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Mathematics
List of top Mathematics Questions asked in KCET
The value of
\(\int\limits_0^1\frac{\log(1+x)}{1+x^2}\ dx\)
is
KCET - 2020
KCET
Mathematics
Definite Integral
The value of
\(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos x}{1+e^x}\ dx\)
is
KCET - 2020
KCET
Mathematics
Definite Integral
The value of
\(\int\limits^{\frac{1}{2}}_{-\frac{1}{2}}\cos^{-1}x\ dx\)
is
KCET - 2020
KCET
Mathematics
Definite Integral
The value of
\(\int e^{\sin x}\sin 2x\ dx\)
is
KCET - 2020
KCET
Mathematics
Definite Integral
If
\(\int\frac{3x+1}{(x-1)(x-2)(x-3)}dx\)
= A log |x - 1| + B log |x - 2| + C log |x - 3| + C, then the values of A, B and C are respectively.
KCET - 2020
KCET
Mathematics
Integration by Partial Fractions
The value of
\(\int\frac{1+x^4}{1+x^6}dx\)
is
KCET - 2020
KCET
Mathematics
Definite Integral
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
KCET - 2020
KCET
Mathematics
Three Dimensional Geometry
The maximum value of
\(\frac{\log_ex}{x}\)
, if x > 0 is
KCET - 2020
KCET
Mathematics
Differential Calculus
If the curves 2x = y
2
and 2xy = K intersect perpendicularly, then the value of K
2
is
KCET - 2020
KCET
Mathematics
Coordinate Geometry
If y = 2x
n+1
+
\(\frac{3}{x^n}\)
then x
2
\(\frac{d^2y}{dx^2}\)
is
KCET - 2020
KCET
Mathematics
Differential Calculus
If (xe)
y
= e
x
, then
\(\frac{dy}{dx}\)
is
KCET - 2020
KCET
Mathematics
Derivatives
If f(x) = sin
-1
\((\frac{2x}{1+x^2})\)
, then f'
\((\sqrt3)\)
is
\(\)
KCET - 2020
KCET
Mathematics
Inverse Trigonometric Functions
If 2
x
+ 2
y
= 2
x+y
, then
\(\frac{dy}{dx}\)
is
KCET - 2020
KCET
Mathematics
Differential Calculus
The right hand and left hand limit of the function
f(x) =
\(\left\{ \begin{aligned} & \frac{e^{1/x}-1}{e^{1/x}+1}\ \ ,\ \ \text{if x}\ne0 \\ & \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ ,\ \ \text{if x = 0} \end{aligned} \right.\)
are respectively
KCET - 2020
KCET
Mathematics
Continuity
If f(x) =
\(\left\{ \begin{aligned} & \frac{1-\cos Kx}{x\sin x} ,\ \ \text{if x}\neq0 \\ &\ \ \ \ \ \ \ \frac{1}{2}\ \ \ \ \ \ \ \ \ ,\ \ \ \text{if x=0} \end{aligned} \right.\)
is continuous at x = 0, then the value of K is
KCET - 2020
KCET
Mathematics
Continuity
If A is a square matrix of order 3 and |A| = 5, then |A adj.A| is
KCET - 2020
KCET
Mathematics
Determinants
If a
1
a
2
a
3
…….. a
9
are in A.P. then the value of
\(\begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \\ \end{vmatrix}\)
is
KCET - 2020
KCET
Mathematics
Arithmetic Progression
If f(x) =
\(\begin{vmatrix} x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0 \\ \end{vmatrix}\)
then
KCET - 2020
KCET
Mathematics
Functions
If
\(\begin{pmatrix} 2 & 1 \\ 3 & 2 \\ \end{pmatrix}A=\begin{pmatrix} 1 & 0 \\ 0 & 1 \\ \end{pmatrix}\)
, then the matrix A is
KCET - 2020
KCET
Mathematics
Matrices
If A and B are square matrices of same order and B is a skew symmetric matrix, then A’BA is
KCET - 2020
KCET
Mathematics
Matrices
If A =
\(\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{pmatrix}\)
, then A
4
is equal to
KCET - 2020
KCET
Mathematics
Matrices
The value of
\(\cos(\sin^{-1}\frac{\pi}{3}+\cos^{-1}\frac{\pi}{3})\)
is
KCET - 2020
KCET
Mathematics
Trigonometric Identities
The domain of the function defined by f(x) =
\(\cos^{-1}\sqrt{x-1}\)
is
KCET - 2020
KCET
Mathematics
Domain of a Function
If A = {a, b, c}, then the number of binary operations on A is
KCET - 2020
KCET
Mathematics
Binary operations
Let f : [2, ∞) → R be the function defined by f(x) = x
2
- 4x + 5 , then the range of f is
KCET - 2020
KCET
Mathematics
Functions
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