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

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

Class 12 Maths MCQs Multiple Choice Questions with Answers

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

Application Of Derivatives Class 12 Engineering Maths MCQ Quiz

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Application Of Derivatives Questions and Answers

Application Of Derivatives Quiz Question Answer
The curve for which the ratio of the length of the segment by any tangent on the Yaxis to the length of the radius vector is constant (K), is (y+x2+y2)xk1=c
The points on the curve 9y2=x3, where the normal to the curve makes equal intercepts with the axes are ........... (4,83)
The angle between the tangents at ant point P and the line joining P to the original, where P is a point on the curve in (x2+y2)=ctan1yx,c is a constnt, is  independent of x
The slope of the tangent to the curve at a point (x,y) on it is proportional to (x2). If the slope of the tangent to the curve at (10,9)  on it is 3. The equation of the curves is . y=316(x2)2+3
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)

Application Of Integrals Class 12 Engineering Maths MCQ Quiz

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Application Of Integrals Questions and Answers

Application Of Integrals Quiz Question Answer
Area of the region bounded by the curve (yx)2=x3 and the line x=1 is 43
Area bounded by the curves y=logex and  y=(logex)2 is ?
e2
Area enclosed by the curve y=f(x) defined parametrical as x=1t21+t2,y=2t1+t2 π sq. units
The area (in sq units) of the region bounded by the curve y=x and the lines y=0,y=x2, is  103
The area bounded by the curve y=x3, x-axis and two ordinates x=1 to x=2 equal to  15/4 sq.unit
Area enclosed by the graph of the function y=ln2x1 lying in the 4th quadrant is 4e
Area bounded by the curves y=sinx, tangent drawn to it at x=0 and the line x=π2 is equal to π222 sq.units
Area bounded by curves x=y1
and y=x+1 is -
16squnit
The area of the region bounded by the curves y=x2 and y=|x| is 13
The area enclosed by the line y = x + 1, X- axis and the lines x = -3 and x = 3 is  10

Continuity And Differentiability Class 12 Engineering Maths MCQ Quiz

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Continuity And Differentiability Questions and Answers

Continuity And Differentiability Quiz Question Answer
Let f(x)=x|x|,g(x)=sinx and h(x)=(gof)(x). Then h(x) is not differentiable at x=0
If f(x)=0 for x<0 and f(x) is differentiable at x=0, then for x0,f(x) may be x3/2
ddx(sin1{1+x+1x2})= 121x2
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: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
Let F(x) = (f(x))2+(f(x))2,F(0)6 where f(x) is a differential  function such that |f(x)|1x[1,1] then choose the correct statement (s) For some c(1,1), F(c)6,F"(c)0
If f(x)=sin1[2x1+x2],then f(x) is differentiable on  R-{-1,1}
ddx(tan1x) 11+x2.
If x+y=xy then dydx equals yxy111xylogx

Determinants Class 12 Engineering Maths MCQ Quiz

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Determinants Questions and Answers

Determinants Quiz Question Answer
If A is a singular matrix, then adj A is singular
If  A=(1235),  then the value of the determinant  |A20095A2008|  is 6
If A=[4131] then the determinant of the matrix (A20162A2015A2014) is 2016
If A=A=[a000a000a],then |A||AdjA| is equal to a9
If A is a square matrix (adjA)(adjA) 2A
If adj B = A, |P| = |Q| = 1, then adj (Q1BP1) is PAQ
There are  12  points in a plane. The number of the straight lines joining any two of them when  3  of them are collinear is. 64
If A is singular matrix, then A.(adjA) is  singular
If A is 4×4 matrix and if ||A|adj(|A|A)|=|A|n, then n is  11
If A=[5ab32] and A(adjA)=AAT then 5a+3b is equal to  5

Differential Equations Class 12 Engineering Maths MCQ Quiz

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Differential Equations Questions and Answers

Differential Equations Quiz Question Answer
The solution of dydx=2xy is: 2x2y=c
The solution of (x2+x)dydx=1+2x is: ey=c(x2+x)
exydx+eyxdy=0
Solve the differential equations.
e2x+e2y=k
The solution to the differential equation ylny+xy=0 wherey(1)=e, is: x(lny)=1
xbcbc.xcaca.xabac=

1
The solution of x2dydx=2 is
y=2x+c
Which of the following differential equation is linear ? (1+x)dydxxy=1
Degree of d3ydx3+2(dydx)4+dydx=cosx is 1
The solution of dydx=elogx is: 2y=x2+c
Check whether the function is homogenous or not. If yes then find the degree of the function
g(x)=4x2.
Not homogenous

Integrals Class 12 Engineering Maths MCQ Quiz

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Integrals Questions and Answers

Integrals Quiz Question Answer
ex3+x21(3x4+2x3+2x2x=h(x)+c then the value of h(1)h(1). 1
1x2(1+x2)1+x4dx is equal to 
12sin1{2xx2+1}+c
Let 1n=12011xndx where n>2, then
In<π6
If Im=e1(lnx)mdx, where mϵN,then I10+10I9 is equal to- e
If for every integer n, n+1nf(x)dx=n2, then the value of 42f(x)dx is - 16
403602x2x+14036xdx=............ 4035
If I1=1x11+t2dt and I2=1/x111+t2dt for x > 0, then  I1=I2
1π2214+x2dx= 14
11x41+ex7dx is 1/5
Evaluate: x4x3dx 2sin1(x322)+c

