Author Archives: Priyanka

In This Post we are  providing Chapter-10 Straight Lines NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON STRAIGHT LINES

Question 1.
The locus of a point, whose abscissa and ordinate are always equal is
(a) x + y + 1 = 0
(b) x – y = 0
(c) x + y = 1
(d) none of these.

Answer: (b) x – y = 0

Question 2.
The equation of straight line passing through the point (1, 2) and parallel to the line y = 3x + 1 is
(a) y + 2 = x + 1
(b) y + 2 = 3 × (x + 1)
(c) y – 2 = 3 × (x – 1)
(d) y – 2 = x – 1

Answer: (c) y – 2 = 3 × (x – 1)

Question 3.
What can be said regarding if a line if its slope is negative
(a) θ is an acute angle
(b) θ is an obtuse angle
(c) Either the line is x-axis or it is parallel to the x-axis.
(d) None of these

Answer: (b) θ is an obtuse angle

Question 4:
The equation of the line which cuts off equal and positive intercepts from the axes and passes through the point (α, β) is
(a) x + y = α + β
(b) x + y = α
(c) x + y = β
(d) None of these

Answer: (a) x + y = α + β

Question 5.
Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are coincident if
(a) a₁/a₂ = b₁/b₂ ≠ c₁/c₂
(b) a₁/a₂ ≠ b₁/b₂ = c₁/c₂
(c) a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
(d) a₁/a₂ = b₁/b₂ = c₁/c₂

Answer: (d) a₁/a₂ = b₁/b₂ = c₁/c₂

Question 6:
The equation of the line passing through the point (2, 3) with slope 2 is
(a) 2x + y – 1 = 0
(b) 2x – y + 1 = 0
(c) 2x – y – 1 = 0
(d) 2x + y + 1 = 0

Answer: (c) 2x – y – 1 = 0

Question 7.
The slope of the line ax + by + c = 0 is
(a) a/b
(b) -a/b
(c) -c/b
(d) c/b

Answer: (b) -a/b

Question 8.
Equation of the line passing through (0, 0) and slope m is
(a) y = mx + c
(b) x = my + c
(c) y = mx
(d) x = my

Answer: (c) y = mx

Question 9.
The angle between the lines x – 2y = y and y – 2x = 5 is
(a) tan^-1 (1/4)
(b) tan^-1 (3/5)
(c) tan^-1 (5/4)
(d) tan^-1 (2/3)

Answer: (c) tan^-1 (5/4)

Question 10.
Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are parallel if
(a) a₁/a₂ = b₁/b₂ ≠ c₁/c₂
(b) a₁/a₂ ≠ b₁/b₂ = c₁/c₂
(c) a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
(d) a₁/a₂ = b₁/b₂ = c₁/c₂

Answer: (a) a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Question 11.
The locus of a point, whose abscissa and ordinate are always equal is
(a) x + y + 1 = 0
(b) x – y = 0
(c) x + y = 1
(d) none of these.

Answer: (b) x – y = 0

Question 12.
In a ΔABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is
(a) (1, 4)
(b) (7, – 2)
(c) none of these
(d) (4, 1)

Answer: (b) (7, – 2)

Question 13.
The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150 degrees with the positive direction of the y-axis. Then the equation of line is
(a) x + y = 14
(b) √3y + x = 14
(c) √3x + y = 14
(d) None of these

Answer: (c) √3x + y = 14

Question 14.
If two vertices of a triangle are (3, -2) and (-2, 3) and its orthocenter is (-6, 1) then its third vertex is
(a) (5, 3)
(b) (-5, 3)
(c) (5, -3)
(d) (-5, -3)

Answer: (d) (-5, -3)

Question 15.
The sum of squares of the distances of a moving point from two fixed points (a, 0) and (-a, 0) is equal to 2c² then the equation of its locus is
(a) x² – y² = c² – a²
(b) x² – y² = c² + a²
(c) x² + y² = c² – a²
(d) x² + y² = c² + a²Answer

Answer: (c) x² + y² = c² – a²

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In This Post we are  providing Chapter-9 Sequences and Series NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON SEQUENCES AND SERIES

Question 1. If in A.P., S_n = qn2 and Sm = qm², where S_r denotes the sum of r terms of the A.P., then Sq equals    
(a) q³/2
(b) mnq
(c) q³
(d) (m + n)q²

