MHT CET 2020 Paper I

In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

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In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

If π∕2<x<π, then ∫x√‌

If π∕2<x<π, then ∫x√‌

A rectangle with one side lying along the x -axis is to be inscribed in the closed region of the xy plane bounded by the lines y=0,y=3x and y= 30−2x. The largest area of such a rectangle is

Q.4 Correct

Q.4 In-correct

Q.4 Unattempt

If f:R→R be a function defined by f(x)=4x3−7. Then

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If f:R→R be a function defined by f(x)=4x3−7. Then

∼((∼p)∧q) is equal to

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∼((∼p)∧q) is equal to

With the usual notation

2

∫

1

([x2]−[x]2)dx is equal to

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With the usual notation

2

∫

1

([x2]−[x]2)dx is equal to

The general solution of x(1+y2)1∕2dx+y(1+x2)1∕2dy=0 is

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The general solution of x(1+y2)1∕2dx+y(1+x2)1∕2dy=0 is

0	0	1
0	1	0
1	0	0

], then A2008 is equal to

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If A=[

0	0	1
0	1	0
1	0	0

], then A2008 is equal to

Three vertices of a parallelogram ABCD are A(3,−1,2),B(1,2,−4) and C(−1,1,2). The coordinates of fourth vertex D are

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Three vertices of a parallelogram ABCD are A(3,−1,2),B(1,2,−4) and C(−1,1,2). The coordinates of fourth vertex D are

The equation of the plane containing the line ‌

and the point (0,7,−7), is

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The equation of the plane containing the line ‌

and the point (0,7,−7), is

The co-ordinates of the foot of perpendicular from the point A(1,1,1) on the line joining the points B(1,4,6) and C(5,4,4) are

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The co-ordinates of the foot of perpendicular from the point A(1,1,1) on the line joining the points B(1,4,6) and C(5,4,4) are

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then :

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Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then :

Let f be the function defined by

Q.16 Correct

Q.16 In-correct

Q.16 Unattempt

The distance of the point (1,−2,3) from the plane x−y+z=5 measured parallel to the line ‌

The distance of the point (1,−2,3) from the plane x−y+z=5 measured parallel to the line ‌

The maximum value of z=6x+8y subject to constraints 2x+y≤30,x+2y≤24 and x≥0, y≥0 is

x‌sin(π[x]−x)‌dx is equal to :

x‌sin(π[x]−x)‌dx is equal to :

The general solution of the equation tan‌θ+tan‌4‌θ+tan‌7‌θ=tan‌θ‌tan‌4‌θ‌tan‌7‌θ

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The general solution of the equation tan‌θ+tan‌4‌θ+tan‌7‌θ=tan‌θ‌tan‌4‌θ‌tan‌7‌θ

For non zero, non collinear vectors

is

For non zero, non collinear vectors

is

Let f(θ)=sin‌θ(sin‌θ+sin‌3‌θ) then

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Let f(θ)=sin‌θ(sin‌θ+sin‌3‌θ) then

The maximum value of z=5x+2y, subject to the constraints x+y≤7,x+2y≤10,x,y≥0 is

Q.24 Correct

Q.24 In-correct

Q.24 Unattempt

The volume of the greatest cylinder which can be inscribed in a cone of height 30cm and semi vertical angle 30∘ is

Q.25 Correct

Q.25 In-correct

Q.25 Unattempt

The equation of the plane through the line x+y+z+3=0=2x−y+3z+1 and parallel to the line ‌

The equation of the plane through the line x+y+z+3=0=2x−y+3z+1 and parallel to the line ‌

be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then [

] in terms of θ is equal to :

be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then [

] in terms of θ is equal to :

General solution of the equation sin‌2‌x−sin‌4‌x+sin‌6‌x=0 is

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General solution of the equation sin‌2‌x−sin‌4‌x+sin‌6‌x=0 is

A focus of an ellipse is at the origin. The directrix is the line x=4 and the eccentricity is ‌

