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MCQ Questions for Class 12 Commerce Maths Quiz with Answers Chapter Wise PDF Download

CBSE Multiple Choice Type Questions for 12th Class Commerce Maths PDF formatted study resources are available for free download. These Grade 12 Commerce Maths CBSE MCQ Mock Test helps you learn & practice the concepts in a fun learning way.

Class 12 Commerce Maths MCQs Multiple Choice Questions with Answers

Here are the chapterwise CBSE MCQ Quiz Test Questions for Class 12th Commerce Maths in pdf format that helps you access & download so that you can practice online/offline easily.

Application Of Derivatives Class 12 Commerce Maths MCQ Quiz

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Application Of Derivatives Questions and Answers

Application Of Derivatives Quiz Question Answer
The tangent at the point (2,2) to the curve, x2y22x=4(1y) does not pass through the point. (2,7)
If the tangent to the conic, y6=x2 at (2, 10) touches the circle, x2+y2+8x2y=k (for some fixed k) at a point (α,β); then (α,β) is; (817,217)
Let b be a nonzero real number. Suppose f:RR is a differentiable function such that f(0)=1.
If the derivative f' of f satisfies the equation f(x)=f(x)b2+x2 for all xR, then which of the following statements is/are TRUE?
f(x)f(x)=1 for all xR
What is the x-coordinate of the point on the curve f(x)=x(7x6), where the tangent is parallel to x-axis? 27
Consider the following statements in respect of the function f(x)=x31,xϵ[1,1]
I. f(x) is increasing in [1,1]
II. f(x) has no root in (1,1).
Which of the statements given above is/ are correct?
Only I
If x2f(4a)=y2f(a25) respresents and ellipse with major axis as y-axis and f is a decreasing function, then  a(1,5)
The values of x at which f(x)=sinx is stationary are given by
(2n+1)π2, nZ

The number of stationary points of f(x)=sinx in [0,2π] are
2
Find the equation of a line passing through (2,3) and parallel to tangent at origin for the circle x2+y2+xy=0 xy+5=0

 Stationary point of y=logxx(x>0) is
(e,1e)

Application Of Integrals Class 12 Commerce Maths MCQ Quiz

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Application Of Integrals Questions and Answers

Application Of Integrals Quiz Question Answer
The area of the region bounded by the parabola (y2)2=x1, the tangent to the parabola at the point (2, 3) and the x-axis is 

9
The area (in square units) of the region bounded by the curves y+2x2=0 and y+3x2=1, is equal to  43
The area (in sq. units) of the region {(x,y):x0,x+y3,x24y and y1+x} is. 52
The area of the region described by A=(x,y):x2+y21 and y21x is: π2+43
The parabolas y2=4x and x2=4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1,S2,S3 are respectively the areas of these parts numbered from top to bottom(Example: S1 is the area bounded by y=4 and x2=4y ); then S1,S2,S3 is  
1:1:1
The area of the region bounded by the curves x+2y2=0 and x+3y2=1 is equal to 
43
 The area bounded by the curves y= cosx and y= sinx between the ordinates x=0 and x=3π2:
422
The area(in sq. units) of the smaller portion enclosed between the curves, x2+y2=4 and y2=3x, is. 13+4π3
The area bounded between the parabolas 4x2=y and x2=9y, and the straight line y=2 is:
2023
The area enclosed between the curves y=ax2 and x=ay2(a>0) is 1 sq. unit, then the value of a is
1/3

Continuity And Differentiability Class 12 Commerce Maths MCQ Quiz

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Continuity And Differentiability Questions and Answers

Continuity And Differentiability Quiz Question Answer
If f(x) is a differentiable function and g(x) is a double differentiable function such that |f(x)|1 and f(x)=g(x). If f2(0)+g2(0)=9such that there exists some c(3,3) such that g(c). g(c)<0, True or false
True
Let f be a polynomial function such that f(3x)=f(x)f(x), for all xR. Then. f(2)f(2)=0
If y=[x+x21]15+[xx21]15, then (x21)d2ydx2+xdydx is equal to. 225y
Let f:RR and g:RR be functions satisfying f(x+y)=f(x)+f(y)+f(x)f(y) and f(x)=xg(x) for all x,yR. If limx0g(x)=1, then which of the following statements is/are TRUE? The derivative f(0) is equal to 1
For the curve x=t21,y=t2t, tangent is parallel to x - axis where,
t=12
ddx(tan1x) 11+x2.
Say true or false.
Every continuous function is always differentiable.
False
d(sin1x)dx
1(1x2)
If y is expressed in terms of a variable x as y=f(x), then y is called Explicit function
The function f(x)=1sinx+cosx1+sinx+cosx is not defined at x=π. The value of f(π) so that f(x) is continuous at x=π is 1

