Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Q: Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.

Recently Viewed Questions of Class 12 Mathematics

y = e^x +1 : yⁿ -y^' = 0

Q: Show that the relation R in the set A of points in a plane given by R = {(P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

Q: If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?

Q: \begin{align} \int\left(2x^2-3Sinx +5\sqrt {x}\right).dx\end{align}

Q: Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

Let f, g and h be functions from R to R. Show that

(f + g)oh = foh + goh

(f . g)oh = (foh) . (goh)

Q: Show that each of the relation R in the set A = { x ∈Z: 0≤x≤12}, A={x} given by
(i) R = { (a,b) : |a - b| is a multiple of 4}
(ii) R = {(a,b):a = b} is an equivalence relation.
Find the set of all elements related to 1 in each case.

Q: Check whether the relation R in R defined as R = {(a, b): a ≤ b³} is reflexive, symmetric or transitive.

Let f : X → Y be an invertible function. Show that f has unique inverse.

(Hint: suppose g1 and g2 are two inverses of f. Then for all y ∈ Y, fog1(y) = 1Y(y) = fog2(y). Use one-one ness of f).

Q: Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = { (a,b) ; |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

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Reference examples and data from the chapter when answering questions about Vector Algebra.
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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 3: Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force....

Classify the following as scalar and vec | Class 12 Mathematics Chapter Vector Algebra, Vector Algebra NCERT Solutions

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