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MHT CET
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Mathematics
List of top Mathematics Questions asked in MHT CET
If $\vec{a} , \vec{b} , \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $[\vec{a} + \vec{b} + \vec{c} \, \, \vec{b} - \vec{a} - \vec{c}] = ?$
MHT CET - 2018
MHT CET
Mathematics
Vectors
If $2 \sin \left( \theta + \frac{\pi}{3}\right) = \cos \left( \theta -\frac{\pi}{6}\right) , $ then $\tan \, \theta = $
MHT CET - 2018
MHT CET
Mathematics
Trigonometric Identities
$\Delta \, ABC$
has vertices at
$A = (2, 3,5), B = (-1,3, 2)$
and
$C = (\lambda , 5, \mu )$
. If the median through A is equally inclined to the axes, then the values of
$\lambda$
and
$\mu$
respectively are
MHT CET - 2017
MHT CET
Mathematics
introduction to three dimensional geometry
The equation of the plane through
$(-1, 1 , 2 ) $
whose normal makes equal acute angles with co-ordinate axes is
MHT CET - 2017
MHT CET
Mathematics
Three Dimensional Geometry
The objective function of $LPP$ defined over the convex set attains its optimum value at
MHT CET - 2017
MHT CET
Mathematics
Linear Programming Problem
If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
MHT CET - 2017
MHT CET
Mathematics
Integrals of Some Particular Functions
If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $
MHT CET - 2017
MHT CET
Mathematics
Integrals of Some Particular Functions
$\int^1_0 x \, \tan^{-1} x\,dx = $
MHT CET - 2017
MHT CET
Mathematics
Integrals of Some Particular Functions
The maximum value of $f(x) = \frac{\log \, x }{x} (x \neq 0 , x \neq 1)$ is
MHT CET - 2017
MHT CET
Mathematics
Application of derivatives
The number of principal solutions of $\tan 2 \theta = 1$ is
MHT CET - 2017
MHT CET
Mathematics
Trigonometric Functions
If the function \[ f(x) = \begin{cases} [ tan (\frac {\pi}{4}+x)]^{1/x} & \quad for\, x \neq 0\\ K \,\,\,\,\,\,\,\,\,\text{if } x =0 \end{cases} \] is continuous at
$x = 0$
, then
$K = ?$
MHT CET - 2017
MHT CET
Mathematics
Differentiability
If
$z_1$
and
$z_2$
are z co-ordinates of the points of trisection of the segment joining the points
$A(2, 1, 4), B _1 + z_2 =$
MHT CET - 2017
MHT CET
Mathematics
introduction to three dimensional geometry
The area of the region bounded by the lines
$y = 2x + 1, y = 3x + 1$
and
$x = 4$
is
MHT CET - 2017
MHT CET
Mathematics
applications of integrals
The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is
MHT CET - 2017
MHT CET
Mathematics
Properties of Inverse Trigonometric Functions
If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is
MHT CET - 2017
MHT CET
Mathematics
Vector Algebra
The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
MHT CET - 2017
MHT CET
Mathematics
Tangents and Normals
If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is
MHT CET - 2017
MHT CET
Mathematics
mathematical reasoning
The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point
MHT CET - 2017
MHT CET
Mathematics
Linear Programming Problem
The differential equation of all parabolas whose axis is $y-axis$ is
MHT CET - 2017
MHT CET
Mathematics
Differential equations
The particular solution of the differential equation
$xdy + 2ydx = 0$
, when
$x = 2, y = 1$
is
MHT CET - 2017
MHT CET
Mathematics
Differential equations
Direction cosines of the line
$\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$
is
MHT CET - 2016
MHT CET
Mathematics
Three Dimensional Geometry
If Matrix $A = \begin{bmatrix}1&2\\ 4&3\end{bmatrix}$ such that $Ax = I$, then $X = $_______
MHT CET - 2016
MHT CET
Mathematics
Determinants
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.
MHT CET - 2016
MHT CET
Mathematics
mathematical reasoning
$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $
MHT CET - 2016
MHT CET
Mathematics
Integrals of Some Particular Functions
If Rolle�s theorem for $f\left(x\right)= e^{x} \left(sinx - cosx\right)$ is verified on $[\pi/4$, $5 \pi/4]$, then the value of $c$ is
MHT CET - 2016
MHT CET
Mathematics
Differentiability
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