and 
, then the value of 
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Topic: NIMCET 2018
How many natural numbers smaller than $2 \times 10^8$ can be formed using the digits 1 and 2 only?
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Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - px + r = 0$ and $\dfrac{\alpha}{2}, 2\beta$ are the roots …
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The coefficient of $x^n$ in the expansion of $(1 - 2x + 3x^2 - 4x^3 + \cdots \text{ to } \infty)^{-n}$ is
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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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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 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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In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students li…
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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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Which of the following function is the inverse of itself?
Topic: NIMCET 2018
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Differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ to
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$f(x) = x + |x|$ is continuous for
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If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors, then $|\mathbf{a} - \mathbf{b}|^2 + |\mathbf{b} - \mathbf{c}|^2 +…
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The vector $\vec{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}$ lies in the plane of the vector $\vec{b} = \hat{i} + \ha…
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Forces $4\hat{i} - 3\hat{j} + 7\hat{k}$ and $-2\hat{i} + 2\hat{j} - 8\hat{k}$ are acting on a particle and displaced it…
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A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3),…
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The value of $\cot\!\left(cosec^{-1}\dfrac{5}{3} + \tan^{-1}\dfrac{2}{3}\right)$ is
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If $\sin\theta = 3\sin(\theta + 2\alpha)$, then value of $\tan(\theta + \alpha) + 2\tan\alpha$ is
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In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of equal to?
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