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Mathematics Quiz - Class 11 Mathematics Permutations And...

Question 1/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x+3) और (g(x)=x-5), तो ((f+g)(x)) क्या है?

If (f(x)=2x+3) and (g(x)=x-5), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (3x-2)

Step 1

Concept

((f+g)(x)=(2x+3)+(x-5)=3x-2). While adding, combine only like terms.

Step 2

Why this answer is correct

The correct answer is A. (3x-2). ((f+g)(x)=(2x+3)+(x-5)=3x-2). While adding, combine only like terms.

Step 3

Exam Tip

((f+g)(x)=(2x+3)+(x-5)=3x-2)। जोड़ते समय समान पदों को ही जोड़ें।

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Question 2/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=7x-4) और (g(x)=2x+9), तो ((f-g)(x)) ज्ञात कीजिए।

If (f(x)=7x-4) and (g(x)=2x+9), find ((f-g)(x)).

Explanation opens after your attempt

Correct Answer

B. (5x-13)

Step 1

Concept

((f-g)(x)=(7x-4)-(2x+9)=5x-13). In subtraction, change all signs of the second bracket.

Step 2

Why this answer is correct

The correct answer is B. (5x-13). ((f-g)(x)=(7x-4)-(2x+9)=5x-13). In subtraction, change all signs of the second bracket.

Step 3

Exam Tip

((f-g)(x)=(7x-4)-(2x+9)=5x-13)। घटाने में दूसरे कोष्ठक के सभी चिह्न बदलें।

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Question 3/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+6) और (g(x)=x-2), तो ((fg)(x)) क्या होगा?

If (f(x)=x+6) and (g(x)=x-2), what will ((fg)(x)) be?

Explanation opens after your attempt

Correct Answer

A. \(x^2+4x-12\)

Step 1

Concept

((fg)(x)=(x+6)(x-2)=x^-2+4x-12). In multiplication, multiply each term correctly.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+4x-12\). ((fg)(x)=(x+6)(x-2)=x^-2+4x-12). In multiplication, multiply each term correctly.

Step 3

Exam Tip

((fg)(x)=(x+6)(x-2)=x^-2+4x-12)। गुणन में हर पद को सही पद से गुणा करें।

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Question 4/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=4x^-2+8x) और (g(x)=4x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

If (f(x)=4x^-2+8x) and (g(x)=4x), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?

Explanation opens after your attempt

Correct Answer

A. (x+2)

Step 1

Concept

(\frac{4x^-2+8x}{4x}=\frac{4x(x+2)}{4x}=x+2), where \(x\neq0\). Check the denominator condition before cancellation.

Step 2

Why this answer is correct

The correct answer is A. (x+2). (\frac{4x^-2+8x}{4x}=\frac{4x(x+2)}{4x}=x+2), where \(x\neq0\). Check the denominator condition before cancellation.

Step 3

Exam Tip

(\frac{4x^-2+8x}{4x}=\frac{4x(x+2)}{4x}=x+2), जहाँ \(x\neq0\)। काटने से पहले हर की शर्त देखें।

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Question 5/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+2) और (g(x)=3x-1), तो ((f+g)(2)) का मान क्या है?

If (f(x)=x^-2+2) and (g(x)=3x-1), what is the value of ((f+g)(2))?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

((f+g)(2)=f(2)+g(2)=6+5=11). Add only after substituting the value.

Step 2

Why this answer is correct

The correct answer is C. (11). ((f+g)(2)=f(2)+g(2)=6+5=11). Add only after substituting the value.

Step 3

Exam Tip

((f+g)(2)=f(2)+g(2)=6+5=11)। मान रखने के बाद ही जोड़ करें।

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Question 6/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=5x+2) और (g(x)=x^-2), तो ((f-g)(3)) का मान क्या होगा?

If (f(x)=5x+2) and (g(x)=x^-2), what will be the value of ((f-g)(3))?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

((f-g)(3)=f(3)-g(3)=17-9=8). Changing the order may change the answer.

Step 2

Why this answer is correct

The correct answer is A. (8). ((f-g)(3)=f(3)-g(3)=17-9=8). Changing the order may change the answer.

Step 3

Exam Tip

((f-g)(3)=f(3)-g(3)=17-9=8)। क्रम बदलने से उत्तर बदल सकता है।

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Question 7/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x-1) और (g(x)=x+4), तो ((fg)(2)) क्या है?

If (f(x)=2x-1) and (g(x)=x+4), what is ((fg)(2))?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

((fg)(2)=f(2)g(2)=3\cdot6=18). In product, multiply the values of the functions.

Step 2

Why this answer is correct

The correct answer is B. (18). ((fg)(2)=f(2)g(2)=3\cdot6=18). In product, multiply the values of the functions.

