# MCQ Questions Chapter 10 Vector Algebra Class 12 Mathematics

Please refer to MCQ Questions Chapter 10 Vector Algebra Class 12 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 12 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 12 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 10 Vector Algebra in Class 12 Mathematics provided below to get more marks in exams.

## Chapter 10 Vector Algebra MCQ Questions

Please refer to the following Chapter 10 Vector Algebra MCQ Questions Class 12 Mathematics with solutions for all important topics in the chapter.

MCQ Questions Answers for Chapter 10 Vector Algebra Class 12 Mathematics

Question. The number of seven letter words that can be formed by using the letters of the word ‘SUCCESS’ so that the two C are together but no two S are together, is
(a) 24
(b) 36
(c) 54
(d) None of these

A

Question. The greatest integer less than or equal to (√2+1)6 is
(a) 196
(b) 197
(c) 198
(d) 199

B

Question. The acute angle between the medians drawn through the acute angle of an isosceles right angled triangle is
(a) cos-1(2/3)
(b) cos-1(3/4)
(c) cos-1(4/5)
(d) cos-1(5/6)

C

Question. The acute angle that the vector 2î – 2ĵ + k̂ makes with the plane contained by the two vectors 2î + 3ĵ – k̂ and î – ĵ + 2k̂ is given by
(a) cos-1(1/√3)
(b) sin-1(1/√5)
(c) tan-1(√2)
(d) cot-1(√2)

D

Question. Statement I : The position vector of point R which divides the line joining two points P(2a + b) and Q(a – 3b) externally in the ratio 1 : 2, is 3a + 5b.
Statement II : P is the mid-point of the line segment RQ.
(a) Only statement I is true
(b) Only statement II is true
(c) Both statements are true
(d) Both statements are false

C

Question. Area of rectangle having vertices A, B, C and D with position vector

(a) 1/2 sq. units
(b) 1 sq. units
(c) 2 sq units
(d) 4 sq. units.

C

Question.

(a) 0
(b) a2 + ab
(c) a2b
(d) a̅.b̅

A

Question. The angle between any two diagonal of a cube is
(a) 45°
(b) 60°
(c) 30°
(d) tan-1(2 √2)

D

Question. The vector

A

Question. The moment about the point î + 2ĵ + 3k̂of a force represented by î + ĵ + k̂acting through the point 2i + 3j + k is
(a) 3î + 3ĵ
(b) 3î + ĵ
(c) -î + ĵ
(d) 3î – 3ĵ

D

Question. Which of the following is true?
(a) ĵ x î =k̂
(b) k̂ x ĵ = î
(c) î x k̂ = -ĵ
(d) All of these

C

Question.

(a) centroid of Δ ABC
(b) circumcentre of Δ ABC
(c) orthocentre of Δ ABC
(d) None of these

C

Question. If G is the centroid of triangle ABC, then the value of

(a) 1/2(G̅B̅ + G̅C̅)
(b) 0
(c) 1/2(G̅B̅ – G̅C̅)
(d) None of these

B

Question. a̅ = 3î – 5ĵ and b̅ = 6î + 3ĵ are two vectors and c̅ is a vector such that c̅ = a̅ x b̅ then |a̅ | : |b̅| : c̅|
(a) √34 : √45 : √39
(b) √34 :√45 : 39
(c) 34 : 39 : 45
(d) 39 : 35 : 34

B

Question. If two vectors a and b are such that a = b, then
(a) they have same magnitude and direction regardless of the positions of their initial points
(b) they have same magnitude and different directions
(c) Both (a) and (b) are true
(d) Both (a) and (b) are false

A

Question. Two forces whose magnitudes are 2 gm wt, and 3 gm wt act on a particle in the directions of the vectors 2î + 4ĵ + 4k̂and 4î + 4ĵ + 2k̂ resepectively. If the particle is displaced from the origin to the point (1, 2, 2), the work done is (the unit of length being 1 cm) :
(a) 6 gm-cm
(b) 4 gm-cm
(c) 5 gm-cm
(d) None of these

A

Question. A particle acted on by constant forces 4î + ĵ – 3k̂and 3î + ĵ – k̂ , which is displaced from the point î + 2ĵ + k̂to the point 5î + 4ĵ – k̂The total work done by the forces is
(a) 50 units
(b) 20 units
(c) 30 units
(d) 40 units

D

Question. If the vectors

are perpendicular to each other then a is equal to:
(a) 5
(b) – 6
(c) – 5
(d) 6

C

Question. For the following table a̅ ≠ o̅ , b̅ ≠ o̅

Codes
A B C D E
(a) 2 2 2 1 1
(b) 1 2 1 2 1
(c) 1 2 1 1 1
(d) 2 1 2 1 2

C

Question.

