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Mathematics
List of top Mathematics Questions asked in KCET
Locus of a point which moves such that its distance from the
$X-axis$
is twice its distance from the line
$x - y = 0$
is
KCET - 2011
KCET
Mathematics
Straight lines
Define a relation
$R$
on
$A =\{1, 2, 3, 4\}$
as
$_xR_y$
if
$x$
divides
$y$
.
$R$
is
KCET - 2011
KCET
Mathematics
Relations and functions
If $\frac {Log\,x}{b-c} = \frac {Log\,y}{c-a}=\frac {Log \,z}{a-b}$ then the value of $ x^{b+c} . y^{c+a}.z^{a+b} $ is
KCET - 2011
KCET
Mathematics
Differential equations
If rth and (r + 1)th terms in the expansion of
$(p + q)^n$
are equal, then
$\frac {(n+1)q} {r(p+q)} $
is
KCET - 2011
KCET
Mathematics
Binomial theorem
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is
KCET - 2011
KCET
Mathematics
Conic sections
If
$\vec{a}, \vec{b}$
and
$\vec{c}$
are unit vectors such that
$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$
then angle between
$\vec{a \text { and }} \vec{b}$
is
KCET - 2011
KCET
Mathematics
Vector Algebra
A value of
$ \theta$
satisfying
$\sin 5 \theta - \sin 3 \theta + \sin \; \theta=0$
such that $0
KCET - 2011
KCET
Mathematics
Trigonometric Functions
The domain of
$ f(x) = sin^{-1} [Log_2 (\frac {x} {2})] $
is
KCET - 2011
KCET
Mathematics
Functions
If lines represented by
$x + 3y - 6 = 0, 2x+y-4=0$
and
$kx - 3y + 1 = 0$
are concurrent, then the value of
$k$
is
KCET - 2011
KCET
Mathematics
Straight lines
The negation of
$p \to (\sim p \vee q) $
is
KCET - 2011
KCET
Mathematics
mathematical reasoning
In any triangle
$ABC$
, the simplified form of
$\frac {Cos 2A}{a^2}-\frac{Cos2B}{b^2}$
is
KCET - 2011
KCET
Mathematics
Trigonometric Functions
The value of
$\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ}-\sin 70^{\circ}$
is
KCET - 2011
KCET
Mathematics
Trigonometric Functions
In Argand's plane, the point corresponding to
$\frac {(1-i\sqrt {3})(1+i)} {(\sqrt {3}+i)}$
lies in
KCET - 2011
KCET
Mathematics
Complex Numbers and Quadratic Equations
If
$a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $
then
$x = $
_____
KCET - 2010
KCET
Mathematics
Inverse Trigonometric Functions
In the binomial expansion of
$(1+x)^{15}$
the coefficients of
$x^r$
and
$x^{r+3}$
are equal Then
$r$
is _______
KCET - 2010
KCET
Mathematics
Binomial theorem
Two circles centered at
$(2, 3) $
and
$(5, 6)$
intersect each other. If the radii are equal, the equation of the common chord is ______
KCET - 2010
KCET
Mathematics
Conic sections
For the curve
$4x^5 = 5y^4$
, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is
KCET - 2010
KCET
Mathematics
Application of derivatives
If
$\vec{a}, \vec {b}$
and
$\vec {c}$
are unit vectors, such that
$\vec {a}+\vec {b} +\vec {c}=0$
then
$3\vec {a}.\vec {b} +\vec {2b}.\vec {c} +\vec {c}.\vec {a}$
KCET - 2010
KCET
Mathematics
Vector Algebra
The general solution of $1+\operatorname{Sin}^{2} x=3 \operatorname{Sin} x \cdot \operatorname{Cos} x, \operatorname{Tan} x \neq \frac{1}{2}$ is ......
KCET - 2010
KCET
Mathematics
Differential equations
A space vector makes the angles
$150^\circ$
and
$60^\circ$
with the positive direction of
$X -$
and
$Y-$
axis. The angle made by the vector with the positive direction of
$Z-$
axis is .............
KCET - 2010
KCET
Mathematics
Three Dimensional Geometry
The derivative of
$e^{ax} \cos\,bx$
with respect to
$x$
is
$re^{ax}$
$\cos\, (bx-Tan^{-1} \frac {b}{a})$
When
$a >0, b > 0$
,the value of
$r$
is ............
KCET - 2010
KCET
Mathematics
Second Order Derivative
The
$n^{th}$
term of the series
$1+3 + 7 + 13 + 21 + $
is
$9901$
. The value of
$n$
is ................
KCET - 2010
KCET
Mathematics
Series
A wire of length
$20\,cm$
is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is ____
KCET - 2010
KCET
Mathematics
Application of derivatives
If
$m$
is the slope of one of the lines represented by
$ax^2 + 2hxy + by^2 = 0,$
then
$(h + bm)^2$
= ______
KCET - 2010
KCET
Mathematics
Straight lines
The line joining
$A (2, -7)$
and
$B(6, 5)$
is divided into
$4$
equal parts by the points
$ P,Q$
and
$R$
such that
$AQ = RP = QB$
. The midpoint of
$ PR$
is _______
KCET - 2010
KCET
Mathematics
Distance of a Point From a Line
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