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Mathematics
List of top Mathematics Questions asked in COMEDK UGET
The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Differentiation
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Equation of Circle
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Plane
What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Equation of Circle
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
limits and derivatives
If \( L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2}}{x^4} \), \( a > 0 \), then:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
limits and derivatives
The coefficients \( a, b, c \) of the quadratic equation \( ax^2 + bx + c = 0 \) are obtained by throwing a die three times. The probability that this equation has equal roots is:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Probability
Evaluate: \( 8^{\log_5 5} \)
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Algebra
What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Equation of Circle
The vector that must be added to
\[ \mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \quad \text{and} \quad 3\mathbf{i} + 6\mathbf{j} - 7\mathbf{k} \]
so resultant vector is a unit vector along the X-axis is:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Vectors
If \( |\mathbf{a}| = 8 \), \( |\mathbf{b}| = 3 \) and \( |\mathbf{a} \times \mathbf{b}| = 12 \), then find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Product of Two Vectors
If for \(\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}\), \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), and \(\vec{c} = -3\hat{i} + \hat{j} + 2\hat{k}\), then find \([\vec{a} \, \vec{b} \, \vec{c}]\).
COMEDK UGET - 2021
COMEDK UGET
Mathematics
Product of Two Vectors
The maximum value of \( x + y \) subject to
\[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \]
is:
COMEDK UGET - 2021
COMEDK UGET
Mathematics
lpp graphical method
Write the solution of the following LPP
\[ \text{Maximize } Z = x + y \] Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \]
Which point the value of \( Z \) is maximum?
COMEDK UGET - 2021
COMEDK UGET
Mathematics
lpp graphical method
$\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Inverse Trigonometric Functions
If
$A = \begin{bmatrix}1&0\\ 1&1\end{bmatrix}$
and
$A^8 = aA +bI,$
then
$(a , b) = $
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Matrices
If
$\int\limits \frac{\cos \, 8x + 1}{ \tan \, 2x - \cot \, 2x} dx = a \, \cos \, 8x + c , $
then
$a$
=
COMEDK UGET - 2015
COMEDK UGET
Mathematics
integral
The angle between the curves
$y^2 = 4ax$
and
$ay = 2x^2$
is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Rate of Change of Quantities
Amplitude of the complex number
$i\, \sin \bigg( \frac{\pi}{19} \bigg)$
is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Complex Numbers and Quadratic Equations
The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y-8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Straight lines
The area in square units bounded by the normal at
$(1, 2)$
to the parabola
$y^2 = 4x, x$
-axis and the curve is given by
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Area between Two Curves
A ladder
$5\,m$
long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of
$2m/sec$
. The speed at which its height on the wall decreases when the foot of the ladder is
$4\, m$
away from the wall is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Application of derivatives
$\tan\left(\cos^{-1}\left( \frac{1}{5\sqrt{2}}\right)-\sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right)$
is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Inverse Trigonometric Functions
An urn contains
$9$
balls,
$2$
of which are white,
$3$
blue and
$4$
black.
$3$
balls are drawn at random from the urn. The chance that
$2$
balls will be of the same colour and the third of a different colour is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Probability
If
$\tan(x + y) = 33$
and
$x = \tan^{-1} \, 3,$
then
$y$
is
COMEDK UGET - 2015
COMEDK UGET
Mathematics
Inverse Trigonometric Functions
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