If $x, y, z$ are distinct real numbers, then $$ \begin{vmatrix} x & x^{2} & 2 + x^{3} \\ y & y^{2} & 2 + y^{3} \\ z & z^{2} & 2 + z^{3} \end{vmatrix} = 0 $$ Then find $xyz$.
Previous 10 Questions — NIMCET 2019
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Let \(x_i, i = 1,2,\ldots n\) be n observations and \(w_i = p x_i + k\), \(i = 1,2,\ldots n\) where p and k are constan…
Topic: NIMCET 2019
A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of e…
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If \(a\) and \(b\) are the greatest values of \(^{2n}C_r\) and \(^{2n-1}C_r\) respectively, then:
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If (1 + x – 2x2)6 = 1 + a1x + a2x2 + ... + a12x12,
then the value a2 + a4 + a6 + ... + a12
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If a, b, c are in GP and log a - log 2b, log 2b - log 3c and log 3c - log a are in AP, then a, b, c are the lengths of …
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The solution set of the inequality is
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Let S be the set $\{a\in Z^+:a\leq100\}$.If the equation
$[tan^2 x]-tan x - a = 0$ has real roots (where [ . ] is the g…
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If \(\sum \limits_{i=1}^{n} x_i = 80\) and \(\sum \limits_{i=1}^{n} x_i^2 = 400\), then a possible value of n among the…
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If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to
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If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabiliti…
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Next 10 Questions — NIMCET 2019
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Let f(x) be a polynomial satisfying \(f(0) = 2\), \(f'(0) = 3\) and \(f''(x) = f(x)\). Then \(f(4)\) is equal to:
Topic: NIMCET 2019
If $a, a, a_2, ., a_{2n-1},b$ are in AP, $a, b_1, b_2,...b_{2n-1}, b $are in GP and $a, c_1, c_2,... c_{2n-1}, b $ are …
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For the two circles $x^2+y^2=16$ and $x^2+y^2-2y=0$, there is/are
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Let $f : \mathbb{R} \to \mathbb{R}$ be defined by
$f(x)=\begin{cases}
x \sin\left(\frac{1}{x}\right), & x>0,\\…
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A particle P starts from the point z0=1+2i, where i=√−1 . It moves first horizontally awa…
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If $\Delta=a^2-(b-c)^2$, where $\Delta$ is the are of the triangle ABC, then $tanA=$
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Two numbers $a$ and $b$ are chosen are random from a set of the first 30
natural numbers, then the probability that $a^…
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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph …
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Decide which of the give conclusions logically follow from from the given students(s) :Statements:All suns are moons.So…
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Ten points are marked on a straight line and eleven points are marked on another straight line. How many tria…
Topic: NIMCET 2019