Answer :  C

Question 2. If tn denotes the n th term of the series 2 + 3 + 6 + 11 + 18 + … then t50 is    
(a) 492 – 1
(b) 492
(c) 502 + 1
(d) 492 + 2

Answer :  D

Question 3. The sum to 200 terms of the series 1 + 4 + 6 + 5 +11 + 6 + ………. is     
(a) 31,200
(b) 29,800
(c) 30,200
(d) None of these

Answer :  C

Question 4. If the sum of the series 54 + 51 + 48 + ……….. is 513, then the number of terms are     
(a) 18
(b) 20
(c) 17
(d) None of these

Answer :  A

Question 5. The sum of 11 terms of an A.P. whose middle term is 30,     
(a) 320
(b) 330
(c) 340
(d) 350

Answer :  B

Question 6. If the sum of the first 2n terms of 2, 5, 8, ……. is equal to the sum of the first n terms of 57, 59,61……., then n is equal to    
(a) 10
(b) 12
(c) 11
(d) 13

Answer :  C

Question 7. There are four arithmetic means between 2 and –18. The means are    
(a) –4, –7, –10, –13
(b) 1, –4, –7, –10
(c) –2, –5, –9, –13
(d) –2, –6, –10, –14

Answer :  D

Question 8. 2, 3, 5 are the following terms of an A.P.:    
(a) 2nd, 3rd, and 5th
(b) 4th, 9th and 25th
(c) 4th, 6th, and 10th
(d) none of the above

Answer :  D

Question 9. The first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms. then the sum of the series is    
(a) 2
(b) 3
(c) 3/2
(d) 5/2

Answer :  C

Question 10. The sum of the first nine terms of an arithmetic progression is 171. Which one of the following statements is not correct about this A.P.?   
(a) The sum of the first and the ninth terms cannot be determined
(b) No term of the A.P. can be determined
(c) The first term of the A.P. cannot be  determined
(d) The common difference cannot be determined

Answer :  A

Question 11. If the nth term of an arithmetic progression is 3n + 7, then what is the sum of its first 50 terms?    
(a) 3925
(b) 4100
(c) 4175
(d) 8200

Answer :  C

Question 12. What is the value of 91/3. 91/19. 91/27…… ∞ ?    
(a) 9
(b) 3
(c) 91/3
(d) 1

Answer :  B

Question 13. The minimum value of the expression    
3^x + 3^{1 – x}, x ∈ R, is
(a) 0
(b) 1/3
(c) 3
(d) 2√3

Answer :  D

Question 14. At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was `₹1250, the value at the end of 5 years is    
(a) 409.6
(b) 409
(c) 408
(d) 409.5

Answer :  A

Question 15. An even number of AM are inserted between two numbers whose sum is 13/6. If the sum of means exceeds their number by 1, what is the number of means?    
(a) 8
(b) 18
(c) 12
(d) 6

Answer :  C

In This Post we are  providing Chapter-8 Binomial Theorem NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON BINOMIAL THEOREM

Question 1.
The coefficient of y in the expansion of (y² + c/y)⁵ is
(a) 10c
(b) 10c²
(c) 10c³
(d) None of these

Answer: (c) 10c³

Question 2:
(1.1)¹⁰⁰⁰⁰ is _____ 1000
(a) greater than
(b) less than
(c) equal to
(d) None of these

Answer: (a) greater than

Question 3.
The fourth term in the expansion (x – 2y)¹² is
(a) -1670 x⁹ × y³
(b) -7160 x⁹ × y³
(c) -1760 x⁹ × y³
(d) -1607 x⁹ × y³

Answer: (c) -1760 x⁹ × y³

Question 4.
If n is a positive integer, then (√3+1)²ⁿ⁺¹ + (√3−1)²ⁿ⁺¹ is
(a) an even positive integer
(b) a rational number
(c) an odd positive integer
(d) an irrational number

Answer: (d) an irrational number

Question 5.
If the third term in the binomial expansion of (1 + x)^m is (-1/8)x² then the rational value of m is
(a) 2
(b) 1/2
(c) 3
(d) 4

Answer: (b) 1/2

Question 6.
The greatest coefficient in the expansion of (1 + x)¹⁰ is
(a) 10!/(5!)
(b) 10!/(5!)²
(c) 10!/(5! × 4!)²
(d) 10!/(5! × 4!)