(a) 5 √2
(b) 50
(c) 10 √2
(d) 10

D

Question. If

(a) î – ĵ + k̂
(b) 2ĵ – k̂
(c) î
(d) 2î

C

Question. Statement I : The point A(1, –2, – 8), B(5, 0, – 2) and C(11, 3, 7) are collinear.
Statement II : The ratio in which B divides AC, is 2 : 3
(a) Only statement I is true
(b) Only statement II is true
(c) Both statements are true
(d) Both statements are false

C

Question. Which among the following is correct statement?
(a) A quantity that has only magnitude is called a vector
(b) A directed line segment is a vector, denoted as |AB| or |a|
(c) The distance between initial and terminal points of a vector is called the magnitude of the vector
(d) None of the above

C

Question. Statement – I: Scalar components of the vector with initial point (2, 1) and terminal point (–5, 7) are – 6 and 7.
Statement – II: Vector components of the vector with initial point (2, 1) and terminal point (–5, 7) are – 7î and 6ĵ .
(a) Only statement I is true
(b) Only statement II is true
(c) Both statements are true
(d) Both statements are false

B

Question.

(a) 3a2 + b2 – c2/2
(b) a2 + 3b2 – c2/2
(c) a2 – b2 + 3c2/2
(d) a2 + 3b2 + c2/2

A

Question. A vector perpendicular to the plane containing the vectors

(a) tan-1√14
(b) sec-1√14
(c) tan-1√15
(d) None of these

A

Question. Which of the following statement is correct?
(a) [a b c] is a scalar quantity
(b) The magnitude of the scalar triple product is the volume of a parallelopiped formed by adjacent sides given by three vectors a, b and c
(c) The volume of a parallelopiped form by three vectors a, b and c is equal to |a. (b × c)|
(d) All are correct

D

Question.

If the vector c̅ lies in the plane of a̅ and b̅ , then x equals
(a) – 4
(b) – 2
(c) 0
(d) 1.

B

Question.

A

Question. If ABCDEF is a regular hexagon and A̅B̅ + A̅C̅ + A̅D̅ + A̅E̅ + A̅F̅ + = nA̅D̅ . Then n is
(a) 1
(b) 2
(c) 3
(d) 5/2 î – ĵ + k̂

C

Question. The integer k for which the inequality x2 – 2(4k-1)x + 15k2 – 2k – 7 > 0 is valid for any x, is
(a) 2
(b) 3
(c) 4
(d) None of these

B

Question. If C is a skew-symmetric matrix of order n and X is n x 1 column matrix, then X’ C X is a
(a) scalar matrix
(b) unit matrix
(c) null matrix
(d) None of these

C

Question. If r is a real number such that | r | <1 and if a = 5 (1 – r ), then
(a) 0 < a < 5
(b) – 5 < a < 5
(c) 0 < a < 10
(d) 0 ≤ a < 10

C

Question. If n is an integer greater than 1, then a – nC1(a-1) + nC2(a-2) + ……+ (-1)n (a-n) is equal to
(a) a
(b) 0
(c) a2
(d) 2n

B

Question. If α , β and g are the roots of the equation
x2(x+e) = e (x+1). Then, the value of the determinant

(a) – 1
(b) 1
(c) 0
(d) 1+1/α + 1/β + 1/γ

C

Question. The greatest term in the expansion of (3-5x)11 when x = 1/5 , is
(a) 55 x 39
(b) 46 x 39
(c) 55 x 36
(d) None of these

A

Question. If x is so small that its two and higher power can be neglected and if (1-2x)-1/2 (1-4x)-5/2 = 1 x kx ,then k is equal to
(a) – 2
(b) 1
(c) 10
(d) 11

D

Question. Let R be a relation defined by R = {(x, x ) : x3 is a prime number <10}, then which of the following is true?
(a) R = {(1, 1), (2, 8), (3, 27), (4, 64), (5, 125),(6, 216), (7, 343), (8, 512), (9, 729)}
(b) R = {(2, 8), (3, 27), (5 , 125), (7, 343)}
(c) R = {(2, 8), (4, 64), (6, 216), (8, 512)}
(d) None of the above