Step 3

Exam Tip

((fg)(2)=f(2)g(2)=3\cdot6=18)। गुणन में फलनों के मानों का गुणा करें।

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Question 8/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-16) और (g(x)=x-4), तो (\left\(\frac{f}{g}\right\)(5)) का मान क्या है?

If (f(x)=x^-2-16) and (g(x)=x-4), what is the value of (\left\(\frac{f}{g}\right\)(5))?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(5)=\frac{25-16}{5-4}=9). In division, the denominator value must not be zero.

Step 2

Why this answer is correct

The correct answer is C. (9). (\left\(\frac{f}{g}\right\)(5)=\frac{25-16}{5-4}=9). In division, the denominator value must not be zero.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(5)=\frac{25-16}{5-4}=9)। भाग में हर का मान शून्य नहीं होना चाहिए।

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Question 9/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=3x^-2) और (g(x)=2x^-2+1), तो ((f+g)(x)) किसके बराबर है?

If (f(x)=3x^-2) and (g(x)=2x^-2+1), then ((f+g)(x)) is equal to which expression?

Explanation opens after your attempt

Correct Answer

A. \(5x^2+1\)

Step 1

Concept

((f+g)(x)=3x^-2+2x^-2+1=5x^-2+1). Add terms with the same power.

Step 2

Why this answer is correct

The correct answer is A. \(5x^2+1\). ((f+g)(x)=3x^-2+2x^-2+1=5x^-2+1). Add terms with the same power.

Step 3

Exam Tip

((f+g)(x)=3x^-2+2x^-2+1=5x^-2+1)। समान घात वाले पद जोड़ें।

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Question 10/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=9x-2) और (g(x)=4x-7), तो ((f-g)(x)) क्या होगा?

If (f(x)=9x-2) and (g(x)=4x-7), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

A. (5x+5)

Step 1

Concept

((f-g)(x)=9x-2-(4x-7)=5x+5). Write (-(-7)) as (+7).

Step 2

Why this answer is correct

The correct answer is A. (5x+5). ((f-g)(x)=9x-2-(4x-7)=5x+5). Write (-(-7)) as (+7).

Step 3

Exam Tip

((f-g)(x)=9x-2-(4x-7)=5x+5)। (-(-7)) को (+7) लिखें।

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Question 11/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-3) और (g(x)=2x), तो ((fg)(x)) क्या होगा?

If (f(x)=x^-3) and (g(x)=2x), what will ((fg)(x)) be?

Explanation opens after your attempt

Correct Answer

C. \(2x^4\)

Step 1

Concept

((fg)(x)=x^-3\cdot2x=2x^-4). Add powers when multiplying the same base.

Step 2

Why this answer is correct

The correct answer is C. \(2x^4\). ((fg)(x)=x^-3\cdot2x=2x^-4). Add powers when multiplying the same base.

Step 3

Exam Tip

((fg)(x)=x^-3\cdot2x=2x^-4)। समान आधार में गुणा करते समय घातें जोड़ें।

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Question 12/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=10x^-3) और (g(x)=5x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

If (f(x)=10x^-3) and (g(x)=5x), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq0\)?

Explanation opens after your attempt

Correct Answer

A. \(2x^2\)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(x)=\frac{10x^-3}{5x}=2x^-2), where \(x\neq0\). In division, powers are subtracted.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2\). (\left\(\frac{f}{g}\right\)(x)=\frac{10x^-3}{5x}=2x^-2), where \(x\neq0\). In division, powers are subtracted.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(x)=\frac{10x^-3}{5x}=2x^-2), जहाँ \(x\neq0\)। भाग में घातें घटती हैं।

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Question 13/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-8), तो ((3f)(x)) क्या है?

If (f(x)=x-8), what is ((3f)(x))?

Explanation opens after your attempt

Correct Answer

C. (3x-24)

Step 1

Concept

((3f)(x)=3(x-8)=3x-24). Multiply all terms by the scalar.

Step 2

Why this answer is correct

The correct answer is C. (3x-24). ((3f)(x)=3(x-8)=3x-24). Multiply all terms by the scalar.

Step 3

Exam Tip

((3f)(x)=3(x-8)=3x-24)। स्थिर गुणक को सभी पदों से गुणा करें।

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Question 14/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=4x+6), तो (\left\(\frac{1}{2}f\right\)(x)) क्या होगा?

If (f(x)=4x+6), what will (\left\(\frac{1}{2}f\right\)(x)) be?

Explanation opens after your attempt

Correct Answer

A. (2x+3)

Step 1

Concept

(\left\(\frac{1}{2}f\right\)(x)=\frac{1}{2}(4x+6)=2x+3). Apply the fractional multiplier to every term.

Step 2

Why this answer is correct

The correct answer is A. (2x+3). (\left\(\frac{1}{2}f\right\)(x)=\frac{1}{2}(4x+6)=2x+3). Apply the fractional multiplier to every term.