1

2

. Then the length of the semi-major axis is

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A focus of an ellipse is at the origin. The directrix is the line x=4 and the eccentricity is ‌

1

2

. Then the length of the semi-major axis is

The locus of a point that is equidistant from the lines x+y−2√2=0 and x+y−√2=0 is

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The locus of a point that is equidistant from the lines x+y−2√2=0 and x+y−√2=0 is

A ray of light coming from the point (1,2) is reflected at a point A on the x -axis and then passes through the point (5,3). The co-ordinates of the point A is

Q.31 Correct

Q.31 In-correct

Q.31 Unattempt

If x∈R−{0}, then tan−1(‌

√1+x2+√1−x2

√1+x2−√1−x2

)

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If x∈R−{0}, then tan−1(‌

)

In a triangle ABC,∠C=90∘, then ‌

In a triangle ABC,∠C=90∘, then ‌

The internal angles of a convex polygon are inA.P. The smallest angle is 120∘ and the common difference is 5∘. The number to sides of the polygon is

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The internal angles of a convex polygon are inA.P. The smallest angle is 120∘ and the common difference is 5∘. The number to sides of the polygon is

In a binomial distribution n=5,P(X=1)=0.4096 and P(X=2)=0.2048, then the mean of the distribution is equal to

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In a binomial distribution n=5,P(X=1)=0.4096 and P(X=2)=0.2048, then the mean of the distribution is equal to

The equation of tangent to the curve y=sin−1‌

The equation of tangent to the curve y=sin−1‌

Let A,B be two events such that the probability of A is ‌

3

10

and conditional probability of A given B is ‌

1

2

. The probability that exactly one of the events A or B happen equals

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Let A,B be two events such that the probability of A is ‌

3

10

and conditional probability of A given B is ‌

1

2

. The probability that exactly one of the events A or B happen equals

If the line passing through P(1,2) making an angle with the x -axis in the positive direction meets the pair of lines x2+4xy+y2 at A and B, then PA⋅PB=

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If the line passing through P(1,2) making an angle with the x -axis in the positive direction meets the pair of lines x2+4xy+y2 at A and B, then PA⋅PB=

If the curves ay+x2=7 and x3=y cut orthogonally at (1,1), then the value of a is.

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If the curves ay+x2=7 and x3=y cut orthogonally at (1,1), then the value of a is.

The value of cos(2cos−1x+sin−1x) at x=‌

The value of cos(2cos−1x+sin−1x) at x=‌

Which of the following is logically equivalent to ∼(∼p⇒q)

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Which of the following is logically equivalent to ∼(∼p⇒q)

The area of the region bounded by the curves y=|x−2|,x=1,x=3 and the x -axis is

Q.43 Correct

Q.43 In-correct

Q.43 Unattempt

If the slope of the tangent at (x,y) to a curvepassing through (1,‌

), then the equation of the curve is :

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If the slope of the tangent at (x,y) to a curvepassing through (1,‌

), then the equation of the curve is :

A fair coin is tossed 99 times. If X is the number of times head occurs, P(X=r) is maximum when r is

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A fair coin is tossed 99 times. If X is the number of times head occurs, P(X=r) is maximum when r is

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

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The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

The eccentricity of the hyperbola x2−3y2=2x+8 is

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The eccentricity of the hyperbola x2−3y2=2x+8 is

Thedifferential equation representing the family of curves y2=2c(x+√c), where c is a positive parameter, is of

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Thedifferential equation representing the family of curves y2=2c(x+√c), where c is a positive parameter, is of

, the number of points of discontinuity of f{f[f(x)]} is :

, the number of points of discontinuity of f{f[f(x)]} is :

If x=a(cos‌t+t‌sin‌t) and y=a(sin‌t−t‌cos‌t) then ‌

If x=a(cos‌t+t‌sin‌t) and y=a(sin‌t−t‌cos‌t) then ‌

The number of solutions of equation x2−x3=1,−x1+2x3=2,x1−2x2=3 is

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The number of solutions of equation x2−x3=1,−x1+2x3=2,x1−2x2=3 is

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