Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

To maintain his health a person must fulfil certain minimum daily requirements for several kinds of nutrients. Assuming that there are only three kinds of nutrients-calcium, protein and calories and the person's diet consists of only two food items, I and II, whose price and nutrient contents are shown in the table below:
 

What combination of two food items will satisfy the daily requirement and entail the least cost? Formulate this as a LPP.

S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S is _______________ .

In the set Z of all integers, which of the following relation R is not an equivalence relation ?

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Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then, R is _______________ .

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The relation S defined on the set R of all real number by the rule aSb if a ≥ b is _______________ .

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The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .

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Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then, R is _____________ .

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Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is ______________ .

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Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is ____________ .

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Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is _____________ .

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For real numbers x and y, define xRy if `x-y+sqrt2` is an irrational number. Then the relation R is ___________ .

Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π).

Determine the order and degree (if defined) of the following differential equation:-

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]

Determine the order and degree (if defined) of the following differential equation:-

y"' + 2y" + y' = 0

Determine the order and degree (if defined) of the following differential equation:-

(y"')² + (y")³ + (y')⁴ + y⁵ = 0

Determine the order and degree (if defined) of the following differential equation:-

y"' + 2y" + y' = 0

Determine the order and degree (if defined) of the following differential equation:-

y" + (y')² + 2y = 0

Determine the order and degree (if defined) of the following differential equation:-

y" + 2y' + sin y = 0

Determine the order and degree (if defined) of the following differential equation:-

y"' + y² + e^y' = 0

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = x² + 2x + C            y' − 2x − 2 = 0