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List of top Mathematics Questions asked in KCET
The number
$(49^2 -4) (49^2 -49)$
is divisible by ..................
KCET - 2010
KCET
Mathematics
binomial expansion formula
The constant term of the polynomial $\begin{vmatrix} {x+3}&{x} &{x+2}\\ {x}&{x+1}& {x-1} \\ {x+2}&{2x}&{3x+1}\\ \end{vmatrix} $ is ________
KCET - 2010
KCET
Mathematics
Applications of Determinants and Matrices
The order and degree of the differential equation y =
$ \frac {dp}{dx}x +\sqrt {a^2p^2+b^2}$
where
$ p=\frac {dy}{dx}$
(here
$a$
and
$b$
are arbitrary constants) respectively are
KCET - 2010
KCET
Mathematics
Order and Degree of Differential Equation
Equation of the circle centered at
$(4, 3)$
touching the circle
$x^2+y^2-1$
externally, is _____
KCET - 2010
KCET
Mathematics
Conic sections
A simple graph contains
$24$
edges. Degree of each vertex is
$3$
. The number of vertices is .................
KCET - 2010
KCET
Mathematics
permutations and combinations
If
$A$
is a
$3 \times 3$
nonsingular matrix and if
$|A | = 3$
, then
$|(2A)^{-1}|$
= _______
KCET - 2010
KCET
Mathematics
Determinants
If
$y =tan ^{-1} \sqrt {x^2-1}$
then the ratio
$\frac {d^2y}{dx^2}: \frac {dy}{dx}$
=_________
KCET - 2010
KCET
Mathematics
Continuity and differentiability
$ \displaystyle\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}$
is
KCET - 2010
KCET
Mathematics
limits and derivatives
Which of the following is NOT true?
KCET - 2010
KCET
Mathematics
mathematical reasoning
The sides of a triangle are
$6+\sqrt {12} , \sqrt {48} $
and
$\sqrt {24}$
. The tangent of the smallest angle of the triangle is
KCET - 2010
KCET
Mathematics
Trigonometric Functions
The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola
$x^2=-8y$
is _______
KCET - 2010
KCET
Mathematics
Conic sections
The points
$(1, 0), (0, 1), (0, 0) $
and
$ (2k, 3k),k \neq 0$
are concyclic if
$k$
= _____
KCET - 2010
KCET
Mathematics
Conic sections
The area bounded by the curve $ y= \begin{cases} x^2,x<0 & \quad\\ x,x \geq 0 & \quad \\ \end{cases}
$ and the line $
y = 4$ is
KCET - 2010
KCET
Mathematics
Area between Two Curves
The eccentric angle of the point
$(2,\sqrt{3})$
lying on
$\frac {x^2}{16}+\frac{y^2}{4}-1$
is _________
KCET - 2010
KCET
Mathematics
Ellipse
If
$x\neq n \pi ,\, x \neq\,(2n+1)\frac {\pi}{2}.n\in Z, $
then
$\frac {Sin^{-1}(Cos x) + Cos^{-1}(Sin x)}{Tan ^{-1}(Cot x)+ Cot^{-1}(Tan x)} $
=
KCET - 2010
KCET
Mathematics
Inverse Trigonometric Functions
In
$\Delta ABC$
, if
$a =2, B = \tan ^{-1} \frac {1}{2}$
and
$C = \tan ^{-1}\frac{1}{3}$
, then
$(A,b)$
=
KCET - 2010
KCET
Mathematics
Inverse Trigonometric Functions
The condition for the line
$y = mx +c$
to be a normal to the parabola
$y = 4ax$
is _______
KCET - 2010
KCET
Mathematics
Conic sections
The set of real values of x for which
$ f(x) = \frac {x}{log\, x}$
increasing, is
KCET - 2010
KCET
Mathematics
Application of derivatives
$P$
is the point of contact of the tangent from the origin to the curve
$y = log_ex$
The length of the perpendicular drawn from the origin to the normal at
$P$
is ______
KCET - 2010
KCET
Mathematics
Application of derivatives
The length of the diameter of the circle which cuts three circles
$x^2 + y^2 - x - y - 14 = 0;$
$x^2 + y^2 + 3x - 5y - 10 = 0 ;$
$x^2 + y^2 - 2x + 3y - 27 = 0$
orthogonally, is
KCET - 2009
KCET
Mathematics
Circle
If If
$n =(2020)$
, then
$\frac {1}{\log_2n}+\frac {1}{\log_3n}+\frac {1}{\log_4n}+............+\frac {1}{\log_{2020} n}$
KCET - 2009
KCET
Mathematics
Sequence and series
If
$\vec{a}+2\vec{b}+3\vec{c}=\vec{0}$
then
$\vec{a} \times \vec{b}+\vec{b} \times \,\vec{c}+\vec{c} \times \vec{a} $
=
KCET - 2009
KCET
Mathematics
Vector Algebra
If
$A$
and
$B$
are square matrices of the same order such that
$(A + B) (A -B) = A^2-B^2$
then
$(ABA^{-1} )^2=$
KCET - 2009
KCET
Mathematics
Matrices
The negation of
$p{\land}(q \to \sim r)$
is
KCET - 2009
KCET
Mathematics
validating statements
On the set of integers
$Z$
. define
$f: Z \to Z$
as $ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 0 & \quad \text{if } n \text{ is odd}\\ \end{cases}
$ then $
'f'$ is
KCET - 2009
KCET
Mathematics
types of functions
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