If the equation $|x^2 – 6x + 8| = a$ has four real solution then find the value of $a$?

1

The graph of function $f(x)=\log _e({x}^3+\sqrt[]{{x}^6+1})$ is symmetric about:

Topic: NIMCET 2023

2

$\lim _{{x}\rightarrow1}\frac{{x}^4-1}{x-1}=\lim _{{x}\rightarrow k}\frac{{x}^3-{k}^2}{{x}^2-{k}^2}=$, then find k

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3

$\int f(x)\mathrm{d}x=g(x)$, then $\int {x}^5f({x}^3)\mathrm{d}x$

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4

If $\vec{a}, \vec{b}$ are unit vectors such that $2\vec{a}+\vec{b} =3$ then which of the following statement is true?

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5

If $\vec{a}=\hat{i}-\hat{k}$, $\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$, t…

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6

The locus of the mid-point of all chords of the parabola $y^2 = 4x$ which are drawn through its vertex is

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7

Find foci of the equation $x^2 + 2x – 4y^2 + 8y – 7 = 0$

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8

If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value of ad?

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9

Let A and B be sets. $A\cap X=B\cap X=\phi$ and $A\cup X=B\cup X$ for some set X, relation between A & B

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10

Let $\vec{A} = 2\hat{i} + \hat{j} – 2\hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$, If $\vec{C}$ is a vector such that $|\…

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1

Largest value of $cos^2\theta -6sin\theta cos\theta+3sin^2\theta+2 $ is

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2

Given to events A and B such that odd in favour A are 2 : 1 and odd in favour of $A \cup B$ are 3 : 1. Consistent with …

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3

If A and B are square matrices such that $B=-A^{-1} BA$, then $(A + B)^2$ is

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4

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random th…

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5

Between any two real roots of the equation $e^x sin x = 1$, the equation $e^x cos x = –1$ has

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6

If f(x) is a polynomial of degree 4, f(n) = n + 1 & f(0) = 25, then find f(5) = ?

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7

The maximum value of $f(x) = (x – 1)^2 (x + 1)^3$ is equal to $\frac{2^p3^q}{3125}$  then the ordered pair of (p, …

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8

The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001…

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9

If ${{x}}_k=\cos \Bigg{(}\frac{2\pi k}{n}\Bigg{)}+i\sin \Bigg{(}\frac{2\pi k}{n}\Bigg{)}$ , then $\sum ^n_{k=1}({{…

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10

Number of point of which f(x) is not differentiable $f(x)=|cosx|+3$ in $[-\pi, \pi]$

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