Let $f(x)=\begin{cases}{{x}^2\sin \frac{1}{x}} & {,\, x\ne0} \\ {0} & {,x=0}\end{cases}$

Then which of the follwoing is true

1

Given a set A with median $m_1 = 2$ and set B with median $m_2 = 4$What can we say about the median of the combined set?

Topic: NIMCET 2024

2

The value of $f(1)$ for $f\Bigg{(}\frac{1-x}{1+x}\Bigg{)}=x+2$ is

Topic: NIMCET 2024

3

Let Z be the set of all integers, and consider the sets $X=\{(x,y)\colon{x}^2+2{y}^2=3,\, x,y\in Z\}$ and $Y=\{(x,y)\co…

Topic: NIMCET 2024

4

Let A and B be two events defined on a sample space $\Omega$. Suppose $A^C$ denotes the complement of A relative to the…

Topic: NIMCET 2024

5

The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:

Topic: NIMCET 2024

6

Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20, leaves the remainders 4, …

Topic: NIMCET 2024

7

A man starts at the origin O and walks a distance of 3 units in the north- east direction and then walks a distance of …

Topic: NIMCET 2024

8

The two parabolas $y^2 = 4a(x + c)$ and $y^2 = 4bx, a > b > 0$ cannot have a common normal unless

Topic: NIMCET 2024

9

A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some i…

Topic: NIMCET 2024

10

For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents two perpendicular lines and two…

Topic: NIMCET 2024

1

A coin is thrown 8 number of times. What is the probability of getting a head in an odd number of throw?

Topic: NIMCET 2024

2

Consider the function $f(x)={x}^{2/3}{(6-x)}^{1/3}$. Which of the following statement is false?

Topic: NIMCET 2024

3

The value of ${{Lt}}_{x\rightarrow0}\frac{{e}^x-{e}^{-x}-2x}{1-\cos x}$ is equal to 

Topic: NIMCET 2024

4

Consider the function $$f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\…

Topic: NIMCET 2024

5

If one AM (Arithmetic mean) 'a' and two GM's (Geometric means) p and q be inserted between any two positive numbers, th…

Topic: NIMCET 2024

6

The equation $3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0$ represents

Topic: NIMCET 2024

7

The points (1,1/2) and (3,-1/2) are

Topic: NIMCET 2024

8

How much work does it take to slide a crate for a distance of 25m along a loading dock by pulling on it with a 180 N fo…

Topic: NIMCET 2024

9

The vector $\vec{A}=(2x+1)\hat{i}+(x^2-6y)\hat{j}+(xy^2+3z)\hat{k}$ is a

Topic: NIMCET 2024

10

Region R is defined as region in first quadrant satisfying the condition $x^2 + y^2 < 4$. Given that a point P=(r,s)…

Topic: NIMCET 2024