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Mathematics
List of top Mathematics Questions asked in KCET
The length of perpendicular drawn from the point (3, -1, 11) to the line
\(\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)
is
KCET - 2023
KCET
Mathematics
Three Dimensional Geometry
If a lines makes an angle of
\(\frac{\pi}{3}\)
with each X and Y axis then the acute angle made by Z-axis is
KCET - 2023
KCET
Mathematics
Three Dimensional Geometry
If
\(\vec{a}+2\vec{b}+3\vec{c}=\vec{0}\)
and
\((\vec{a}\times\vec{b})+(\vec{b}\times\vec{c})+(\vec{c}\times\vec{a})=\lambda(\vec{b}\times\vec{c})\)
then the value of λ is equal to
KCET - 2023
KCET
Mathematics
Vector Algebra
In the interval (0, π/2), area lying between the curves y = tan x and y = cot x and the X-axis is
KCET - 2023
KCET
Mathematics
Area between Two Curves
The component of
\(\hat{i}\)
in the direction of the vector
\(\hat{i}+\hat{j}+2\hat{k}\)
is
KCET - 2023
KCET
Mathematics
Vectors
If
\(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\)
then
KCET - 2023
KCET
Mathematics
Vector Algebra
The degree of the differential equation
\(1+(\frac{dy}{dx})^2+(\frac{d^2y}{dx^2})^2= \sqrt[3]{\frac{d^2y}{dx^2}+1}\)
is
KCET - 2023
KCET
Mathematics
Order and Degree of Differential Equation
If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point
KCET - 2023
KCET
Mathematics
Coordinate Geometry
The area of the region bounded by the line y = x +1, and the lines x = 3 and x = 5 is
KCET - 2023
KCET
Mathematics
Area between Two Curves
\(\int\sqrt{5-2x+x^2}\ dx=\)
KCET - 2023
KCET
Mathematics
Definite Integral
\(\int\limits^{\pi}_{0}\frac{x\tan x}{\sec x.\cosec x}\ dx=\)
KCET - 2023
KCET
Mathematics
Trigonometric Identities
\(\int\limits_{-2}^{0}(x^3+3x^2+3x+3+(x+1)\cos(x+1))\ dx=\)
KCET - 2023
KCET
Mathematics
Definite Integral
\(\int\frac{1}{1+3\sin^2 x+8 \cos^2 x}\ dx=\)
KCET - 2023
KCET
Mathematics
Trigonometric Identities
If f(x) and g(x) are two functions with g(x) =
\(x-\frac{1}{x}\)
and fog(x) =
\(x^3-\frac{1}{x^3}\)
then f'(x) =
KCET - 2023
KCET
Mathematics
composite of functions
An enemy fighter jet is flying along the curve given by y = x
2
+ 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is
KCET - 2023
KCET
Mathematics
Differential Calculus
\(\int\sqrt{\cosec x-\sin x}\ dx=\)
KCET - 2023
KCET
Mathematics
Definite Integral
\(\int\limits_{2}^{8}\frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}}\ dx=\)
KCET - 2023
KCET
Mathematics
Definite Integral
A particle moves along the curve
\(\frac{x^2}{16}+\frac{y^2}{4}=1\)
. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is
KCET - 2023
KCET
Mathematics
Conic sections
The distance ‘s’ in meters travelled by a particle in ‘t’ seconds is given by s =
\(\frac{2t^3}{3}-18t+\frac{5}{3}.\)
The acceleration when the particle comes to rest is
KCET - 2023
KCET
Mathematics
Differential Calculus
A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing when the radius is 5.2 cm is
KCET - 2023
KCET
Mathematics
Derivatives
If A =
\(\begin{bmatrix} 1 & \tan\ \alpha/2 \\ -\tan\ \alpha/2 & 1 \end{bmatrix}\)
and AB=I then B =
KCET - 2023
KCET
Mathematics
Matrices
If f(x) = 1 + nx +
\(\frac{n(n-1)}{2}x^2+\frac{n(n-1)(n-2)}{6}x^3+...+x^n\)
then f"(1) =
KCET - 2023
KCET
Mathematics
Sequence and series
If y = a sin x + b cos x, then y
2
+
\((\frac{dy}{dx})^2\)
is a
KCET - 2023
KCET
Mathematics
Trigonometric Functions
If the function of f(x) =
\(\frac{1}{x+2}\)
, then the point of discontinuity of the composite function y = f(f(x)) is
KCET - 2023
KCET
Mathematics
composite of functions
The function f(x) = cot x is discontiuous on every point of the set
KCET - 2023
KCET
Mathematics
Continuity
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