MHT CET 2021 Paper I

A line through the point A(2,0) which makes an angle of 30∘ with the positive direction of X-axis is rotated about A in clockwise direction
through an angle of 15∘. Then, the equation of the straight line in the new position is

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A line through the point A(2,0) which makes an angle of 30∘ with the positive direction of X-axis is rotated about A in clockwise direction
through an angle of 15∘. Then, the equation of the straight line in the new position is

Find the value of cos(‌

and x lies in third quadrant.

Find the value of cos(‌

and x lies in third quadrant.

Q.8 Correct

Q.8 In-correct

Q.8 Unattempt

The locus of a point which moves, so that the ratio of the length of the tangents to the circles x2+y2+4x+3=0 and x2+y2−6x+5=0 is 2:3, is

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The locus of a point which moves, so that the ratio of the length of the tangents to the circles x2+y2+4x+3=0 and x2+y2−6x+5=0 is 2:3, is

The circles x2+y2+6x+6y=0 and x2+y2−12x−12y=0

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The circles x2+y2+6x+6y=0 and x2+y2−12x−12y=0

The mean and variance of n observations x1,x2,x3,...,xn are 5 and 0 , respectively. If

n

∑

x=1

xi2=400, then the value of n is equal to

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The mean and variance of n observations x1,x2,x3,...,xn are 5 and 0 , respectively. If

n

∑

x=1

xi2=400, then the value of n is equal to

The variance of first n natural numbers is

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The variance of first n natural numbers is

Out of 50 tickets numbered 00,01,02,...,49, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7 , given that the sum of the digits is 8 , is

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Out of 50 tickets numbered 00,01,02,...,49, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7 , given that the sum of the digits is 8 , is

The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is

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The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is

Consider the following statements
r : If a number is a multiple of 9 , then it is multiple of 3.
Let p and q denote the statements
p: A number is a multiple of 9.
q : A number is a multiple of 3 .
Then, if p then q is the same as

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Consider the following statements
r : If a number is a multiple of 9 , then it is multiple of 3.
Let p and q denote the statements
p: A number is a multiple of 9.
q : A number is a multiple of 3 .
Then, if p then q is the same as

The negation of the statement 7 is greater than 4 or 6 is less than 7 .

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The negation of the statement 7 is greater than 4 or 6 is less than 7 .

For an invertible matrix A, if A(adjA)=|

20	0
0	20

|, then |A|=

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For an invertible matrix A, if A(adjA)=|

20	0
0	20

1	−1
2	3

], then A2−4A+5I is where I is a unit matrix.

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If matrix A=[

1	−1
2	3

], then A2−4A+5I is where I is a unit matrix.

is continuous at x=0, then the value of k is

is continuous at x=0, then the value of k is

is continuous in [0,1] then a equals

is continuous in [0,1] then a equals

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

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The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

The order and degree of the differential equation √‌

The order and degree of the differential equation √‌

The solution of the differential equation e−x(y+1)dy+(cos2x−sin‌2‌x)ydx=0 subjected to the condition that y=1, when x=0 is

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The solution of the differential equation e−x(y+1)dy+(cos2x−sin‌2‌x)ydx=0 subjected to the condition that y=1, when x=0 is

The number of ways of arranging letters of the 'HAVANA', so that V and N do not appear together, is

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The number of ways of arranging letters of the 'HAVANA', so that V and N do not appear together, is

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is

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Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is

If f(x)=sin2x+sin2(x+‌

)=1, then gof(x) is equal to

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If f(x)=sin2x+sin2(x+‌

)=1, then gof(x) is equal to

Range of the function f(x)=‌

x

1+x2

is

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Range of the function f(x)=‌

is

The domain of f(x)=sin−1[log2(‌

x

2

)] is

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The domain of f(x)=sin−1[log2(‌

)] is

is a probability distribution of a random variable X that can take on the values x=0,1,2,3,4. Then, k is equal to

is a probability distribution of a random variable X that can take on the values x=0,1,2,3,4. Then, k is equal to

.

.

What will be projection of the vector 4

on the line joining the points (2,3,−1) and (−2,−4,3) ?

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What will be projection of the vector 4

on the line joining the points (2,3,−1) and (−2,−4,3) ?

, then |a−2b| will be

, then |a−2b| will be

What will be the equation of plane passing through a point (1,4,−2) and parallel to the given plane −2x+y−3z=9 ?

