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List of top Mathematics Questions asked in KCET
If
\(\int \frac{dx}{(x+2)(x^2 + 1)} = a \log |1+x^2| + b \tan^{-1} x + \frac{1}{5} \log |x+2| + c\)
, then
KCET - 2022
KCET
Mathematics
Differential equations
\(\int\limits_{0}^1\frac{xe^x}{(2+x)^3}\ dx\)
is equal to
KCET - 2022
KCET
Mathematics
Definite Integral
\(\int\limits_{0}^{\frac{\pi}{2}}\frac{\cos x\sin x}{1+\sin x}\ dx\)
is equal to
KCET - 2022
KCET
Mathematics
Definite Integral
Evaluate
\(\int\limits_{2}^3x^2\ dx\)
as the limit of a sum
KCET - 2022
KCET
Mathematics
Definite Integral
Area of the region bounded by the curve
\(y = tan x\)
, the x- axis and the line
\(x = \frac{\pi}{3}\)
is
KCET - 2022
KCET
Mathematics
Area under Simple Curves
If
\(\frac{dy}{dx} + \frac{y}{x} = x^2\)
then
\(2y (2) - y (1) =\)
KCET - 2022
KCET
Mathematics
Trigonometric Functions
\(\int\limits_{0}^{\frac{\pi}{2}}\sqrt{\sin \theta}\cos^3\theta\ d\theta\)
is equal to
KCET - 2022
KCET
Mathematics
Definite Integral
If
\(e^y + xy = e\)
the ordered pair
\(\left(\frac{dy}{dx}, \frac{d^2y}{dx^2}\right)\)
at
\(x = 0\)
is equal to
KCET - 2022
KCET
Mathematics
Differential equations
If
\([x]\)
is the greatest integer function not greater than x, then
\(\int [x]\)
\(dx\)
is equal to
KCET - 2022
KCET
Mathematics
Definite Integral
The co-ordinates of the point on the
\(\sqrt{x} + \sqrt{y} = 6\)
at which the tangent is equally inclined to the axes is
KCET - 2022
KCET
Mathematics
Straight lines
\(\int \frac{\cos(2x) - \cos(2\alpha)}{\cos(x) - \cos(\alpha)} \, dx\) is equal to
KCET - 2022
KCET
Mathematics
Definite Integral
If
\(x = e^\theta \sin \theta, \quad y = e^\theta \cos \theta\)
, where
\(θ\)
is a parameter , then
\(\left. \frac{dy}{dx} \right|_{(1,1)}\)
is equal to
KCET - 2022
KCET
Mathematics
Sets
If
\(f(1) = 1, \quad f'(1) = 3\)
then the derivative of
\(f(f(f(x))) + (f(x))^2\)
at
\(x= 1\)
is
KCET - 2022
KCET
Mathematics
composite of functions
If A
n
=
\(\begin{bmatrix} 1-n & n \\ n & 1-n \\ \end{bmatrix}\)
then | A
1
| + | A
2
| + ….. + | A
2021
| =
KCET - 2022
KCET
Mathematics
Determinants
If
\(y = (1+x^2) \tan^{-1}(x) - x\)
. Then
\(\frac{dy}{dx}\)
is
KCET - 2022
KCET
Mathematics
Trigonometric Functions
If
\(y = x^{\sin(x)} + (\sin(x))^x\)
, then
\(\left. \frac{dy}{dx} \right|_{x = \frac{\pi}{2}}\)
is
KCET - 2022
KCET
Mathematics
Trigonometric Functions
If the vertices of triangle are (-2,6), (3,-6) and (1,5), then the area of the triangle is
KCET - 2022
KCET
Mathematics
Trigonometric Functions
If A =
\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}\)
then
\((aI + bA)^n\)
is (where I is the identity matrix of order 2)
KCET - 2022
KCET
Mathematics
Matrices
If A is a 3x3 Matrix such that \(|5 \cdot \text{adj}(A)| = 5, \text{ then } |A|\) is equal to
KCET - 2022
KCET
Mathematics
Sets
Domain of
\(cos^{-1} [x]\)
, where
\([. ]\)
denotes a greatest integer function
KCET - 2022
KCET
Mathematics
Order and Degree of Differential Equation
If there are two values of ‘a’ which makes determinant
\(\Delta=\begin{bmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \\ \end{bmatrix}=86\)
Then the sum of these numbers
KCET - 2022
KCET
Mathematics
Determinants
If A=
\([\begin{smallmatrix} 2 & -1 \\ 3 & -2 \end{smallmatrix}]\)
,then the inverse of the matrix A
3
is
KCET - 2022
KCET
Mathematics
Probability
If A is matrix of order 3x3, then \((A^2)^{-1}\) is equal to
KCET - 2022
KCET
Mathematics
Trigonometric Functions
\(\lim_{{y \to 0}} \frac{\sqrt{3} + y^3 - \sqrt{3}}{y^3}\)
KCET - 2022
KCET
Mathematics
coordinates of a point in space
If
\(f: \mathbb{R} \rightarrow \mathbb{R}\)
be defined by
\(f(x) = \begin{cases} 2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases}\)
. Then
\(f(-1) + f (2) + f(4)\)
is
KCET - 2022
KCET
Mathematics
Matrices
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