Science (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the ratio of the coefficients of x^p and x^q in the expansion of \[\left( 1 + x \right)^{p + q}\] .

If a and b are the coefficients of xⁿ in the expansion of  \[\left( 1 + x \right)^{2n} \text{ and }  \left( 1 + x \right)^{2n - 1}\]  respectively, find  \[\frac{a}{b}\]

If  \[\left( 1 - x + x^2 \right)^n = a_0 + a_1 x + a_2 x^2 + . . . + a_{2n} x^{2n}\] , find the value of  \[a_0 + a_2 + a_4 + . . . + a_{2n}\] .

If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then ris equal to

The coefficient of  \[x^{- 17}\]  in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] is 

If P(0, 1, 2), Q(4, –2, 1) and O(0, 0, 0) are three points, then ∠POQ = 

If the extremities of the diagonal of a square are (1, –2, 3 and (2, –3, 5), then the length of the side is 

The points (5, –4, 2), (4, –3, 1), (7, 6, 4) and (8, –7, 5) are the vertices of 

In a three dimensional space the equation x² – 5x + 6 = 0 represents

Find out the following  sentence is a statement and is not. Justify your answer.

Listen to me, Ravi !

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 Every set is a finite set.

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Two non-empty sets have always a non-empty intersection.

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The cat pussy is black.

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 Are all circles round?

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 All triangles have three sides.

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Every rhombus is a square.

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 x² + 5 | x | + 6 = 0 has no real roots.

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 This sentence is a statement.

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Is the earth round?