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List of top Mathematics Questions asked in KCET
If
\(u=\sin^{-1}(\frac{2x}{1+x^2})\)
and
\(v=\tan^{-1}(\frac{2x}{1-x^2})\)
then
\(\frac{du}{dv}\)
is
KCET - 2023
KCET
Mathematics
Derivatives
If
\(\sin^{-1}(\frac{2a}{1+a^2})+\cos^{-1}(\frac{1-a^2}{1+a^2})=\tan^{-1}(\frac{2x}{1-x^2})\)
where a, x ∈ (0, 1) then the value of x is
KCET - 2023
KCET
Mathematics
Inverse Trigonometric Functions
If
\(\Delta=\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}\)
and
\(\Delta_1=\begin{vmatrix} 1 & 1 & 1 \\ bc & ca & ab \\ a & b & c \end{vmatrix}\)
then
KCET - 2023
KCET
Mathematics
Matrices
The area of a triangle with vertices(-3,0),(3, 0) and (0, k) is 9 sq.units, the value of k is
KCET - 2023
KCET
Mathematics
Coordinate Geometry
If A =
\(\begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix}\)
is a singular matrix, then the value of 5k - k
2
is equal to
KCET - 2023
KCET
Mathematics
Matrices
If A and B are two matrices such that AB=B and BA=A then A
2
+ B
2
=
KCET - 2023
KCET
Mathematics
Matrices
If
\(x\begin{bmatrix} 3 \\ 2 \end{bmatrix}+y\begin{bmatrix} 1 \\ -1 \end{bmatrix}=\begin{bmatrix} 15 \\ 5\end{bmatrix}\)
then the value of x and y are
KCET - 2023
KCET
Mathematics
solution of system of linear inequalities in two variables
The value of
\(\cot^{-1}[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}]\)
where x ∈
\((0,\frac{\pi}{4})\)
is
KCET - 2023
KCET
Mathematics
Trigonometry
The contrapositive of the statement
“If two lines do not intersect in the same plane then they are parallel.” is
KCET - 2023
KCET
Mathematics
mathematical reasoning
Let f(x) = sin 2x + cos 2x and g(x)=x
2
-1, then g(f(x)) is invertible in the domain
KCET - 2023
KCET
Mathematics
composite of functions
Let the relation R be defined in N by aRb if 3a + 2b = 27 then R is
KCET - 2023
KCET
Mathematics
Relations and Functions
Let f : R→R be defined by f(x)= 3x
2
-5 and g : R→R by g(x)=
\(\frac{x}{x^2+1}\)
then gof is
KCET - 2023
KCET
Mathematics
composite of functions
f : R → R and g : [0, ∞) → R are defined by f(x) = x
2
and g(x)=
\(\sqrt{x}\)
. Which one of the following is not true ?
KCET - 2023
KCET
Mathematics
Functions
The mean of 100 observations is 50 and their standard deviation is 5. Then the sum of squares of all observations is
KCET - 2023
KCET
Mathematics
Statistics
If n is even and the middle term in the expansion of
\((x^2+\frac{1}{x})^n\)
is 924 x
6
, then n is equal to
KCET - 2023
KCET
Mathematics
Binomial theorem
If
\(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)
= A cos B, then the values of A and B respectively are
KCET - 2023
KCET
Mathematics
limits of trigonometric functions
The distance between the foci of a hyperbola is 16 and its eccentricity is
\(\sqrt2\)
. Its equation is
KCET - 2023
KCET
Mathematics
Hyperbola
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
KCET - 2023
KCET
Mathematics
Various Forms of the Equation of a Line
If
\(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\)
are in A.P., then p, q, r
KCET - 2023
KCET
Mathematics
Arithmetic Progression
n
th
term of the series
\(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+...\)
is
KCET - 2023
KCET
Mathematics
Sequence and series
If the set x contains 7 elements and set y contains 8 elements, then the number of bijections from x to y is
KCET - 2022
KCET
Mathematics
Matrices
If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is 19th word ?
KCET - 2022
KCET
Mathematics
permutations and combinations
If
\(\vec{\alpha}=\hat{i}-3\hat{j},\vec{\beta}=\hat{i}+2\hat{j}-\hat{k}\)
then express If |a×b|+|a.b|=36 and |a|=3 then |b| is equal to
\(\vec{\beta}\)
in the form
\(\vec{β}=\vec{β_1}+\vec{β_2}\)
where
\(\vec{β}_1\)
is parellel to
\(\vec{\alpha}\)
and
\(\vec{β}_2\)
is perpendicular to
\(\vec{\alpha}\)
then
\(\vec{β_1}\)
is given by
KCET - 2022
KCET
Mathematics
Vectors
The degree measure of
\(\frac{\pi}{32}\)
is equal to
KCET - 2022
KCET
Mathematics
Trigonometric Functions
If
\(y =\)
\(e^{\sqrt{x\sqrt{x\sqrt{x\ldots}}}}\)
\(x>1,\)
then
\(\left. \frac{{d^2y}}{{dx^2}} \right|_{x = \log_e 3}\)
is
KCET - 2022
KCET
Mathematics
Exponential and Logarithmic Functions
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