Answer: (b) 10!/(5!)²

Question 7.
The coefficient of xⁿ in the expansion of (1 – 2x + 3x² – 4x³ + ……..)^-n is
(a) (2n)!/n!
(b) (2n)!/(n!)²
(c) (2n)!/{2×(n!)²}
(d) None of these

Answer: (b) (2n)!/(n!)²

Question 8.
The value of n in the expansion of (a + b)ⁿ if the first three terms of the expansion are 729, 7290 and 30375, respectively is
(a) 2
(b) 4
(c) 6
(d) 8

Answer: (c) 6

Question 9.
If α and β are the roots of the equation x² – x + 1 = 0 then the value of α²⁰⁰⁹ + β²⁰⁰⁹ is
(a) 0
(b) 1
(c) -1
(d) 10

Answer: (b) 1

Question 10.
The general term of the expansion (a + b)ⁿ is
(a) T_r+1 = ⁿC_r × a^r × b^r
(b) T_r+1 = ⁿC_r × a^r × b^n-r
(c) T_r+1 = ⁿC_r × a^n-r × b^n-r
(d) T_r+1 = ⁿC_r × a^n-r × b^r

Answer: (d) T_r+1 = ⁿC_r × a^n-r × b^r

Question 11.
The coefficient of xⁿ in the expansion (1 + x + x² + …..)^-n is
(a) 1
(b) (-1)ⁿ
(c) n
(d) n+1

Answer: (b) (-1)ⁿ

Question 12.
If n is a positive integer, then (√5+1)²ⁿ + 1 − (√5−1)²ⁿ + 1 is
(a) an odd positive integer
(b) not an integer
(c) none of these
(d) an even positive integer

Answer: (b) not an integer

Question 13.
In the expansion of (a + b)ⁿ, if n is even then the middle term is
(a) (n/2 + 1)^th term
(b) (n/2)^th term
(c) n^th term
(d) (n/2 – 1)^th term

Answer: (a) (n/2 + 1)^th term

Question 14.
In the expansion of (a + b)ⁿ, if n is odd then the number of middle term is/are
(a) 0
(b) 1
(c) 2
(d) More than 2

Answer: (c) 2

Question 15.
if n is a positive integer then 2³ⁿn – 7n – 1 is divisible by
(a) 7
(b) 9
(c) 49
(d) 81

Answer: (c) 49

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In This Post we are  providing Chapter-7 Permutations and Combinations NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON PERMUTATIONS AND COMBINATIONS

Question 1. In how many ways can a consonants and a vowel be chosen out of the word COURAGE?
(a) ⁷C₂
(b) ⁷P₂
(c) ⁴P₁× ³P₁
(d) ⁴P₁+ ³P1

Answer :   C

Question 2. How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together :
(a) 4140
(b) 4320
(c) 432
(d) 43

Answer :  B

Question 3. Numbers lying between 999 and 10000 than can be formed from the digits 0, 2, 3, 6, 7, 8 (repetition of digits not allowed) are :
(a) 100
(b) 200
(c) 300
(d) 400

Answer :  C

Question 4. How many numbers of 6 digits can be formed from the digits of the number 112233?
(a) 30
(b) 60
(c) 90
(d) 120

Answer :  C

Question 5. The sum of all five digit numbers that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is not allowed, is
(a) 366000
(b) 660000
(c) 360000
(d) 3999960

Answer :  D

Question 6. How many 10 digit numbers can be written by using the digits 1 and 2 :
(a) 10C1 + 9C2
(b) 210
(c) 10C2
(d) 10!

Answer :  B

Question 7. In a test there were n questions. In the test 2n – i students gave wrong answers to i questions i = 1, 2, 3, ……..n. If the total number of wrong answers given is 2047 then n is
(a) 12
(b) 11
(c) 10
(d) None of these

Answer :  C

Question 8. A set contains (2n + 1) elements. If the number of subsets of this set which contain at most n elements is 4096, then the value of n is
(a) 6
(b) 15
(c) 21
(d) None of these

Answer :  D

Question 9. The number of numbers of 9 different non-zero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than the digit in the middle is
(a) 2 (4 !)
(b) (4 !) 2
(c) 8 !
(d) None of these

Answer :  B

Question 10. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:
(a) 6
(b) 9
(c) 18
(d) 12

Answer :  C

Question 11. Ten different letters of an alphabet are given, words with five letters are formed. The number of words which at least one letter repeated is :
(a) 69760
(b) 30240
(c) 99748
(d) 37120

