MHT CET 2016 Paper I

with respect to sin^-1(3x-4x³) is ______

Derivative of

with respect to sin^-1(3x-4x³) is ______

Q.3 Correct

Q.3 In-correct

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The differential equation of the family of circles touching y-axis at the origin is

, then a₁₁A₂₁+a₁₂A₂₂+a₁₃A₂₃=

If

, then a₁₁A₂₁+a₁₂A₂₂+a₁₃A₂₃=

Q.5 Correct

Q.5 In-correct

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If Rolle's theorem for f(x) = e^x (sinx - cosx) is verified on [π/4 , 5π/4] then the value of c is

Q.6 Correct

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The joint equation of lines passing through the origin and trisecting the first quadrant is______.

Q.7 Correct

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If 2 tan^-1 (cosx) = tan^-1 (2 cosecx) then find the value of sinx + cosx =. Then n=

Q.8 Correct

Q.8 In-correct

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Direction cosines of the line

are _____

Direction cosines of the line

The approximate value of f(x) = x³ + 5x² — 7x + 9 at x = 1.1 is

Q.11 Correct

Q.11 In-correct

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If r.v. X: waiting time in minutes for bus and p.d.f. of X is given by

, then probability of waiting time not more than 4 minutes is = ____

If r.v. X: waiting time in minutes for bus and p.d.f. of X is given by

, then probability of waiting time not more than 4 minutes is = ____

The joint equation of bisectors of angles between lines x = 5 and y = 3 is ____

Q.15 Correct

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The point on the curve 6y = x³ + 2 at which y — co-ordinate is changing 8 times as fast as x— co-ordinate is

Q.16 Correct

Q.16 In-correct

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If the function f(x) defined by
f(x) = x sin

for x

0
=k for x = 0
is continuous at x = 0, then k = _____

If the function f(x) defined by
f(x) = x sin

for x

0
=k for x = 0
is continuous at x = 0, then k = _____

= Ax + B log-/ 2e^x - 5 /+ c then

For what value of k, the function defined by

for x

0 is continuous at x = 0 ?

For what value of k, the function defined by

for x

0 is continuous at x = 0 ?

The degree and order of the differential equation

respectively are

The degree and order of the differential equation

The acute angle between the line

and the plane

The acute angle between the line

The area of the region bounded by the curve y = 2x - x² and x - axis is

If A and B are foot of perpendicular drawn from point Q (a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is ________

If the p.d.f. of a r.v. X is given as

Then F(0)=

If the p.d.f. of a r.v. X is given as

The particular solution of the differential equation

when
x = e, y = e² is

The particular solution of the differential equation

when
x = e, y = e² is

Q.33 Correct

Q.33 In-correct

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M and N are the midpoints of the diagonals AC and BD respectively of quadrilateral AB CD, then

________

M and N are the midpoints of the diagonals AC and BD respectively of quadrilateral AB CD, then

If sinx is the integrating factor (I.F.) of the linear differential equation

, then P is dx

If sinx is the integrating factor (I.F.) of the linear differential equation

Which of the following equation does not represent a pair of lines?

Q.36 Correct

Q.36 In-correct

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Probability of guessing correctly atleast 7 out of 10 answers in a "True" or "False" test is = _________

Q.37 Correct

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Principal solutions of the equation sin 2x + cos 2x = 0, where it

are

Principal solutions of the equation sin 2x + cos 2x = 0, where it

If line joining points A and B having position vectors

and

respectively, and the line joining the points C and D having position vectors

and

intersect, then their point of intersection is

If line joining points A and B having position vectors

and

respectively, and the line joining the points C and D having position vectors

and

intersect, then their point of intersection is

If p: Every square is a rectangle
q: Every rhombus is a kite then truth values of p → q and p ↔ q are ______and _____ respectively.

are centroid, orthocenter and circumcenter of a triangle and

then (x, y, z) = ______

If

and

are centroid, orthocenter and circumcenter of a triangle and

then (x, y, z) = ______

Q.42 Correct

Q.42 In-correct

Q.42 Unattempt

Which of the following quantified statement is true?

Q.43 Correct

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The general solution of the equation tan²x =1 is

Q.44 Correct

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The shaded part of given figure indicates the feasible region

then the constraints are

The shaded part of given figure indicates the feasible region

then the constraints are

Q.45 Correct

Q.45 In-correct

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Directions ration of the line which is perpendicular to the lines with direction rations -1,2,2 and 0,2,1 are

such that Ax = I, then x = ____

If Matrix

such that Ax = I, then x = ____

then P(2 < X < 4) = _______

If

then P(2 < X < 4) = _______

Q.49 Correct

Q.49 In-correct

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The objective function

, subject to

,

has maximum value _____of the feasible region.

The objective function

, subject to

,

has maximum value _____of the feasible region.

Q.50 Correct

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Symbolic form of the given switching circuit is equivalent to ______