Step 3

Exam Tip

(\left\(\frac{1}{2}f\right\)(x)=\frac{1}{2}(4x+6)=2x+3)। भिन्न गुणक को हर पद पर लगाएँ।

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Question 15/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x^-2-5), तो ((-f)(x)) किसके बराबर है?

If (f(x)=2x^-2-5), what is ((-f)(x)) equal to?

Explanation opens after your attempt

Correct Answer

A. \(-2x^2+5\)

Step 1

Concept

((-f)(x)=-\(2x^2-5\)=-2x^-2+5). The negative sign applies to the whole function.

Step 2

Why this answer is correct

The correct answer is A. \(-2x^2+5\). ((-f)(x)=-\(2x^2-5\)=-2x^-2+5). The negative sign applies to the whole function.

Step 3

Exam Tip

((-f)(x)=-\(2x^2-5\)=-2x^-2+5)। ऋण चिह्न पूरे फलन पर लगता है।

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Question 16/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+4x), तो ((f+f)(x)) क्या होगा?

If (f(x)=x^-2+4x), what will ((f+f)(x)) be?

Explanation opens after your attempt

Correct Answer

B. \(2x^2+8x\)

Step 1

Concept

((f+f)(x)=2f(x)=2x^-2+8x). Adding the same function equals (2f).

Step 2

Why this answer is correct

The correct answer is B. \(2x^2+8x\). ((f+f)(x)=2f(x)=2x^-2+8x). Adding the same function equals (2f).

Step 3

Exam Tip

((f+f)(x)=2f(x)=2x^-2+8x)। समान फलन जोड़ना (2f) के बराबर है।

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Question 17/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-3), तो ((ff)(x)) क्या है?

If (f(x)=x-3), what is ((ff)(x))?

Explanation opens after your attempt

Correct Answer

C. \(x^2-6x+9\)

Step 1

Concept

((ff)(x)=f(x)f(x)=(x-3)²=x^-2-6x+9). Do not treat ((ff)(x)) as ((f+f)(x)).

Step 2

Why this answer is correct

The correct answer is C. \(x^2-6x+9\). ((ff)(x)=f(x)f(x)=(x-3)²=x^-2-6x+9). Do not treat ((ff)(x)) as ((f+f)(x)).

Step 3

Exam Tip

((ff)(x)=f(x)f(x)=(x-3)²=x^-2-6x+9)। ((ff)(x)) को ((f+f)(x)) न मानें।

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Question 18/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x+10) और (g(x)=2x+10), तो ((f-g)(x)) क्या है?

If (f(x)=2x+10) and (g(x)=2x+10), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

The difference of equal functions is (0), so ((f-g)(x)=0). In exams, first notice if both functions are equal.

Step 2

Why this answer is correct

The correct answer is A. (0). The difference of equal functions is (0), so ((f-g)(x)=0). In exams, first notice if both functions are equal.

Step 3

Exam Tip

समान फलनों का अंतर (0) होता है, इसलिए ((f-g)(x)=0)। परीक्षा में पहले पहचानें कि दोनों फलन समान हैं।

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Question 19/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=0) और (g(x)=3x^-2-2), तो ((fg)(x)) क्या होगा?

If (f(x)=0) and (g(x)=3x^-2-2), what will ((fg)(x)) be?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

Multiplying by the zero function gives ((fg)(x)=0). In multiplication, (0) makes the whole product zero.

Step 2

Why this answer is correct

The correct answer is B. (0). Multiplying by the zero function gives ((fg)(x)=0). In multiplication, (0) makes the whole product zero.

Step 3

Exam Tip

शून्य फलन से गुणा करने पर ((fg)(x)=0) होता है। गुणन में (0) पूरे गुणनफल को शून्य कर देता है।

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Question 20/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=1) और (g(x)=5x-6), तो ((f+g)(x)) क्या है?

If (f(x)=1) and (g(x)=5x-6), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (5x-5)

Step 1

Concept

((f+g)(x)=1+(5x-6)=5x-5). Add constant terms carefully.

Step 2

Why this answer is correct

The correct answer is A. (5x-5). ((f+g)(x)=1+(5x-6)=5x-5). Add constant terms carefully.

Step 3

Exam Tip

((f+g)(x)=1+(5x-6)=5x-5)। स्थिर पदों को ध्यान से जोड़ें।

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Question 21/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+9) और (g(x)=9-x), तो ((f+g)(x)) क्या होगा?

If (f(x)=x+9) and (g(x)=9-x), what will ((f+g)(x)) be?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

((f+g)(x)=(x+9)+(9-x)=18). The terms (x) and (-x) cancel out.

Step 2

Why this answer is correct

The correct answer is B. (18). ((f+g)(x)=(x+9)+(9-x)=18). The terms (x) and (-x) cancel out.

Step 3

Exam Tip

((f+g)(x)=(x+9)+(9-x)=18)। (x) और (-x) कट जाते हैं।

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Question 22/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+5x) और (g(x)=x^-2+2x), तो ((f-g)(x)) क्या है?

