For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represents two perpendicular lines and two lines inclined at an angle of $\pi/4$.
Previous 10 Questions — NIMCET 2024
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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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A critical orthopedic surgery is performed on 3 patients. The probability of recovering
a patient is 0.6. Then the prob…
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If for non-zero x, $cf(x)+df\Bigg{(}\frac{1}{x}\Bigg{)}=|\log |x||+3,$ where $c\ne 0$, then $\int ^e_1f(x)dx=$
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At how many points the following curves intersect $\frac{{y}^2}{9}-\frac{{x}^2}{16}=1$ and $\frac{{x}^2}{4}+\…
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Find the cardinality of the set C which is defined as $C={\{x|\, \sin 4x=\frac{1}{2}\, forx\in(-9\pi,3\pi)}\}$.
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A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either se…
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If F|= 40N (Newtons), |D| = 3m, and $\theta={60^{\circ}}$, then the work done by F actingfrom P to Q is
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Which of the following is TRUE?A. If $f$ is continuous on $[a,b]$, then $\int ^b_axf(x)\mathrm{d}x=x\int ^b_af(x)\mathr…
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Next 10 Questions — NIMCET 2024
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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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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 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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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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The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:
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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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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…
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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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