Answer :  A

Question 12. There are 10 points in a plane, out of which 4 points are collinear. The number of triangles formed with vertices as there points is:
(a) 20
(b) 120
(c) 40
(d) 116

Answer :  D

Question 13. In a college of 300 students, every student read 5 newspapers and every newspaper is read by 60 students. The number of newspaper is:
(a) at least 30
(b) at most 20
(c) exactly 25
(d) none of these

Answer :  C

Question 14. The number of ways in which 6 rings can be worn on four fingers of one hand is :
(a) 46
(b) 6C4
(c) 64
(d) 24

Answer :  C

Question 15. In a chess tournament where the participants were to play one game with one another, two players fell ill having played 6 games each, without playing among themselves. If the total number of games is 117, then the number of participants at the beginning was :
(a) 15
(b) 16
(c) 17
(d) 18

Answer :  A

In This Post we are  providing Chapter-6 Linear Inequalities NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON LINEAR INEQUALITIES

Question 1.
Sum of two rational numbers is ______ number.
(a) rational
(b) irrational
(c) Integer
(d) Both 1, 2 and 3

Answer: (a) rational

Question 2.
If x² = -4 then the value of x is
(a) (-2, 2)
(b) (-2, ∞)
(c) (2, ∞)
(d) No solution

Answer: (d) No solution

Question 3.
Solve: (x + 1)² + (x² + 3x + 2)² = 0
(a) x = -1, -2
(b) x = -1
(c) x = -2
(d) None of these

Answer: (b) x = -1

Question 4.
If (x + 3)/(x – 2) > 1/2 then x lies in the interval
(a) (-8, ∞)
(b) (8, ∞)
(c) (∞, -8)
(d) (∞, 8)

Answer: (a) (-8, ∞)

Question 5.
The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is
(a) unbounded
(b) a polygon
(c) none of these
(d) exterior of a triangle

Answer: (c) none of these

Question 6.
The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is
(a) x > 2
(b) 2 < x and x < 1
(c) 2 < x < 1 and x < 3
(d) 2 < x < 3 and x < 1

Answer: (d) 2 < x < 3 and x < 1

Question 7.
If -2 < 2x – 1 < 2 then the value of x lies in the interval
(a) (1/2, 3/2)
(b) (-1/2, 3/2)
(c) (3/2, 1/2)
(d) (3/2, -1/2)

Answer: (b) (-1/2, 3/2)

Question 8.
The solution of the inequality |x – 1| < 2 is
(a) (1, ∞)
(b) (-1, 3)
(c) (1, -3)
(d) (∞, 1)

Answer: (b) (-1, 3)

Question 9.
If | x − 1| > 5, then
(a) x∈(−∞, −4)∪(6, ∞]
(b) x∈[6, ∞)
(c) x∈(6, ∞)
(d) x∈(−∞, −4)∪(6, ∞)Answer

Answer: (d) x∈(−∞, −4)∪(6, ∞)

Question 10.
The solution of |2/(x – 4)| > 1 where x ≠ 4 is
(a) (2, 6)
(b) (2, 4) ∪ (4, 6)
(c) (2, 4) ∪ (4, ∞)
(d) (-∞, 4) ∪ (4, 6)

Answer: (b) (2, 4) ∪ (4, 6)

Question 11.
If (|x| – 1)/(|x| – 2) ‎≥ 0, x ∈ R, x ‎± 2 then the interval of x is
(a) (-∞, -2) ∪ [-1, 1]
(b) [-1, 1] ∪ (2, ∞)
(c) (-∞, -2) ∪ (2, ∞)
(d) (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Answer: (d) (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Question 12.
The solution of the -12 < (4 -3x)/(-5) < 2 is
(a) 56/3 < x < 14/3
(b) -56/3 < x < -14/3
(c) 56/3 < x < -14/3
(d) -56/3 < x < 14/3

Answer: (d) -56/3 < x < 14

Question 13.
If x² = -4 then the value of x is
(a) (-2, 2)
(b) (-2, ∞)
(c) (2, ∞)
(d) No solution

Answer: (d) No solution

Question 14.
Solve: |x – 3| < 5
(a) (2, 8)
(b) (-2, 8)
(c) (8, 2)
(d) (8, -2)

Answer: (b) (-2, 8)

Question 15.
The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is
(a) none of these
(b) interior of a triangle including the points on the sides
(c) in the 2nd quadrant
(d) exterior of a triangle

