28 cm
- B) 22 cm
- C) 18 cm
- D) 12 cm
Answer: A) 28 cm
The perimeter of a triangle is the sum of the lengths of its sides. So, 7+9+12=287 + 9 + 12 = 287+9+12=28 cm.
50. The solution of x2=16x^2 = 16×2=16 is:
- A) x=4x = 4x=4
- B) x=−4x = -4x=−4
- C) x=±4x = \pm 4x=±4
- D) x=16x = 16x=16
Answer: C) x=±4x = \pm 4x=±4
Solving x2=16x^2 = 16×2=16, we get two solutions: x=4x = 4x=4 and x=−4x = -4x=−4.
This concludes the set of additional Class 11 Maths MCQs. Keep practicing to sharpen your skills!
Also Read: 50 MCQs of Maths for Class 9
You may also like to read: “25 Key MCQs on Life Processes for Class 10 Students”
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