If (f(x)=x^-2+5x) and (g(x)=x^-2+2x), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

B. (3x)

Step 1

Concept

((f-g)(x)=x^-2+5x-\(x^2+2x\)=3x). The like \(x^2\) terms cancel out.

Step 2

Why this answer is correct

The correct answer is B. (3x). ((f-g)(x)=x^-2+5x-\(x^2+2x\)=3x). The like \(x^2\) terms cancel out.

Step 3

Exam Tip

((f-g)(x)=x^-2+5x-\(x^2+2x\)=3x)। समान \(x^2\) पद कट जाते हैं।

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Question 23/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+7) और (g(x)=3x-2), तो ((fg)(1)) का मान क्या है?

If (f(x)=x+7) and (g(x)=3x-2), what is the value of ((fg)(1))?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

((fg)(1)=f(1)g(1)=8\cdot1=8). First find both values.

Step 2

Why this answer is correct

The correct answer is A. (8). ((fg)(1)=f(1)g(1)=8\cdot1=8). First find both values.

Step 3

Exam Tip

((fg)(1)=f(1)g(1)=8\cdot1=8)। पहले दोनों मान निकालें।

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Question 24/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+10) और (g(x)=x^-2+4), तो ((f-g)(1)) क्या है?

If (f(x)=x^-2+10) and (g(x)=x^-2+4), what is ((f-g)(1))?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

((f-g)(1)=f(1)-g(1)=11-5=6). Here the \(x^2\) terms effectively cancel.

Step 2

Why this answer is correct

The correct answer is C. (6). ((f-g)(1)=f(1)-g(1)=11-5=6). Here the \(x^2\) terms effectively cancel.

Step 3

Exam Tip

((f-g)(1)=f(1)-g(1)=11-5=6)। यहाँ \(x^2\) पद प्रभावी रूप से कट जाते हैं।

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Question 25/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=6x+1) और (g(x)=2x+3), तो (\left\(\frac{f}{g}\right\)(0)) क्या होगा?

If (f(x)=6x+1) and (g(x)=2x+3), what will (\left\(\frac{f}{g}\right\)(0)) be?

Explanation opens after your attempt

Correct Answer

A. \(\frac{1}{3}\)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(0)=\frac{1}{3}). The denominator is (3), so the quotient is valid.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{3}\). (\left\(\frac{f}{g}\right\)(0)=\frac{1}{3}). The denominator is (3), so the quotient is valid.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(0)=\frac{1}{3})। हर (3) है, इसलिए भाग मान्य है।

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Question 26/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\sqrt{x+5}) और (g(x)=x), तो ((f+g)(4)) का मान क्या है?

If (f(x)=\sqrt{x+5}) and (g(x)=x), what is the value of ((f+g)(4))?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

((f+g)(4)=\sqrt{9}+4=3+4=7). For a radical term, first find the inside value.

Step 2

Why this answer is correct

The correct answer is C. (7). ((f+g)(4)=\sqrt{9}+4=3+4=7). For a radical term, first find the inside value.

Step 3

Exam Tip

((f+g)(4)=\sqrt{9}+4=3+4=7)। मूल वाले पद में पहले अंदर का मान निकालें।

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Question 27/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+1) और (g(x)=\sqrt{x}), तो ((fg)(4)) क्या होगा?

If (f(x)=x^-2+1) and (g(x)=\sqrt{x}), what will ((fg)(4)) be?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

((fg)(4)=f(4)g(4)=17\cdot2=34). Finding separate values is the safest method.

Step 2

Why this answer is correct

The correct answer is B. (34). ((fg)(4)=f(4)g(4)=17\cdot2=34). Finding separate values is the safest method.

Step 3

Exam Tip

((fg)(4)=f(4)g(4)=17\cdot2=34)। अलग-अलग मान निकालना सबसे सुरक्षित तरीका है।

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Question 28/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{2}{x}) और (g(x)=x^-2), तो ((fg)(3)) का मान क्या है?

If (f(x)=\frac{2}{x}) and (g(x)=x^-2), what is the value of ((fg)(3))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

((fg)(3)=\frac{2}{3}\cdot9=6). A reciprocal-type function keeps the condition \(x\neq0\).

Step 2

Why this answer is correct

The correct answer is A. (6). ((fg)(3)=\frac{2}{3}\cdot9=6). A reciprocal-type function keeps the condition \(x\neq0\).

Step 3

Exam Tip

((fg)(3)=\frac{2}{3}\cdot9=6)। भिन्न फलन में \(x\neq0\) शर्त रहती है।

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Question 29/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+12) और (g(x)=x+3), तो (\left\(\frac{f}{g}\right\)(3)) क्या है?

If (f(x)=x+12) and (g(x)=x+3), what is (\left\(\frac{f}{g}\right\)(3))?