Answer: (b) interior of a triangle including the points on the sides

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In This Post we are  providing Chapter-5 Complex Numbers and Quadratic Equation NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON COMPLEX NUMBERS AND QUADRATIC EQUATION

1. Let Z1 = 10+ 6i and Z2 = 4+6i . If Z be a complex number such that    Then |Z – 7 -9i| =

(a) 3√2

(b) 4√2

(c) 2√2

(d) √2

Answer► (a) 3√2

2. The number of the integer solutions of x2 + 9 < (x + 3)2 < 8x + 25 is

(a) 1

(b) 2

(c) 3

(d) None of these

Answer► (d) None of these

3. If (a₁ +ib₁)(a₂ +ib₂) ….(an + ibn) = A +iB, then  is equal to

(a) 1

(b) (A² + B²)

(c) (A + B)

(d) (1/A² + 1/B²)

Answer► (b) (A² + B²)

4. The set of all solutions of the inequality (1/2)x²-2x < 1/4 contains the set

(a) (–∞, 0)

(b) (–∞, 1)

(c) (1, ∞)

(d) (3, ∞)

Answer► (d) (3, ∞)

5. The number of solutions of the equation  is

(a) 2

(b) 3

(c) 4

(d) 1

Answer► (c) 4

6. If two roots of the equation x³ – px² + qx – r = 0 are equal in magnitude but opposite in sign, then

(a) pr = q

(b) qr = p

(c) pq = r

(d) None of these

Answer► (c) pq = r

7. The equation π^x = –2x² + 6x – 9 has

(a) No solution

(b) One solution

(c) Two solutions

(d) Infinite solutions

Answer► (a) No solution

8. Two real numbers a & b are such that a + b = 3 & |a – b| = 4, then a & b are the roots of the quadratic equation

(a) 4x² – 12x – 7 = 0

(b) 4x² – 12x + 7 = 0

(c) 4x² – 12x + 25 = 0 

(d) None of these

Answer► (a) 4x² – 12x – 7 = 0

9. The values of k, for which the equation x² + 2(k – 1) x + k + 5 = 0 possess at least one positive root, are

(a) [4, ∞) 

(b) (∞, – 1] ∪ [4, ∞)

(c) [–1, 4] 

(d) (–∞, – 1]

Answer► (d) (–∞, – 1]

10. If α (≠ 1) is a fifth root of unity and b (≠ 1) is a fourth root of unity, then z = (1 + α) (1 + β) (1 + α²) (1 + β²) (1 + α³) (1 + β³) equals

(a) α

(b) β

(c) αβ

(d) 0

Answer► (d) 0

11. The value of   is

(a) 2i

(b) –2i

(c) 2

(d) 1

Answer► (a) 2i

12. If | z – 3i| = 3, (where i = √-1) and arg z ∈ (0, π/2), then cot (arg (z)) -6/z is equal to 

(a) 0

(b) –i

(c) i

(d) π

Answer► (c) i

13. Let a, b and c are real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax² + bx + c = 0 has

(a) Real roots

(b) Imaginary roots 

(c) Exactly one root 

(d) None of these

Answer► (a) Real roots

14. If both the roots of the quadratic equation x2 – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

(a) [4, 5]

(b) (– ∞, 4)

(c) (6, ∞)

(d) (5, 6]

Answer► (b) (– ∞, 4)

15. For all complex numbers z₁ ,z₂ satisfying |z₁| = 12 and |z₂ – 3 – 4i| = 5 , the minimum value of  |z1 -z2| is 

(a) 0

(b) 7

(c) 2

(d) 17

Answer► (c) 2

In This Post we are  providing Chapter-4 Principle of Mathematical Induction NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON PRINCIPLE OF MATHEMATICAL INDUCTION

Principle of Mathematical Induction Class 11 MCQs Questions with Answers

Question 1.
The sum of the series 1³ + 2³ + 3³ + ………..n³ is
(a) {(n + 1)/2}²
(b) {n/2}²
(c) n(n + 1)/2
(d) {n(n + 1)/2}²

Answer: (d) {n(n + 1)/2}²

Question 2.
If n is an odd positive integer, then an + bn is divisible by :
(a) a² + b²
(b) a + b
(c) a – b
(d) none of these

Answer: (b) a + b

Question 3.
1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}
(a) n(n + 1)
(b) n/(n + 1)
(c) 2n/(n + 1)
(d) 3n/(n + 1)

Answer: (b) n/(n + 1)

Question 4.
The sum of the series 1² + 2² + 3² + ………..n² is
(a) n(n + 1)(2n + 1)
(b) n(n + 1)(2n + 1)/2
(c) n(n + 1)(2n + 1)/3
(d) n(n + 1)(2n + 1)/6

Answer: (d) n(n + 1)(2n + 1)/6

Question 5.
{1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
(a) 1/(n + 1) for all n ∈ N.
(b) 1/(n + 1) for all n ∈ R
(c) n/(n + 1) for all n ∈ N.
(d) n/(n + 1) for all n ∈ R

Answer: (a) 1/(n + 1) for all n ∈ N.