Determinants Class 12 Commerce Maths MCQ Quiz

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Determinants Questions and Answers

Determinants Quiz Question Answer
The number of distinct real roots of the equation, |cosxsinxsinxsinxcosxsinxsinxsinxcosx|=0 
in the interval [π4,π4] is/are :
2
The points (0,83),(1,3) and (82,30) : lie on a straight line.
If A=[2341], then adj (3A2+12A) is  equal to. [51638472]
Let P=[aij] be a 3 × 3 matrix and let Q=[bij], where bij=2i+jaij for 1i,j3. If the determinant of P is 2, then the determinant of the matrix Q is 213
Consider three points P=(sin(βα),cosβ),Q=(cos(βα),sinβ) and R=(cos(βα+θ),sin(βθ)) , where 0<α, β, θ<π4. Then
P,Q,R are non-collinear
The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p, is 2p1
Let k be a positive real number and let A=[2k12k2k2k12k2k2k1] and B=[02k1k12k02kk2k0] . 
If det (adjA)+det(adjB)=106,then[k] is equal to 

[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k].
4
The value of |U| is
3
A=[1234],B=[2134] then |(BTAT)1| is equal to 1
If three points (k,2k),(2k,3k),(3,1) are collinear, then k is equal to:
2

Differential Equations Class 12 Commerce Maths MCQ Quiz

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Differential Equations Questions and Answers

Differential Equations Quiz Question Answer
For xϵR,x0, if y(x) is a differentiable function such that xx1y(t)dt=(x+1)x1ty(t)dt, then y(x) equals:
(Where C is a constant)
Cx3e1x
The differential equation dydx=1y2y determines a family of circles with:
fixed radius 1 and variable centres along the x-axis
Check whether the function is homogenous or not. If yes then find the degree of the function
g(x)=x28x3.
Not homogenous
Solution of differential equation dydx=sinx+2x, is y=x2cosx+c
Which of the following is/are correct regarding homogenous functions?
Denoted by: f(kx)=knf(v), where n is the degree
The solution of dydx=elogx is: 2y=x2+c
The solution of dydx=2x3y2 is: y3x2=c
The solution of dydx2xy1+x2=0 is y=c(1+x2)
The solution of x2dydx=2 is
y=2x+c
Check whether the function is homogenous or not. If yes then find the degree of the function
g(x)=8x4.
Homogenous with degree 4

Integrals Class 12 Commerce Maths MCQ Quiz

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Integrals Questions and Answers

Integrals Quiz Question Answer
Let F(x)=f(x)+f(1x), where f(x)=xllogtl+tdt. Then F(e) equals 12
The following integral π/2π/4(2cosecx)17dx is equal to log(1+2)02(eu+eu)16du
The value of g(12) is? π
xlogxdx is equal to x24(2logx1)+c
dxx10x2;x>1= ______ +C. 14sec1(x4)
Evaluate the integral
1011+x2dx
π/4
The value of etanθ(secθsinθ)dθ is equal to ?
etanθcosθ+C
 Find π20cos3x dx 23
10tan1(x1x2)dx π21
10ex.x(x+1)2dx= e21

Inverse Trigonometric Functions Class 12 Commerce Maths MCQ Quiz

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Inverse Trigonometric Functions Questions and Answers

Inverse Trigonometric Functions Quiz Question Answer
Statement I :  The equation (sin1x)3+(cos1x)3aπ3=0 has a solution for all a132.
Statement II : For any xϵR,sin1x+cos1x=π2 and 0(sin1xπ4)29π216.
Statement I is false and statement II is true.
If cos1xcos1y2=α, then 4x24xycosα+y2 is equal to 4sin2α
If sin1(2a1+a2)cos1(1b21+b2)=tan1(2x1x2), then what is the value of x? ab1+ab
The value of tan1(1)+cos1(12)+sin1(12) is equal to  3π4
cos1{12x2+1x2.1x24}=cos1x2cos1x holds for

