Equation of the common tangents with a positive slope to the circle $x^2+y^2-8x=0$ and$\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ is
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The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where…
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The circles whose equations are $x^2+y^2+c^2=2ax$ and $x^2+y^2+x^2-2by=0$ will touch one another externally, if
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If $\dfrac{\tan x}{2} = \dfrac{\tan y}{3} = \dfrac{\tan z}{5}$ and $x + y + z = \pi$, then the value of $\tan^2 x + \ta…
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Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and
$Q = \{\theta : \sin\theta + \cos\theta = \s…
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In an acute-angled ΔABC the least value of secA+secB+secC is
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The number of solutions of the equation sinx + sin5x = sin3x lying in the interval $[0, \pi]$ is
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The point of intersection os circle $x^2+y^2+10x-12y+51=0$ and the line $3y+x=3$ is
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If the radius of the circle changes at the rate of $-\dfrac{2}{\pi}$ m/s, at what rate does the circle's area change wh…
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The slope of two-lines $6x^2-xy-2y^2=0$ differ by
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Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ |x - 2| & \text{if } x \geq 0 …
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Next 10 Questions — NIMCET 2018
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The area enclosed between the curves $y^2=x$ and $y=|x|$ is
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Equation of the line perpendicular to x-2y=1 and passing through (1,1) is
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If $A = \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix}$ and $f(x) = 1 + x + x^2 + \cdots + x^{16}$, then $f(A) =$
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9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging o…
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Which of the following function is the inverse of itself?
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A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and t…
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In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students li…
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If A and B are two events and $P(A \cup B) = \dfrac{5}{6}$, $P(A \cap B) = \dfrac{1}{2}$, the A and B are two events wh…
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If $a_1, a_2,...a_n$ are positive real numbers whose product is a fixed number c, then the minimum of $a_1, …
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If \(a, b, c\) are the roots of the equation \(x^3 - 3x^2 + 3x + 7 = 0\), then the value of\[\begin{vmatrix}2bc - a^2 &…
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