Explanation opens after your attempt

Correct Answer

A. \(\frac{5}{2}\)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(3)=\frac{15}{6}=\frac{5}{2}). Write the final answer in simplest fraction form.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{5}{2}\). (\left\(\frac{f}{g}\right\)(3)=\frac{15}{6}=\frac{5}{2}). Write the final answer in simplest fraction form.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(3)=\frac{15}{6}=\frac{5}{2})। अंतिम उत्तर को सरल भिन्न में लिखें।

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Question 30/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+4) और (g(x)=x-4), तो ((fg)(x)) को सरल करने के लिए कौन-सी पहचान उपयोगी है?

If (f(x)=x+4) and (g(x)=x-4), which identity is useful to simplify ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(a^2-b^2\)

Step 1

Concept

((x+4)(x-4)) uses \(a^2-b^2\). It gives the answer \(x^2-16\).

Step 2

Why this answer is correct

The correct answer is A. \(a^2-b^2\). ((x+4)(x-4)) uses \(a^2-b^2\). It gives the answer \(x^2-16\).

Step 3

Exam Tip

((x+4)(x-4)) में \(a^2-b^2\) लगता है। इससे उत्तर \(x^2-16\) मिलता है।

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Question 31/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x^-2+3) और (g(x)=x+5), तो ((f+g)(1)) क्या है?

If (f(x)=2x^-2+3) and (g(x)=x+5), what is ((f+g)(1))?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

((f+g)(1)=f(1)+g(1)=5+6=11). First put (x=1), then add.

Step 2

Why this answer is correct

The correct answer is C. (11). ((f+g)(1)=f(1)+g(1)=5+6=11). First put (x=1), then add.

Step 3

Exam Tip

((f+g)(1)=f(1)+g(1)=5+6=11)। पहले (x=1) रखें, फिर जोड़ें।

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Question 32/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=5x^-2+2) और (g(x)=2x^-2-7), तो ((f-g)(x)) क्या होगा?

If (f(x)=5x^-2+2) and (g(x)=2x^-2-7), what will ((f-g)(x)) be?

Explanation opens after your attempt

Correct Answer

C. \(3x^2+9\)

Step 1

Concept

((f-g)(x)=5x^-2+2-\(2x^2-7\)=3x^-2+9). Applying the minus to (-7) gives (+7).

Step 2

Why this answer is correct

The correct answer is C. \(3x^2+9\). ((f-g)(x)=5x^-2+2-\(2x^2-7\)=3x^-2+9). Applying the minus to (-7) gives (+7).

Step 3

Exam Tip

((f-g)(x)=5x^-2+2-\(2x^2-7\)=3x^-2+9)। ऋण को (-7) पर लगाने से (+7) आता है।

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Question 33/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-6) और (g(x)=x), तो ((fg)(x)) क्या है?

If (f(x)=x-6) and (g(x)=x), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-6x\)

Step 1

Concept

((fg)(x)=(x-6)x=x^-2-6x). Multiply (x) with both terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-6x\). ((fg)(x)=(x-6)x=x^-2-6x). Multiply (x) with both terms.

Step 3

Exam Tip

((fg)(x)=(x-6)x=x^-2-6x)। (x) को दोनों पदों से गुणा करें।

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Question 34/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=4x+11) और (g(x)=x-6), तो ((f+g)(x)) क्या है?

If (f(x)=4x+11) and (g(x)=x-6), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (5x+5)

Step 1

Concept

((f+g)(x)=4x+11+x-6=5x+5). Add (x)-terms and constant terms separately.

Step 2

Why this answer is correct

The correct answer is A. (5x+5). ((f+g)(x)=4x+11+x-6=5x+5). Add (x)-terms and constant terms separately.

Step 3

Exam Tip

((f+g)(x)=4x+11+x-6=5x+5)। (x) पद और स्थिर पद अलग-अलग जोड़ें।

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Question 35/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=8) और (g(x)=x^-2-3x), तो ((f-g)(x)) क्या है?

If (f(x)=8) and (g(x)=x^-2-3x), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

B. \(8-x^2+3x\)

Step 1

Concept

((f-g)(x)=8-\(x^2-3x\)=8-x^-2+3x). In subtraction, signs of the whole (g(x)) change.

Step 2

Why this answer is correct

The correct answer is B. \(8-x^2+3x\). ((f-g)(x)=8-\(x^2-3x\)=8-x^-2+3x). In subtraction, signs of the whole (g(x)) change.

Step 3

Exam Tip

((f-g)(x)=8-\(x^2-3x\)=8-x^-2+3x)। घटाने में पूरे (g(x)) के चिह्न बदलते हैं।

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Question 36/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-25) और (g(x)=x+5), तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\neq-5\)?

If (f(x)=x^-2-25) and (g(x)=x+5), what is the simplified form of (\left\(\frac{f}{g}\right\)(x)), where \(x\neq-5\)?