0x1
Solve: tan1(xy)tan1xyx+y is equal to π4
Value of tan1{sin21cos2} is 1π4
The number of triplets (x,y,z) satisfies the equation f(x,y,z)=sin1x+sin1y+sin1z=3π2 is 1
Sin-1 (35)+Sin1(513)=sin1X thenx=
5665
If sec1x+sec1y+sec1z=3π, then xy+yz+zx= _______. 3

Linear Programming Class 12 Commerce Maths MCQ Quiz

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Linear Programming Questions and Answers

Linear Programming Quiz Question Answer
Minimise Z=nj=1mi=1cij.xij
Subject to mi=1xij=bj,j=1,2,......n
nj=1xij=bj,j=1,2,......,m is a LPP with number of constraints
m+n
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region. feasible
Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that The value of the objective function for a maximization problem will likely be less than that for the simplex solution.
If a = b then ax = ........... bx
The bar graph shows the grades obtained by a group of pupils in a test.
If grade C is the passing mark, how many pupils passed the test?

407807_3f3eaf2b94e44e8b8e7a4309fee6bd7f.png
30
An iso-profit line represents An infinite number of solutions all of which yield the same profit
In linear programming, lack of points for a solution set is said to have no feasible solution
If  x + y = 3 and xy = 2, then the value of x3y3 is equal to  7
If the constraints in linear programming problem are changed the problem is to be re-evaluated
The bar graph shows the number of cakes sold at a shop in four days.
What is the difference in number of cakes between the highest and the lowest daily sale?

407804_a50f8fd2015f46a7986020a56d31adcb.png
20

Matrices Class 12 Commerce Maths MCQ Quiz

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Matrices Questions and Answers

Matrices Quiz Question Answer
Let X and Y be two arbitrary, 3×3, non-zero, skew-symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric? X23+Y23
If A=[3112] and I=[1001], then the correct statement is: A25A+7I=O
If AB = AC then  B need not be equal to C
If A2=A, B2=B, AB=BA=O (Null Matrix), then (A+B)2=
A+B
I A=[0110],  A4=
(I is an identity matrix.)
I
lf A=[ocbcoabao]and B=[a2abacabb2bcacbcc2], then AB=
O
lIf A=[a0a0], B=[00bb], then AB= 
O
If A=[123425] and B=[234521], then 
AB, BA exist and are not equal
[x00y][abcd]=
[axbXycdy]
If A=[134134134], then A2=
Null matrix

Probability Class 12 Commerce Maths MCQ Quiz

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Probability Questions and Answers

Probability Quiz Question Answer
Let A and E be any two events with positive probabilities :
Statement - 1 : P(EA)P(AE)P(E)
Statement - 2 : P(AE)P(AE)
Both the statement are true
If C and D are two events such that CD and P(D)0, then the correct statement among the following is 
P(CD)P(C)
If A and B are any two events such that P(A)=25 and P(AB)=320, then the conditional probability, P(A|(AB)), where A' denotes the complement of A, is equal to: 517
It is given that the events A and B are such that P(A)=14, P(A|B)=12 and P(B|A)=23. Then P(B) is 

13
Assertion is False, Reason is True
A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T1) =10P (computer turns out to be defective given that it is produced in plant T2).
where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2 is
7893
One of the two boxes, box I and box II, was selected at random and balls are drawn randomly out of this box. The ball was found to be red.If the probability that this red ball was drawn from box II is 13, then the correct option options with the possible values of n1,n2,n3 and n4 is (are)
n1=3,n2=6,n3=10,n4=50
A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required.
The conditional probability that X6 given X>3 equals
2536
Let Ec denote the complement of an event E. Let E, F, G be pairwise independent events with P(G)>0 and P(EFG)=0. Then P(EcFc|G) equals 
P(Ec)P(F)
Let X and Y be two events such that P(X)=13,P(X/Y)=12 and P(Y/X)=25. Then P(X|Y)=12