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What will be the equation of plane passing through a point (1,4,−2) and parallel to the given plane −2x+y−3z=9 ?

If the line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15∘, then the equation of the line in new position is

dx

dx

dx=

dx=

The slant height of a right circular cone is 3cm. The height of the cone for maximum volume is

Q.39 Correct

Q.39 In-correct

Q.39 Unattempt

If y=p[x(x−2)]2 is an increasing function then the value of x is

=

=

) is

) is

The region represented by the inequation system x,y≥0,y≤6,x+y≤3 is

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The region represented by the inequation system x,y≥0,y≤6,x+y≤3 is

The constraints −x1+x2≤1,−x1+3x2≤9 and x1,x2≥0 defines on

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The constraints −x1+x2≤1,−x1+3x2≤9 and x1,x2≥0 defines on

, then |z| is equal to

, then |z| is equal to

=a+ib, then [(a−2)2+b2] is equal to

=a+ib, then [(a−2)2+b2] is equal to

A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective, is

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A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective, is

A random variable X has the probability distribution given below.

Its variance is

A random variable X has the probability distribution given below.

The area (in sq. units) of the region bounded by the curves y2=4ax and x2=4ay,a>0 is

The area in the positive quadrant enclosed by the circles x2+y2=4, the line x=y√3 and X-axis is

dx=

dx=

If sin‌A+cos‌A=√2, then the value of cos2A is

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If sin‌A+cos‌A=√2, then the value of cos2A is

The number of solutions of equation tan‌x+sec‌x=2‌cos‌x lying in the interval [0,2π] is

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The number of solutions of equation tan‌x+sec‌x=2‌cos‌x lying in the interval [0,2π] is

The value of tan‌75∘−cot‌75∘ is

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The value of tan‌75∘−cot‌75∘ is

cos−1α+cos−1β+cos−1γ=3π, then α(β+γ)+β(γ+α)+γ(α+β) equals

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cos−1α+cos−1β+cos−1γ=3π, then α(β+γ)+β(γ+α)+γ(α+β) equals

A line has slope m and y-intercept 4. The distance between the origin and the line is equal to

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A line has slope m and y-intercept 4. The distance between the origin and the line is equal to

If a line with y-intercept 2 , is perpendicular to the line 3x−2y=6, then its x-intercept is

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If a line with y-intercept 2 , is perpendicular to the line 3x−2y=6, then its x-intercept is

A line passes through the point of intersection of the lines 3x+y+1=0 and 2x−y+3=0 and makes equal intercepts with axes. Then, equation of the line is

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A line passes through the point of intersection of the lines 3x+y+1=0 and 2x−y+3=0 and makes equal intercepts with axes. Then, equation of the line is

If the circles x2+y2=9 and x2+y2+2αx+2y+1=0 touch each other internally, then α is equal to

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If the circles x2+y2=9 and x2+y2+2αx+2y+1=0 touch each other internally, then α is equal to

The length of the common chord of the two circles x2+y2−4y=0 and x2+y2−8x−4y+11=0 is

Q.60 Correct

Q.60 In-correct

Q.60 Unattempt

If x1,x2,...,x18 are observations such that

(xj−8)2=45, then standard deviation of these observations is

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If x1,x2,...,x18 are observations such that

(xj−8)2=45, then standard deviation of these observations is

The sum of the deviations of the variates from the arithmetic mean is always

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The sum of the deviations of the variates from the arithmetic mean is always

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is p,0<p<1. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

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A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is p,0<p<1. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B.
If a red ball is drawn from the selected box, then the probability that it has come from box B, is

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Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B.
If a red ball is drawn from the selected box, then the probability that it has come from box B, is

The contrapositive of the statement. 'If 22=5, then I get first class' is

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The contrapositive of the statement. 'If 22=5, then I get first class' is

The truth value of the statement 'Patna is in Bihar or 5+6=111′ is

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The truth value of the statement 'Patna is in Bihar or 5+6=111′ is

1	−1
−1	1

], then A3 is

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If A=[

1	−1
−1	1

5a	−b
3	2

] and A adj A=AAT, then 5a+b is equal to

©

If A=[

5a	−b
3	2

] and A adj A=AAT, then 5a+b is equal to

The value of f at x=0, so that function f(x)=‌

2x−2−x

x

,x≠0 is continuous at x=0, is

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The value of f at x=0, so that function f(x)=‌

2x−2−x

x

,x≠0 is continuous at x=0, is

ax+3	x≤2
a2x−1	x>2.

