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 $Y=\{(x,y)\colon x{\gt}y,\, x,y\in Z\}$. Then the number of elements in $X\cap Y$ is:
Previous 10 Questions — NIMCET 2024
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Let A and B be two events defined on a sample space $\Omega$. Suppose $A^C$ denotes
the complement of A relative to the…
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The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:
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Among the given numbers below, the smallest number which will be divided by 9, 10,
15 and 20, leaves the remainders 4, …
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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 …
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The two parabolas $y^2 = 4a(x + c)$ and $y^2 = 4bx, a > b > 0$ cannot
have a common normal unless
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A speaks truth in 40% and B in 50% of the cases. The probability that they contradict
each other while narrating some i…
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For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents
two perpendicular lines and two…
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For an invertible matrix A, which of the following is not always true:
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If $\sin x=\sin y$ and $\cos x=\cos y$, then the value of x-y is
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The value of $\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is
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The value of $f(1)$ for $f\Bigg{(}\frac{1-x}{1+x}\Bigg{)}=x+2$ is
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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?
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Let $f(x)=\begin{cases}{{x}^2\sin \frac{1}{x}} & {,\, x\ne0} \\ {0} & {,x=0}\end{cases}$Then which of the …
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A coin is thrown 8 number of times. What is the probability of getting a head in an odd
number of throw?
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Consider the function $f(x)={x}^{2/3}{(6-x)}^{1/3}$. Which of the following statement is false?
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The value of ${{Lt}}_{x\rightarrow0}\frac{{e}^x-{e}^{-x}-2x}{1-\cos x}$ is equal to
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Consider the function $$f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\…
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If one AM (Arithmetic mean) 'a' and two GM's (Geometric means) p and q be inserted between any two positive numbers, th…
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The equation $3x^2 + 10xy + 11y^2 + 14x + 12y + 5 = 0$ represents
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The points (1,1/2) and (3,-1/2) are
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