Consider the function $f$ defined by $f(x)=\begin{cases} x^2-1, & x<3 \ 2ax, & x\geq 3 \end{cases}$ for all real number $x$. If $f$ is continuous at $x=3$, then value of $a$ is

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The sum of the expression $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\cdot…

Topic: NIMCET 2016

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The probability that $A$ speaks truth is $4/5$ while this probability for $B$ is $3/4$. The probability that they contr…

Topic: NIMCET 2016

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Two finite sets $A$ and $B$ are having $m$ and $n$ elements. The total number of subsets of the first set is $56$ more …

Topic: NIMCET 2016

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For any two events $A$ and $B$, the probability that atleast one of them occur is $0.6$. If $A$ and $B$ occur simultane…

Topic: NIMCET 2016

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The minimum value of $a$, for which the sum of the squares of the roots of the equation $x^2-(a-2)x-(a+1)=0$

Topic: NIMCET 2016

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors, no two of which are collinear, if the vector $\vec{a}+2…

Topic: NIMCET 2016

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An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consi…

Topic: NIMCET 2016

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If $\cos\theta = \dfrac{5}{13},; \dfrac{3\pi}{2} < \theta < 2\pi$, then $\tan 2\theta$ is

Topic: NIMCET 2016

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In a triangle $ABC$, $a = 4$, $b = 3$, $\angle BAC = 60^\circ$, then the equation for which $c$ is the root is

Topic: NIMCET 2016

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The area of region bounded by the lines $y = |x - 1|$ and $y = 3 - |x|$ is

Topic: NIMCET 2016

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Three house are available in a locality. Three persons apply for the houses. Each applies for one house without consult…

Topic: NIMCET 2016

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Five horse are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select…

Topic: NIMCET 2016

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If $3^x = 4^{x-1}$, then $x=$

Topic: NIMCET 2016

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The matrix $A$ has $x$ rows and $(x+5)$ columns and the matrix $B$ has $y$ rows and $(11-y)$ columns. If both the matri…

Topic: NIMCET 2016

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A circus artist is climbing a $20$ m long rope, which is tightly streached and tied from the top of a vertical pole to …

Topic: NIMCET 2016

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There are n equally spaced points 1,2,...,n marked on the circumference of a circle. If the point 15 is directly opposi…

Topic: NIMCET 2016

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Let S={1,2,....,n}. The number of possible pairs of the form (A,B) with $A \subseteq B$ for subsets $A,B$ of $S$ is

Topic: NIMCET 2016

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Sum of the roots of the equation $4^x - 3(2^{x+3}) + 128 = 0$ is

Topic: NIMCET 2016

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If the sum of the slopes of the lines given by $x^2 - 2cxy - 7y^2 = 0$ is four times their product, then the value of $…

Topic: NIMCET 2016

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The system of equationsx + y + 2z = ax + z = b2x + y + 3z = chas a solution if

Topic: NIMCET 2016