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The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
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The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
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In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
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In a survey of 100 students, the number of students studying the various languages were found to be : English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, no language 24. Find:
(i) How many students were studying Hindi?
(ii) How many students were studying English and Hindi?
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If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
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Using binomial theorem determine which number is larger (1.2)4000 or 800?
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Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.
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Show that \[2^{4n + 4} - 15n - 16\] , where n ∈ \[\mathbb{N}\] is divisible by 225.
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The mid-points of the sides of a triangle ABC are given by (–2, 3, 5), (4, –1, 7) and (6, 5, 3). Find the coordinates of A, B and C.
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A(1, 2, 3), B(0, 4, 1), C(–1, –1, –3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.
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Find the coordinates of the points which tisect the line segment joining the points P(4, 2, –6) and Q(10, –16, 6).
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Using section formula, show that he points A(2, –3, 4), B(–1, 2, 1) and C(0, 1/3, 2) are collinear.
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Given that P(3, 2, –4), Q(5, 4, –6) and R(9, 8, –10) are collinear. Find the ratio in which Qdivides PR.
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Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz-plane.
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Find the coordinates of a point equidistant from the origin and points A (a, 0, 0), B (0, b, 0) andC(0, 0, c).
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Write the coordinates of the point P which is five-sixth of the way from A(−2, 0, 6) to B(10, −6, −12).
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If a parallelopiped is formed by the planes drawn through the points (2,3,5) and (5, 9, 7) parallel to the coordinate planes, then write the lengths of edges of the parallelopiped and length of the diagonal.
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Determine the point on yz-plane which is equidistant from points A(2, 0, 3), B(0, 3,2) and C(0, 0,1).
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If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(−2, b −5) and C (4, 7, c), find the values of a, b, c.
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Find k so that \[\lim_{x \to 2} f\left( x \right)\] \[f\left( x \right) = \begin{cases}2x + 3, & x \leq 2 \\ x + k, & x > 2\end{cases} .\]
Concept: undefined >> undefined
