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Mathematics
List of top Mathematics Questions asked in KCET
If the conjugate of
$(x + iy) (1 - 2i)$
is
$1 + i,$
then
KCET - 2012
KCET
Mathematics
Complex Numbers and Quadratic Equations
If
$(\vec{a} \times \vec{b})^2+(\vec{a}.\vec{b})^2=144$
and
$|\vec{a}|$
then
$ |\vec{b}|$
=
KCET - 2012
KCET
Mathematics
Vector Algebra
If
$\alpha ,\beta,\gamma$
are the roots of the equation
$x^3+4x+2=0$
then
$\alpha^3+\beta^3+\gamma^3$
KCET - 2012
KCET
Mathematics
Complex Numbers and Quadratic Equations
The value of
$^{10}C_1+^{10}C_2+^{10}C_3+....+^{10}C_9 $
is
KCET - 2012
KCET
Mathematics
Combinations
The digit in the unit's place of
$7^{171} +(177)!$
is
KCET - 2011
KCET
Mathematics
binomial distribution
$G = \left\{\begin{bmatrix} x&x \\[0.3em] x & x \end{bmatrix} , x \text{ is a nonzero real number} \right\}
$ is a group with respect to matrix multiplication. In this group, the inverse of $
\begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\[0.3em] \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ is
KCET - 2011
KCET
Mathematics
Matrices
$\begin{vmatrix} {Sin \alpha}&{ \cos\alpha} &Sin ({\alpha+ \delta })\\ {Sin \beta}&{ Cos \beta}& Sin ({\beta+\delta}) \\ {Sin \gamma}&{ Cos \gamma}&Sin ({\gamma+\delta})\\ \end{vmatrix} $ is equal to
KCET - 2011
KCET
Mathematics
Properties of Determinants
Suppose
$ P(2,\,y,\,z) $
lies on the line through
$ A(3,-1,4) $
and
$ B(-4,2,1) $
. Then, the value of z is equal to
KCET - 2011
KCET
Mathematics
Various Forms of the Equation of a Line
In
$n$
is an odd positive integer and
$(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$
then
$a_0 -a_1+a_2-a_3 +\dots -a_{3n}$
is equal to
KCET - 2011
KCET
Mathematics
Binomial theorem
Angles of elevation of the top of a tower from three points (collinear)
$A, B$
and
$ C$
on a road leading to the foot of the tower are
$30^\circ$
,
$45^\circ$
and
$60^\circ$
respectively. The ratio of
$AB$
to
$BC$
is
KCET - 2011
KCET
Mathematics
Trigonometric Functions
The derivative of
$tan ^{-1}[\frac{Sin x}{1+ Cos x}]$
with respect to
$tan^{-1}[\frac{Cos x}{1+Sin x}]$
is
KCET - 2011
KCET
Mathematics
Differentiability
The value of
$\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$
is
KCET - 2011
KCET
Mathematics
Algebra of Complex Numbers
The sum of the first n terms
$ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$
$\dots$
is
KCET - 2011
KCET
Mathematics
Sequence and series
If
$\alpha , \beta ,\gamma$
are the roots of
$x^3-2x+1=0$
, then the value of
$(\sum \frac {1} {\alpha +\beta -\gamma}$
) is
KCET - 2011
KCET
Mathematics
Complex Numbers and Quadratic Equations
If the focii of
$\frac {x^2}{16}+\frac{y^2}{4}=1 $
and
$\frac {x^2}{a^2}-\frac{y^2}{3}=1 $
coincide, then value of
$a$
is
KCET - 2011
KCET
Mathematics
Conic sections
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
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
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 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
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