Question 6.
For any natural number n, 7ⁿ – 2ⁿ is divisible by
(a) 3
(b) 4
(c) 5
(d) 7

Answer: (c) 5

Question 7.
1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =
(a) {n(n + 3)}/{4(n + 1)(n + 2)}
(b) (n + 3)/{4(n + 1)(n + 2)}
(c) n/{4(n + 1)(n + 2)}
(d) None of these

Answer: (a) {n(n + 3)}/{4(n + 1)(n + 2)}
.

Question 8.
The nth terms of the series 3 + 7 + 13 + 21 +………. is
(a) 4n – 1
(b) n² + n + 1
(c) none of these
(d) n + 2

Answer: (b) n² + n + 1

Question 9.
n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
(a) 2
(b) 3
(c) 5
(d) 7

Answer: (b) 3.

Question 10.
Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
(a) n(n+1)(n+2)/3
(b) n(n+1)(n+2)/6
(c) n(n+2)/6
(d) (n+1)(n+2)/6

Answer: (b) n(n+1)(n+2)/6

Question 11.
For any natural number n, 7ⁿ – 2ⁿ is divisible by
(a) 3
(b) 4
(c) 5
(d) 7

Answer: (c) 5

Question 12.
(n² + n) is ____ for all n ∈ N.
(a) Even
(b) odd
(c) Either even or odd
(d) None of these

Answer: (a) Even

Question 13.
For all n ∈ N, 3×5²ⁿ⁺¹ + 2³ⁿ⁺¹ is divisible by
(a) 19
(b) 17
(c) 23
(d) 25

Answer: (b) 17

Question 14.
Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
(a) n(n+1)(n+2)/3
(b) n(n+1)(n+2)/6
(c) n(n+2)/6
(d) (n+1)(n+2)/6

Answer: (b) n(n+1)(n+2)/6

Question 15.
{1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
(a) 1/(n + 1) for all n ∈ N.
(b) 1/(n + 1) for all n ∈ R
(c) n/(n + 1) for all n ∈ N.
(d) n/(n + 1) for all n ∈ R

Answer: (a) 1/(n + 1) for all n ∈ N.

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In This Post we are  providing Chapter-3 Trigonometric Function NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON TRIGONOMETRIC FUNCTION

1. If tan x = tan α , then the general solution of the equation is

(a) nπ – α

(b) 2nπ- α

(c) nπ + α

(d) 2nπ + α

Answer► (c) nπ + α

2. If cos a + 2cos b + cos c = 2 then a, b, c are in

(a) 2b = a + c

(b) b² = a × c

(c) a = b = c

(d) None of these

Answer► (a) 2b = a + c

3. In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠DAB = π/6 and ∠ABE =π/3, then the area of the ΔABC is

(a) 8/3

(b) 16/3

(c) 32/3√3

(d) 64/3

Answer► (c) 32/3√3

4. What is the value of tan 3θ ? if tan θ = 1/2

(a) 1/5

(b) -11/2

(c) -1/5

(d) 11/2

Answer► (d) 11/2

5. The solution set of inequality 

(a) 

(b) 

(c) 

(d) 

► (d) 

6. If the median AD of a triangle ABC divides the angle ∠BAC in the ratio 1 : 2, then sinB/sinC is equal to

(a) 2 cos (A/3)

(b) (1/2) sec (A/3)

(c) (1/2) sin (A/3)

(d) 2 cosec (A/3)

Answer► (b) (1/2) sec (A/3)

7. The general solution of sin = 0 is

(a) nπ where n is a real number

(b) nπ, where n is an integer

(c) 2π

(d) π

Answer► (b) nπ, where n is an integer

8. If cos A = sin/2sinC, then ΔABC is

(a) Equilateral

(b) Isosceles

(c) Right angled

(d) None of these

Answer► (b) Isosceles

9. The solutions of the equation 4 cos² x + 6 sin² x = 5 are 

(a) 

