Suppose that the temperature at a point (x,y), on a metal plate is $T(x,y)=4x^2-4xy+y^2$, An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

1

The correct expression for $cos^{-1} (-x)$ is

Topic: NIMCET 2022

2

Let $\vec{a}, \vec{b}, \vec{c} $ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{…

Topic: NIMCET 2022

3

Inverse of the function $f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}}$ is 

Topic: NIMCET 2022

1

The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

Topic: NIMCET 2022

2

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of t…

Topic: NIMCET 2022

3

If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1…

Topic: NIMCET 2022

4

A particle is at rest at the origin. It moves along the x −axis with an acceleration $x-x^2$ , where x is the distance…

Topic: NIMCET 2022

5

If $a{\lt}b$ then $\int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx$ is equal to

Topic: NIMCET 2022

6

The domain of the function $f(x)=\frac{{\cos }^{-1}x}{[x]}$ is

Topic: NIMCET 2022

7

If the volume of the parallelepiped whose adjacent edges are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\al…

Topic: NIMCET 2022

8

Let $a$ be the distance between the lines $−2x + y = 2$ and $2x − y = 2$, and $b$ be the distance between the lines $4x…

Topic: NIMCET 2022

9

If $cosec\theta-cot \theta=2$, then the value of $cosec\theta$ is

Topic: NIMCET 2022

10

The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are

Topic: NIMCET 2022