Explanation opens after your attempt

Correct Answer

A. (x-5)

Step 1

Concept

(\frac{x^-2-25}{x+5}=\frac{(x-5)(x+5)}{x+5}=x-5). Keep the condition \(x\neq-5\).

Step 2

Why this answer is correct

The correct answer is A. (x-5). (\frac{x^-2-25}{x+5}=\frac{(x-5)(x+5)}{x+5}=x-5). Keep the condition \(x\neq-5\).

Step 3

Exam Tip

(\frac{x^-2-25}{x+5}=\frac{(x-5)(x+5)}{x+5}=x-5)। शर्त \(x\neq-5\) साथ रखें।

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Question 37/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-4x+4) और (g(x)=x-2), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq2\)?

If (f(x)=x^-2-4x+4) and (g(x)=x-2), what is (\left\(\frac{f}{g}\right\)(x)), where \(x\neq2\)?

Explanation opens after your attempt

Correct Answer

B. (x-2)

Step 1

Concept

Since (x^-2-4x+4=(x-2)²), the quotient is (x-2). Remove (x=2) from the domain.

Step 2

Why this answer is correct

The correct answer is B. (x-2). Since (x^-2-4x+4=(x-2)²), the quotient is (x-2). Remove (x=2) from the domain.

Step 3

Exam Tip

क्योंकि (x^-2-4x+4=(x-2)²), इसलिए भागफल (x-2) है। (x=2) को डोमेन से हटाएँ।

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Question 38/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-1) और (g(x)=x+10), तो ((f+g)(1)) क्या होगा?

If (f(x)=x-1) and (g(x)=x+10), what will ((f+g)(1)) be?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

((f+g)(1)=f(1)+g(1)=0+11=11). Include the zero value in the sum.

Step 2

Why this answer is correct

The correct answer is B. (11). ((f+g)(1)=f(1)+g(1)=0+11=11). Include the zero value in the sum.

Step 3

Exam Tip

((f+g)(1)=f(1)+g(1)=0+11=11)। शून्य मान को जोड़ में शामिल करें।

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Question 39/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=5x) और (g(x)=x+1), तो ((fg)(3)) का मान क्या है?

If (f(x)=5x) and (g(x)=x+1), what is the value of ((fg)(3))?

Explanation opens after your attempt

Correct Answer

B. (60)

Step 1

Concept

((fg)(3)=f(3)g(3)=15\cdot4=60). (fg) means product of functions.

Step 2

Why this answer is correct

The correct answer is B. (60). ((fg)(3)=f(3)g(3)=15\cdot4=60). (fg) means product of functions.

Step 3

Exam Tip

((fg)(3)=f(3)g(3)=15\cdot4=60)। (fg) का अर्थ फलनों का गुणन है।

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Question 40/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-4) और (g(x)=x^-2+4), तो ((f+g)(x)) क्या है?

If (f(x)=x^-2-4) and (g(x)=x^-2+4), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(2x^2\)

Step 1

Concept

((f+g)(x)=x^-2-4+x^-2+4=2x^-2). Opposite constant terms cancel out.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2\). ((f+g)(x)=x^-2-4+x^-2+4=2x^-2). Opposite constant terms cancel out.

Step 3

Exam Tip

((f+g)(x)=x^-2-4+x^-2+4=2x^-2)। विपरीत स्थिर पद कट जाते हैं।

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Question 41/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=4x^-2-3) और (g(x)=x^-2+8), तो ((f-g)(x)) क्या होगा?

If (f(x)=4x^-2-3) and (g(x)=x^-2+8), what will ((f-g)(x)) be?

Explanation opens after your attempt

Correct Answer

B. \(3x^2-11\)

Step 1

Concept

((f-g)(x)=4x^-2-3-\(x^2+8\)=3x^-2-11). Pay attention to constant terms after brackets.

Step 2

Why this answer is correct

The correct answer is B. \(3x^2-11\). ((f-g)(x)=4x^-2-3-\(x^2+8\)=3x^-2-11). Pay attention to constant terms after brackets.

Step 3

Exam Tip

((f-g)(x)=4x^-2-3-\(x^2+8\)=3x^-2-11)। कोष्ठक के बाद स्थिर पदों पर ध्यान दें।

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Question 42/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-5) और (g(x)=3), तो ((fg)(x)) क्या है?

If (f(x)=x-5) and (g(x)=3), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. (3x-15)

Step 1

Concept

((fg)(x)=(x-5)\cdot3=3x-15). Multiplication by a constant function multiplies all terms.

Step 2

Why this answer is correct

The correct answer is A. (3x-15). ((fg)(x)=(x-5)\cdot3=3x-15). Multiplication by a constant function multiplies all terms.

Step 3

Exam Tip

((fg)(x)=(x-5)\cdot3=3x-15)। स्थिर फलन से गुणा में सभी पद गुणित होते हैं।

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Question 43/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=12x-6) और (g(x)=6), तो (\left\(\frac{f}{g}\right\)(x)) क्या है?