(b) 

(c) 

(d) 

Answer► (a) 

10. The sum of the radii of inscribed and circumscribed circle for an n sided regular polygon of side a, is

(a) a cot (π/n) 

(b) a/2 cot(π/2n)

(c) a cot (π/2n)

(d) a/4 cot(π/2n)

Answer► (b) a/2 cot(π/2n)

11. The number of values of x in the interval [0, 3π] satisfying the equation 2 sin² x + 5 sin x – 3 = 0 is 

(a) 6

(b) 1

(c) 2

(d) 4 

Answer► (d) 4 

12. tan(π + x)=

(a) -tan x

(b) tan π + tan x

(c) 0

(d) tan x

Answer► (d) tan x

13. The vertices angle of a triangle is divided into two parts, such that the tangent of one part is 3 times the tangent of the other and the difference of these parts is 30º, then the triangle is

(a) Isosceles 

(b) Right angled 

(c) Obtuse angled

(d) None of these

Answer► (b) Right angled 

14. The number of solutions for the equation sin 2x + cos 4x = 2 is

(a) 0

(b) 1

(c) 2

(d) ∞

Answer► (a) 0

15. The number of pairs (x, y) satisfying the equations sin x + sin y = sin (x + y) and |x| + |y| = 1 is

(a) 0

(b) 2

(c) 4

(d) 6 

Answer► (d) 6 

In This Post we are  providing Chapter-2 Relations and Functions NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON RELATIONS AND FUNCTIONS

1. The domain of the function f = {(1, 3), (3, 5), (2, 6)} is 

(a) 1, 3 and 2(b) {1, 3, 2}(c) {3, 5, 6}(d) 3, 5 and 6

Answer► (b) {1, 3, 2}

2. If n(A) = p and n(B) = q, then how many relations are there from A to B?

(a) pq(b) 3^pq(c) 2^pq(d) (pq)²

Answer► (c) 2^pq

3. In the set W of whole numbers an equivalence relation R defined as follow : aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by

(a) {1, 6, 11, 16, ….}(b) [0, 5, 10, 15,…}(c) {2, 7, 12, 17…}(d) {4, 9, 14, 19, …}

Answer► (a) {1, 6, 11, 16, ….}

4. The point on the curve y = x² which is nearest to (3, 0) is

(a) (1, -1)(b) (-1,1)(c) (-1,-1)(d) (1,1)

Answer► (d) (1,1)

5. If f(x) is an odd differentiable function on R, then df(x)/dx is a/an

(a) Even function(b) Odd function(c) Either even or odd function(d) Neither even nor odd function

Answer► (a) Even function

6. Let S = {1, 2, 3}. The function f : S → S defined as below have inverse for

 (a) f = {(1, 2), (2, 2), (3, 3)}(b) f = {(1, 2), (2, 1), (3, 1)}(c) f = {(1, 3), (3, 2), (2, 1)}(d) f = {(1, 3), (2, 3), (2, 1)}

Answer► (c) f = {(1, 3), (3, 2), (2, 1)}

7. The function f(x) = x – [x] has period of

(a) 0(b) 1(c) 2(d) 3

Answer► (b) 1

8. If f (0) = 0, f (1) = 1, f (2) = 2 and f (x) = f (x – 2) + f (x – 3) for x = 3, 4, 5,&.., then f(9) =

 (a) 12(b) 13(c) 14(d) 10

Answer► (d) 10

9. Let f (x) = x² and g (x) = √x, then

(a) (fog) (2) = 4(b) (gof) (- 2) = 2(c) (gof) (2) = 4(d) (fog) (3) = 6

Answer► (b) (gof) (- 2) = 2

10. If A = [a, b], B = [c,d], C = [d, e] then {(a, c), (a, d), (a,e), (b,c), (b, d), (b, e)} is equal to

(a) A∪(B∩C)(b) A∩(B∪C)(c) A×(B∩C)(d) A×(B∪C)

