Suppose r integers, 0 < r < 10, are chosen from (0, 1, 2, ...,9) at random and with replacement. The probability that no two are equal, is
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A normal to the curve $x^{2} = 4y$ passes through the point (1, 2). The distance of the origin from the
normal is
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If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the
angles A, B and C…
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If the sets A and B are defined as A = {(x, y) | y = 1 / x, 0 ≠ x ∈ R}, B = {(x, y)|y = -x ∈ R} then
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If $x$ is so small that $x^{2}$ and higher powers of $x$ can be neglected, then $\frac{(9+2x)^{1/2}(3+4x)}{(1-x)^{1/5}…
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There are 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in …
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If the foci of the ellipse $b^{2}x^{2}+16y^{2}=16b^{2}$ and the hyperbola $81x^{2}-144y^{2}=\frac{81 \times 144}{25}$ c…
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If n and r are integers such that 1 ≤ r ≤ n, then the value of n n-1Cr-1is
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A condition that $x^{3} + ax^{2} + bx + c$ may have no extremum is
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If $sin x + a cos x = b$, then $|a sin x - cos x|$ is:
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If $x = 1$ is the directrix of the parabola $y^{2} = kx - 8$, then k is:
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If $x^{2} + 2ax + 10 - 3a > 0$ for all x ∈ R, then
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A box contains 3 coins, one coin is fair, one coin is two headed and one coin is weighted, so that the
probability of h…
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If a vector $\vec{a}$ makes an equal angle with the coordinate axes and has magnitude 3, then the angle between $\vec{a…
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If $f(x)=\left\{\begin{matrix} \frac{sin[x]}{[x]} &, [x]\ne0 \\ 0 &, [x]=0 \end{matrix}\right.$ , where [x] is the larg…
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If tan A - tan B = x and cot B - cot A = y, then cot (A - B) is equal to
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If $a = log_{12}^{18}$, $b = log_{24}^{54}$, then $ab + 5(a - b)$ is
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A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is…
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The condition that the line lx + my + n = 0 becomes a tangent to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1…
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The value of sin 20° sin 40° sin 80° is
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Two non-negative numbers whose sum is 9 and the product of the one number and square of the other number is maximum, are
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