B

Question. If x = – 5 is a root of

= 0 , then the other two roots are
(a) 3, 3.5
(b) 1, 3.5
(c) 3, 6
(d) 2, 6

B

Question. From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. Atmost 19 passed Mathematics and Physics, atmost 29 passed Mathematics and Chemistry and atmost 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is
(a) 11
(b) 12
(c) 13
(d) 14

D

Question. The determinant

(a) x,y,z are in AP
(b) x,y,z are in GP
(c) x,y,z are in HP
(d) xy,yz,zx are in AP

B

Question. In an examination a candidate has to pass in each of the papers to be successful. If the total number of ways to fail is 63, how many papers are there in the examination?
(a) 6
(b) 8
(c) 10
(d) 12

A

Question. The common roots of the equations z3 + 2z2 + 2z + 1 = 0 and z1985 + z100 + 1 = 0 are
(a) -1,ω
(b) -1 ,ω2
(c) ω,ω2
(d) None of these

C

Question. The value of the natural numbers n such that inequality 2n > n + is valid, is
(a) for n ≥ 3
(b) for n < 3
(c) formn
(d) for any n

A

Question. Let w = cos(2π/7) + i sin (2π/7) and α = w + w2 + w4 and β = w3 + w5 + w6 , then α+β s equal to
(a) 0
(b) -1
(c) -2
(d) 1

B

Question. The 8th term of (3x + 2/3x2)12 when expanded in ascending power of x, is
(a) 228096/x3
(b) 228096/x9
(c) 328179/x9
(d) None of these

A

Question. If log0.5 (x-1) < log0.25(x-1) , then x lies in the interval
(a) (2, ∞)
(b) (3, ∞)
(c) (-∞, 0)
(d) (0, 3)

A

Question. If the roots of the equation x2-2ax + a2 + a – 3 = 0 are real and less than 3, then
(a) a < 2
(b) 2 ≤ a ≤ 3
(c) 3 ≤ a ≤ 4
(d) a > 4

A

Question. LetTn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides.
If Tn+1 – Tn = 21 , then n equals
(a) 4
(b) 6
(c) 7
(d) None of the

C

Question. If A andB are square matrices such thatB = -A-1 BA , then
(a) AB + BA = O
(b) (A + B)2 = A2 – B2
(c) (A + B)2 = A2 + 2AB + B2
(d) (A + B)2 = A + B

A

Question. Let H(x) = f(x)/g(x) , where f(x) =1 – 2 sin2 x and g(x) = cos 2x , ∀f : R → [-1,1] and g :R → [-1,1].
Domain and range of H(x ) are respectively
(a) R and {1}
(b) R and {0, 1}
(c) R ~ {(2n + 1) π/4} and {1},n ∈ I
(d) R ~ {(2n+1)π/2} and {0, 1},n ∈ I

C

Question. If the sets A and B are defined as A = {(x,y) : y = 1/x , 0 ≠ x ∈ R} and B = {(x,y) : y = -x , x ∈ R} , then
(a) A ∩ B = A
(b) A ∩ B = B
(c) A ∩ B = φ
(d) None of these

C

(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
(c) Statement I is true; Statement II is false
(d) Statement I is false; Statement II is true

Question. The general term in the expansion of (a+x)n is nCr , an-r xr .
Statement I The third term in the expansion of (2x + 1/x2)m does not contain x . The value of x for which that term equal to the second term in the expansion of (1+x3)30 is 2 .
Statement II

B

Question. Sets A and B have four and eight elements, respectively.
Statement I The minimum number of elements in A È B is 8.
Statement II A ∩ B = 5

C

Question. Let a ≠ 0,p ≠ 0 and Δ =

Statement I If the equations ax2 + bx + c = 0 and px + q = 0 have a common root, then Δ = 0.
Statement II If Δ = 0, then the equations ax2 + bx + c = 0 and px + q = 0 have a common root.

C

Question.
Statement I The number of natural numbers which divide 102009 but not 102008 is 4019.
Statement II If p is a prime, then number of divisors of Pn is pn+1 – 1 .

C

Question. Suppose A =

matrices such that X’ AX = B.
Statement I X is non-singular and det (X) = ± 2 .
Statement II X is a singular matrix.

C

Assertion – Reason Type Questions :

(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.

Question. Assertion :

Reason: If

B

Question. Assertion : For any three vectors a, b and c, [a b c] = [b c a] = [c a b]
Reason : Cyclic permutation of three vectors does not change the value of the scalar triple product.

A

Question. Assertion : The adjacent sides of a parallelogram are along

Reason : Two vectors are perpendicular to each other if their dot product is zero.

D

Question. Assertion :

Reason :