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Q1. Let n(A) = m and n, then the total number of non- empty relations that can be defined from A to B is
Choice (a) is correct. We have, n(A) = m and n(B) = n n(A × B) =n (A).n(B) =mn Number of subsets of A × B = 2ᵐⁿ Number of non-empty subsets of A × B = 2ᵐⁿ -1 Number of non-empty relation from A to B = 2ᵐⁿ -1 This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations aRead more
Choice (a) is correct.
We have, n(A) = m and n(B) = n
n(A × B) =n (A).n(B) =mn
Number of subsets of A × B = 2ᵐⁿ
Number of non-empty subsets of A × B = 2ᵐⁿ -1
Number of non-empty relation from A to B = 2ᵐⁿ -1
This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding.
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Let f(x) = √1 + x², then
Choice (b) is correct. We have, f(x) = √1 + x² f(y) = √1 + y² and f(xy) = √1 + (xy)² = √1 + x²y² f(x).f(y) = √1 + x². √1 + y² = √1 + x² + y² + x²y² √1+ x²y² ≤ √1 + x² + y² + x²y² f(xy) ≤ f(x)f(y) This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions.Read more
Choice (b) is correct.
We have, f(x) = √1 + x²
f(y) = √1 + y² and f(xy) = √1 + (xy)² = √1 + x²y²
f(x).f(y) = √1 + x². √1 + y² = √1 + x² + y² + x²y²
√1+ x²y² ≤ √1 + x² + y² + x²y²
f(xy) ≤ f(x)f(y)
This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding.
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If f be the exponential function and g be the logarithmic function, the fg(1) is
Choice (a) is correct. We have f(x) = eˣ = g(x) = logₑ x Now, fg(x) = f(x)g(x) = eˣlogₑ x fg(1) = f(1)g(1) = e¹logₑ 1 = e × 0 = 0 This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding. For more please visiRead more
Choice (a) is correct. We have f(x) = eˣ = g(x) = logₑ x
Now, fg(x) = f(x)g(x) = eˣlogₑ x
fg(1) = f(1)g(1) = e¹logₑ 1 = e × 0 = 0
This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding.
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Domain of function √a² – x² (a > 0) is
Choice (b) is correct Let y = √a² - x² The function y is defined if a² = x² ≥ 0 ⇒ a² ≥ x² ⇒ x² ≤ a² ⇒ -a ≤ x ≤ a Domain = [-a, a] This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding. For more please visiRead more
Choice (b) is correct
Let y = √a² – x²
The function y is defined if a² = x² ≥ 0 ⇒ a² ≥ x² ⇒ x² ≤ a² ⇒ -a ≤ x ≤ a
Domain = [-a, a]
This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding.
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Domain of real valued function f(x) = 1/2x +1 is
Choice (c). is correct. f(x) = 1/2x + 1 For domain, 2x + 1= 0 ⇒ 2x ≠ - 1 ⇒ x ≠ -(1/2) x can take any real value except x = -(1/2). Domain = R - {-(1/2)} This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understandingRead more
Choice (c). is correct. f(x) = 1/2x + 1
For domain, 2x + 1= 0 ⇒ 2x ≠ – 1 ⇒ x ≠ -(1/2)
x can take any real value except x = -(1/2).
Domain = R – {-(1/2)}
This question related to Chapter 2 maths Class 11th NCERT. From the Chapter 2: Relations and Functions. Give answer according to your understanding.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/maths/#chapter-2