, then the values of a for which f is continuous for all x are

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If f(x)={

ax+3	x≤2
a2x−1	x>2.

, then the values of a for which f is continuous for all x are

are coplanar, then the value of λ is

are coplanar, then the value of λ is

A △OAB is determined by the vector a and b as show in the figure what will be area of triangle?

lies in the plane x+3y−αz+β=0, then value of αβ is

lies in the plane x+3y−αz+β=0, then value of αβ is

Find the angle between the lines whose direction cosines are given by the equations 3l+m+5n=0,6mn−2nl+5lm=0

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Find the angle between the lines whose direction cosines are given by the equations 3l+m+5n=0,6mn−2nl+5lm=0

Find the shortest distance between the lines r=

Find the shortest distance between the lines r=

A spherical raindrop evaporates at a rate proportional to its surface originally is 3mm and 1h later has been reduced to 2mm, then radius r of the raindrop at any time t is (where 0≤t<3 )

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A spherical raindrop evaporates at a rate proportional to its surface originally is 3mm and 1h later has been reduced to 2mm, then radius r of the raindrop at any time t is (where 0≤t<3 )

If y=sin−1(6x√1−9x2),−‌

is

If y=sin−1(6x√1−9x2),−‌

is

If y=(sin‌x)x+sin−1√x, then ‌

dy

dx

©

If y=(sin‌x)x+sin−1√x, then ‌

The side of an equilateral triangle is increasing at the rate of 2cm∕s. If the side of the triangle is 20cm2 the rate of area increasing is

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The side of an equilateral triangle is increasing at the rate of 2cm∕s. If the side of the triangle is 20cm2 the rate of area increasing is

The maximum value Z=11x+7y, subject to x≤3,y≤2,x≥0 and y≥0 is

Q.84 Correct

Q.84 In-correct

Q.84 Unattempt

The minimum value Z=13x−15y subject to x+y≤7,2x−3y+6≥0,x≥0 and y≥0 is

If z1,z2,...,zn are complex numbers such that z1|=z2|=...=zn|=1, then z1+z2+...+zn| is equal to

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If z1,z2,...,zn are complex numbers such that z1|=z2|=...=zn|=1, then z1+z2+...+zn| is equal to

If 2α=−1−i√3 and 2β=−1+i√3, then 5α4+5β4+7α−1β−1 is equal to

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If 2α=−1−i√3 and 2β=−1+i√3, then 5α4+5β4+7α−1β−1 is equal to

If a fair coin is tossed 20 times and we get head n times, then probability that n is odd, is

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If a fair coin is tossed 20 times and we get head n times, then probability that n is odd, is

If the records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is

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If the records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is

Area bounded by the curve x=0 and x+2y|=1 is

Q.90 Correct

Q.90 In-correct

Q.90 Unattempt

The area bounded by the curves y=√5−x2 and y=|x−1| is

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The area bounded by the curves y=√5−x2 and y=|x−1| is

dx is

dx is

The particular solution of the differential equation ‌

, when x=2 and y=1 is

©

The particular solution of the differential equation ‌

, when x=2 and y=1 is

The differential equation of all circles which passes through the origin and whose centre lies on Y-axis, is

©

The differential equation of all circles which passes through the origin and whose centre lies on Y-axis, is

The solution of the equation (x2+xy)dy=(x2+y2)dx is

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The solution of the equation (x2+xy)dy=(x2+y2)dx is

How many 5-digit telephone number can be constructed using the digits 0 to 9 , if each number starts with 67 and no digits appears more than once?

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How many 5-digit telephone number can be constructed using the digits 0 to 9 , if each number starts with 67 and no digits appears more than once?

The number of selecting atleast 4 candidates from 8 candidates is

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The number of selecting atleast 4 candidates from 8 candidates is

,x≠−5, then f−1(x) is equal to

,x≠−5, then f−1(x) is equal to

,x≠−1, for what values of α is f(f(x))=x?

,x≠−1, for what values of α is f(f(x))=x?

If A and B are two events with P(Ac)=0.3, P(B)=0.4 and P(A∩Bc)=0.5. Then, P[(B)∕(A∩Bc)] is equal to

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If A and B are two events with P(Ac)=0.3, P(B)=0.4 and P(A∩Bc)=0.5. Then, P[(B)∕(A∩Bc)] is equal to

©