If the roots of the quadratic equation $x^2+px+q=0$ are tan 30° and tan 15° respectively, then the value of 2 + p - q is
Previous 10 Questions — NIMCET 2022
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In a Harmonic Progression, $p^{th}$ term is $q$ and
the $q^{th}$ term is $p$. Then $pq^{th}$ term is
Topic: NIMCET 2022
Solutions of the equation ${\tan }^{-1}\sqrt[]{{x}^2+x}+{\sin }^{-1}\sqrt[]{{x}^2+x+1}=\frac{\pi}{2}$ are
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If $a_1, a_2, a_3,...a_n$, are in Arithmetic Progression
with common difference d, then the sum $(sind) (cosec a_1 . c…
Topic: NIMCET 2022
If $\alpha , \beta$ are the roots of $x^2-x-1=0$ and $A_n=\alpha^n+\beta^n$, the Arithmetic mean of $A_{n-1}$ and $A_n$…
Topic: NIMCET 2022
If ${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$, $(a{\gt}b)$ and ${x}^2-{y}^2={c}^2$ cut at righ…
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The area enclosed within the curve |x|+|y|=2 is
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The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then…
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The function $f(x)=\log (x+\sqrt[]{{x}^2+1})$ is
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If $\vec{a}=\lambda \hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=\hat{i}+\lambda \hat{j}-2\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}…
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For $a\in R$ (the set of al real numbers), $a \ne 1$, $\lim _{{n}\rightarrow\infty}\frac{({1}^a+{2}^a+{\ldots+{n}^a})}{…
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Next 10 Questions — NIMCET 2022
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A straight line through the point (4, 5) is
such that its intercept between the axes is
bisected at A, then its equat…
Topic: NIMCET 2022
The value of $\int \frac{({x}^2-1)}{{x}^3\sqrt[]{2{x}^4-2{x}^2+1}}dx$
Topic: NIMCET 2022
Coordinate of the focus of the parabola $4y^2+12x-20y+67=0$ is
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There are two circles in xy −plane whose
equations are $x^2+y^2-2y=0$ and $x^2+y^2-2y-3=0$. A point $(x,y)$ is
chosen…
Topic: NIMCET 2022
In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half th…
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If $x^my^n$=$(x+y)^{m+n}$, then $\frac{dy}{dx}$ is
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If $cos^{-1} \frac{x}{2}+cos^{-1} \frac{y}{3}=\phi$, then $9x^2-12xy cos\phi+4y^2$ is
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The value of ${3}^{3-\log _35}$ is
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There are two sets A and B with |A| = m and
|B| = n. If |P(A)| − |P(B)| = 112 then
choose the wrong option (where |A|…
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The eccentricity of an ellipse, with its center
at the origin is $\frac{1}{3}$
. If one of the directrices is
$x=9$, …
Topic: NIMCET 2022