Relations And Functions Class 12 Commerce Maths MCQ Quiz

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Relations And Functions Questions and Answers

Relations And Functions Quiz Question Answer
If f(x)=x+tanx and f is inverse of g, then g(x) is equal to 12+(xg(x))2
f:RR is a function defined by f(x)=10x7.  If  g=f1  then  g(x)=  
x+710
A constant function f:AB will be one-one if n(A)=1
If f:NN and f(x)=x2 then the function is
one to one function
f(x)=1, if x is rational and f(x)=0, if x is irrational
then  (fof)(5)=
1
If f(x)=3x+2,g(x)=x2+1, then the value of (fog)(x2+1) is 3x4+6x2+8
If f:AB is surjective then every element of B has at least one pre-image in A
If f:(0,)(0,) is defined by f(x)=x2, then f1(x)=
x
f:RR,g:RR and  f(x)=sinx, g(x)=x2 then fog(x)=
sinx2
Find the value of (gf)(6) if g(x)=x2+52 and f(x)=x41.
2.75

Three Dimensional Geometry Class 12 Commerce Maths MCQ Quiz

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Three Dimensional Geometry Questions and Answers

Three Dimensional Geometry Quiz Question Answer
If a line makes an angle of π/4 with the positive direction of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is π2
A line AB in three-dimensional space makes angles 45o and 120o with the positive x-axis and the positive y-axis respectively. lf AB makes an acute angle e with the positive z-axis, then e equals
60o
A line makes the same angle Θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that sin2β=3sin2Θ, then cos2Θ equals: 
35
A line in the 3-dimensional space makes an angle θ(0<θπ2) with both the x and y axes, then the set of all values of θ is the interval : [π4,π2]
The points with position vectors 60ˆi+3ˆj, 40ˆi8ˆj, aˆi52ˆj are collinear if a=40
The vector equation r=i2jk+t(6jk) represents a straight line passing through the points: (1,2,1) and (1,4,2)
A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin2β=3sin2θ, then cos2θ equals 35
The points with position vectors 60i+3j,40i8j and ai52j are collinear if
a=40
Equation to a line parallel to the vector 2ˆiˆj+ˆk and passing through the point ˆi+ˆj+ˆk
(x1)ˆi+(y1)ˆj+(z1)ˆk=λ(2ˆiˆj+ˆk)
The direction ratios of the diagonal of the cube joining the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes)
1,1,1

Vector Algebra Class 12 Commerce Maths MCQ Quiz

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Vector Algebra Questions and Answers

Vector Algebra Quiz Question Answer
If |C|2=60 and C×(ˆi+2ˆj+5ˆk)=0, then a value of C(7ˆi+2ˆj+3ˆk) is :
122
In a parallelogram ABCD, |AB|=a,|AD|=b and |AC|=c, then DB.AB has the value 12(a2+b2c2)
Let P, Q, R and S be the points on the plane with position vectors 2ˆiˆj, 4ˆi, 3ˆi+3ˆj and 3ˆi+2ˆj respectively. The quadrilateral PQRS must be a
parallelogram, which is neither a rhombus nor a rectangle
Statement -1 is True, Statement -2 is False
ABCD is a parallelogram and AC,BD be its diagonals Then AC+BD is
2BC
The triangle ABC is defined by the vertices A=(0,7,10) , B=(1,6,6) and C=(4,9,6). Let D be the foot of the attitude from B to the side AC then BD is
¯i+2¯j+2¯k
The point C=(125,15,45) divides the line segment AB in the ratio 3:2. If B=(2,1,2) then A is
(3,1,1)
Let A=ˆi+6i+6k,B=4ˆi+9ˆi+6ˆk,G=53ˆi+223ˆj+223ˆk. If G is the centroid then the triangle ABC is
A right angled isosceles triangle
If A(¯a) , B(¯b) and C(¯c) be the vertices of a triangle ABC whose circumcentre is the origin then orthocentre is given by
¯a+¯b+¯c
Let a,b,c,d be the position vectors of the points A,B,C,D respectively. The condition for the figure ABCD to be a parallelogram is
ˆa+ˆc=ˆb+ˆd

Commerce Maths MCQ Questions for Class 12 - Practice Test with Solutions 

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