Inverse Trigonometric Functions Class 12 Engineering Maths MCQ Quiz

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Inverse Trigonometric Functions Questions and Answers

Inverse Trigonometric Functions Quiz Question Answer
ifx>0thentanh1(x21x2+1) logex
If cos1xcos1(y2)=α ax24xycosα+y2= 4sin2α
cot1(cosα)tan1(cosα)=x, then sinx is equal to tan2α2
cos1(x3)+cos1(y2)=(θ2) , then the value of 4x2-12xy cos(θ2)+9y2 is equal to  18(1cosθ)
cos1{12x2+1x2.1x24}=cos1x2cos1x holds for 0x1
tan1y=tan1x+tan1(2x1x2) where |x|<13. Then a value of y is: 3xx313x2
4tan115tan1170+tan1199= π
cos1(cos7π6) is equal to 5π6
The value of sin1(cos(cos1(cosx)+sin1(sinx))),wherex(π2,π), is equal to  π2
The value of sin1(sin3)+cos1(cos7)tan1(tan5) is π1

Linear Programming Class 12 Engineering Maths MCQ Quiz

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Linear Programming Questions and Answers

Linear Programming Quiz Question Answer
Solution of LPP to minimize z = 2x + 3y, such that x0,y0,1x+2y10 is x=0,y=12
The point which provides the solution to the linear programming problem : Max P= 2x+3y subject to constraints :x0,y0,2x+2y9,2x+y7,x+2y8, is (1,3.5)
Feasible region is the set of points which satisfy all the given constraints
If the corner points of the feasible solution are (0, 10), (2, 2) and (4, 0), then the point of minimum z = 3x + 2y is  (2, 2)
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

Matrices Class 12 Engineering Maths MCQ Quiz

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Matrices Questions and Answers

Matrices Quiz Question Answer
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
A=[012103230] then A+AT=
[020200000]
[x00y][abcd]=
[axbXycdy]
If A=[134134134], then A2=
Null matrix

Probability Class 12 Engineering Maths MCQ Quiz

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Probability Questions and Answers

Probability Quiz Question Answer
Three number are chosen at random without replacement from {1,2,3,...8}. The probability that their minimum is 3, given that their maximum is 6 is  328
Difference between sample space and subset of sample space is considered as  complementary events.
If A and B are two events in a sample space S such that P(A)0,  then  P(BA)= P(AB)P(A)
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
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

Relations And Functions Class 12 Engineering Maths MCQ Quiz

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Relations And Functions Questions and Answers

Relations And Functions Quiz Question Answer
If f:NN,f(x)=x+3, then f1(x)=..... does not exist
If f(x)=8x3 and g(x)=x1/3 then (gof)(x)=? 2x
Which of the following functions are one-one?
h:RR given by h(x)=x3+4 for all xR
A mapping function f:XY is one-one, if
f(x1)=f(x2)x1=x2 for all x1,x2X
Let R be a relation from a set A to a set B,then
RA×B
Number of one-one functions from A to B where n(A)=4,n(B)=5. 120
Find the value of (gf)(6) if g(x)=x2+52 and f(x)=x41.
2.75
The first component of all ordered pairs is called Domain
Find the correct expression for f(g(x)) given that f(x)=4x+1 and g(x)=x22 4x27
The second component of all ordered pairs of a relation is Range

Three Dimensional Geometry Class 12 Engineering Maths MCQ Quiz

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Three Dimensional Geometry Questions and Answers

Three Dimensional Geometry Quiz Question Answer
The equation of a plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c) is given by? xa+yb+zc=1
The direction consines of the line drawn from P(5,3,1)toQ(1,5,2) is (67,27,37)
If a straight line makes an angle of 60 with each of the X and Y axes, the angle which it makes with the Z axis is 3π4
The points (p+1,1),(2p+1,3) and (2p+2,2p) are collinear if  p=12
In a plane there are 10 points, no three are in same straight line except 4 points which are collinear, then the number of straight lines are 45
The st lines whose direction cosines satisfy:
al+bm+cn=0 and fmn+gnl+hlm=0 are perpendicular if: 
fa+gb+hc=0
The equation of the plane which passes through the x-axis and perpendicular to the line (x1)cosθ=(y+2)sinθ=(z3)0 is xcosθ+ysinθ=0
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines , will be (m1n2 - m2n1), (n1l2 - n2l1), (l1m2 - l2m1)
The point collinder with (1,-2,-3) and (2,0,0) amoung the following is  (0, -4, -6)
A line with direction ratio 2,7,-5 is drawn to intersect the lines xy3=y71=z+21 and x+33=y32=z64 at P and Q respectively, then length of PQ is- 78

Vector Algebra Class 12 Engineering Maths MCQ Quiz

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Vector Algebra Questions and Answers

Vector Algebra Quiz Question Answer
The position vector of A is 2i+3j+4kAB=5i+7j+6k, then the position vector of B is 7i10j10k
Line passing through (3,4,5) and (4,5,6) has direction ratios 1,1,1
In a parallelogram ABCD, |AB|=a,|AD|=b and |AC|=c, then DB.AB has the value 12(a2+b2c2)
If |C|2=60 and C×(ˆi+2ˆj+5ˆk)=0, then a value of C(7ˆi+2ˆj+3ˆk) is :
122
If a×b=b×a, then a=kb
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)

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