If (f(x)=12x-6) and (g(x)=6), what is (\left\(\frac{f}{g}\right\)(x))?

Explanation opens after your attempt

Correct Answer

A. (2x-1)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(x)=\frac{12x-6}{6}=2x-1). Divide every numerator term by (6).

Step 2

Why this answer is correct

The correct answer is A. (2x-1). (\left\(\frac{f}{g}\right\)(x)=\frac{12x-6}{6}=2x-1). Divide every numerator term by (6).

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(x)=\frac{12x-6}{6}=2x-1)। अंश के हर पद को (6) से भाग दें।

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Question 44/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x-11) और (g(x)=11-2x), तो ((f+g)(x)) क्या होगा?

If (f(x)=2x-11) and (g(x)=11-2x), what will ((f+g)(x)) be?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

((f+g)(x)=(2x-11)+(11-2x)=0). These two functions are additive inverses.

Step 2

Why this answer is correct

The correct answer is A. (0). ((f+g)(x)=(2x-11)+(11-2x)=0). These two functions are additive inverses.

Step 3

Exam Tip

((f+g)(x)=(2x-11)+(11-2x)=0)। ये दोनों फलन योगात्मक प्रतिलोम हैं।

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Question 45/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=3x+8) और (g(x)=3x-8), तो ((f-g)(x)) क्या है?

If (f(x)=3x+8) and (g(x)=3x-8), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

((f-g)(x)=3x+8-(3x-8)=16). The (3x) terms cancel out.

Step 2

Why this answer is correct

The correct answer is B. (16). ((f-g)(x)=3x+8-(3x-8)=16). The (3x) terms cancel out.

Step 3

Exam Tip

((f-g)(x)=3x+8-(3x-8)=16)। (3x) पद कट जाते हैं।

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Question 46/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-5) और (g(x)=x^-2), तो ((fg)(x)) क्या है?

If (f(x)=x^-5) and (g(x)=x^-2), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^7\)

Step 1

Concept

((fg)(x)=x^-5\cdot x^-2=x^-7). Add powers while multiplying the same base.

Step 2

Why this answer is correct

The correct answer is A. \(x^7\). ((fg)(x)=x^-5\cdot x^-2=x^-7). Add powers while multiplying the same base.

Step 3

Exam Tip

((fg)(x)=x^-5\cdot x^-2=x^-7)। समान आधार में गुणा करते समय घातों को जोड़ें।

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Question 47/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-6) और (g(x)=x^-3), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा, जहाँ \(x\neq0\)?

If (f(x)=x^-6) and (g(x)=x^-3), what will (\left\(\frac{f}{g}\right\)(x)) be, where \(x\neq0\)?

Explanation opens after your attempt

Correct Answer

B. \(x^3\)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(x)=\frac{x^-6}{x^-3}=x^-3), where \(x\neq0\). In division, subtract powers of the same base.

Step 2

Why this answer is correct

The correct answer is B. \(x^3\). (\left\(\frac{f}{g}\right\)(x)=\frac{x^-6}{x^-3}=x^-3), where \(x\neq0\). In division, subtract powers of the same base.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(x)=\frac{x^-6}{x^-3}=x^-3), जहाँ \(x\neq0\)। भाग में समान आधार की घातें घटाएँ।

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Question 48/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x+1) और (g(x)=x^-2+3), दोनों का डोमेन \(\mathbb{R}\) है, तो ((fg)(x)) का डोमेन क्या है?

If (f(x)=2x+1) and (g(x)=x^-2+3), both have domain \(\mathbb{R}\), what is the domain of ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(\mathbb{R}\)

Step 1

Concept

Both polynomials are defined on all \(\mathbb{R}\), so the product domain is \(\mathbb{R}\). The domain is the set of common allowed values.

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}\). Both polynomials are defined on all \(\mathbb{R}\), so the product domain is \(\mathbb{R}\). The domain is the set of common allowed values.

Step 3

Exam Tip

दोनों बहुपद पूरे \(\mathbb{R}\) पर परिभाषित हैं, इसलिए गुणनफल का डोमेन \(\mathbb{R}\) है। डोमेन सामान्य मानों का समुच्चय होता है।

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Question 49/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\sqrt{x}) और (g(x)=x+2), तो ((f+g)(x)) का डोमेन क्या है?

If (f(x)=\sqrt{x}) and (g(x)=x+2), what is the domain of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \([0,\infty\))

Step 1

Concept

For \(\sqrt{x}\), we need \(x\geq0\), so the domain of the sum is \([0,\infty\)). Take the common domain.

Step 2

Why this answer is correct

The correct answer is A. \([0,\infty\)). For \(\sqrt{x}\), we need \(x\geq0\), so the domain of the sum is \([0,\infty\)). Take the common domain.