Answer► (d) A×(B∪C)r

11. If f(x) = x² and g(x) = x are two functions from R to R then f(g(2)) is

(a) 4(b) 8(c) 1(d) 2

Answer► (b) 8

12. The number of binary operations on the set {a, b} are

(a) 2(b) 4(c) 8(d) 16

Answer► (d) 16

13. If f (x) is a function such that f (x + y) = f (x) f (y) and f (3) = 125 then f (x) =

(a) 5(b) x⁵(c) 5^x(d) 5x

Answer► (c) 5^x

14. The function f : C → C defined by f (x) = ax + b/cx + d for x ∈ C where bd ≠ 0 reduces to a constant function if

(a) a = c(b) b = d(c) ad = bc(d) ab = cd

Answer► (c) ad = bc

15. If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is

(a) 3²(b) 2³(c) 2 x 3(d) 2⁶

Answer► (d) 2⁶

In This Post we are  providing Chapter-1 Sets NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON SETS

Question 1. If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is :
(a) 31
(b) 38
(c) 48
(d) 54

Answer : A

Question 2. The cardinality of the set P(P(P(f))) is
(a) 0
(b) 1
(c) 2
(d) 4
[P(A) represents power set of the set A]

Answer : D

Question 3. Let P be a set of squares, Q be set of parallelograms, R be a set of quadrilaterals and S be a set of rectangles. Consider the following :
1. P Ì Q
2. R Ì P
3. P Ì S
4. SÌ R
Which of the above are correct?
(a) 1, 2 and 3
(b) 1, 3 and 4
(c) 1, 2 and 4
(d) 3 and 4

Answer : B

Question 4. If A and B are finite sets, then which one of the following is the correct equation?
(a) n (A – B) = n (A) – n (B)
(b) n (A – B) = n (B – A)
(c) n (A – B) = n (A) – n (A ∩ B)
(d) n (A – B) = n (B) – n (A ∩ B)
[n (A) denotes the number of elements in A]

Answer : C

Question 5. If A = {x, y} then the power set of A is :
(a) {xx, yy}
(b) {f, x, y}
(c) {f,{x},{2y}}
(d) {f,{x},{y},{x,y}}

Answer : D

Question 6. Consider the following equations :
1. A – B = A – (A ∩ B)
2. A = (A ∩ B) ∪ (A – B)
3. A – (B ∪ C) = (A – B) ∪ (A – C)
Which of these is/are correct ?
(a) 1 and 3
(b) 2 only
(c) 2 and 3
(d) 1 and 2

Answer : D

Question 7. If A∪B ¹ f, then n(A∪B) = ?
(a) n(A) + n(B) – n(A∩B)
(b) n(A) – n(B) + n(A∩B)
(c) n(A) – n(B) – n(A∩ B)
(d) n(A) + n(B) + n(A∩ B)

Answer : A

Question 8. Let V = {a, e, i, o, u} and B = {a, i, k, u}. Value of V – B and B – V are respectively
(a) {e, 0} and {k}
(b) {e} and {k}
(c) {0} and {k}
(d) {e, 0} and {k, i}

Answer : A

Question 9. If A = {1, 2, 3, 4}, B = {2, 3, 5, 6} and C = {3, 4, 6,7}, then
(a) A – (B ∩ C) = {1, 3, 4}
(b) A – (B ∩ C) = {1, 2, 4}
(c) A – (B ∪ C) = {2, 3}
(d) A – (B ∪ C) = {f}

Answer : B

Question 10. If A and B are two sets, then A ∩ (A ∪ B)’ equals :
(a) A
(b) B
(c) f
(d) None

Answer : C

Question 11. How many elements has P(A), if A = f ?
(a) two
(b) one
(c) three
(d) zero

Answer : B

Question 12. Let A = {a, b}, B = {a, b, c}. What is A∪B ?
(a) {a, b}
(b) {a, c}
(c) {a, b, c}
(d) {b, c}

Answer : C

Question 13. Which of the following is correct?
(a) A∪B¹A∪A’
(b) (A∩B)’ = A’∪B’
(c) (A’ ∪B’) ¹A’∪A
(d) (A∩B)’ = A’∩B’

Answer : D

Question 14. What is the simplified representation of
(A´ ∩ B´∩C) ∪ (B∩C) ∪ (A ∩ C), where A,B, C are subsets of a set X?
(a) A
(b) B
(c) C
(d) X∩ ( A∪ B∪ C)

Answer : C

Question 15. What does the shaded portion of the Venn diagram given above represent?

(a) (P∩Q)∩(P∩R)
(b) ((P∩Q) – R)∪((P∩R) -Q)
(c) ((P∪Q) -R)∩((P∩R) -Q)
(d) ((P∩Q)∪R)∩((P∪Q) -R)

Answer : B