Step 3

Exam Tip

\(\sqrt{x}\) के लिए \(x\geq0\) चाहिए, इसलिए योग का डोमेन \([0,\infty\)) है। साझा डोमेन लें।

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Question 50/50 Easy Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+4) और (g(x)=x^-2-9), तो (\left\(\frac{f}{g}\right\)(x)) का डोमेन क्या है?

If (f(x)=x+4) and (g(x)=x^-2-9), what is the domain of (\left\(\frac{f}{g}\right\)(x))?

Explanation opens after your attempt

Correct Answer

A. \(\mathbb{R}-{-3,3}\)

Step 1

Concept

In division, (g(x)\neq0) is needed, and \(x^2-9=0\) gives \(x=\pm3\). So the domain is \(\mathbb{R}-{-3,3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}-{-3,3}\). In division, (g(x)\neq0) is needed, and \(x^2-9=0\) gives \(x=\pm3\). So the domain is \(\mathbb{R}-{-3,3}\).

Step 3

Exam Tip

भाग में (g(x)\neq0) चाहिए, और \(x^2-9=0\) से \(x=\pm3\) मिलता है। इसलिए डोमेन \(\mathbb{R}-{-3,3}\) है।

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Class 11 Mathematics - Permutations And Combinations - Combinations Easy Quiz

यदि (f(x)=2x+3) और (g(x)=x-5), तो ((f+g)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=7x-4) और (g(x)=2x+9), तो ((f-g)(x)) ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x+6) और (g(x)=x-2), तो ((fg)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=4x-2+8x) और (g(x)=4x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2+2) और (g(x)=3x-1), तो ((f+g)(2)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=5x+2) और (g(x)=x-2), तो ((f-g)(3)) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x-1) और (g(x)=x+4), तो ((fg)(2)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-16) और (g(x)=x-4), तो (\left\(\frac{f}{g}\right\)(5)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=3x-2) और (g(x)=2x-2+1), तो ((f+g)(x)) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=9x-2) और (g(x)=4x-7), तो ((f-g)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-3) और (g(x)=2x), तो ((fg)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=10x-3) और (g(x)=5x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-8), तो ((3f)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=4x+6), तो (\left\(\frac{1}{2}f\right\)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x-2-5), तो ((-f)(x)) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2+4x), तो ((f+f)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-3), तो ((ff)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x+10) और (g(x)=2x+10), तो ((f-g)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=0) और (g(x)=3x-2-2), तो ((fg)(x)) क्या होगा?

Concept

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Exam Tip

यदि (f(x)=1) और (g(x)=5x-6), तो ((f+g)(x)) क्या है?

Concept

Why this answer is correct

यदि (f(x)=4x^-2+8x) और (g(x)=4x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

यदि (f(x)=x^-2+2) और (g(x)=3x-1), तो ((f+g)(2)) का मान क्या है?

यदि (f(x)=5x+2) और (g(x)=x^-2), तो ((f-g)(3)) का मान क्या होगा?

यदि (f(x)=x^-2-16) और (g(x)=x-4), तो (\left\(\frac{f}{g}\right\)(5)) का मान क्या है?

यदि (f(x)=3x^-2) और (g(x)=2x^-2+1), तो ((f+g)(x)) किसके बराबर है?

यदि (f(x)=x^-3) और (g(x)=2x), तो ((fg)(x)) क्या होगा?

यदि (f(x)=10x^-3) और (g(x)=5x), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq0\)?

यदि (f(x)=2x^-2-5), तो ((-f)(x)) किसके बराबर है?

यदि (f(x)=x^-2+4x), तो ((f+f)(x)) क्या होगा?

यदि (f(x)=0) और (g(x)=3x^-2-2), तो ((fg)(x)) क्या होगा?

यदि (f(x)=x^-2+5x) और (g(x)=x^-2+2x), तो ((f-g)(x)) क्या है?

यदि (f(x)=x^-2+10) और (g(x)=x^-2+4), तो ((f-g)(1)) क्या है?

यदि (f(x)=x^-2+1) और (g(x)=\sqrt{x}), तो ((fg)(4)) क्या होगा?

यदि (f(x)=\frac{2}{x}) और (g(x)=x^-2), तो ((fg)(3)) का मान क्या है?

यदि (f(x)=2x^-2+3) और (g(x)=x+5), तो ((f+g)(1)) क्या है?

यदि (f(x)=5x^-2+2) और (g(x)=2x^-2-7), तो ((f-g)(x)) क्या होगा?

यदि (f(x)=8) और (g(x)=x^-2-3x), तो ((f-g)(x)) क्या है?

यदि (f(x)=x^-2-25) और (g(x)=x+5), तो (\left\(\frac{f}{g}\right\)(x)) का सरल रूप क्या है, जहाँ \(x\neq-5\)?

यदि (f(x)=x^-2-4x+4) और (g(x)=x-2), तो (\left\(\frac{f}{g}\right\)(x)) क्या है, जहाँ \(x\neq2\)?