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Mathematics Quiz - Class 11 Mathematics Relations And Fun...

Question 1/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|x-5|-2) के आलेख का शीर्ष कौन सा है?

What is the vertex of the graph of (f(x)=|x-5|-2)?

Explanation opens after your attempt

Correct Answer

A. ((5,-2))

Step 1

Concept

(|x-5|) becomes zero at (x=5), and (-2) is added outside. So the vertex is ((5,-2)).

Step 2

Why this answer is correct

The correct answer is A. ((5,-2)). (|x-5|) becomes zero at (x=5), and (-2) is added outside. So the vertex is ((5,-2)).

Step 3

Exam Tip

(|x-5|) शून्य (x=5) पर होता है और बाहर (-2) जुड़ता है। इसलिए शीर्ष ((5,-2)) है।

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Question 2/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|2x+4|+1) का न्यूनतम मान क्या है?

What is the minimum value of (f(x)=|2x+4|+1)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The minimum value of a modulus is (0). Therefore the minimum value of (|2x+4|+1) is (1).

Step 2

Why this answer is correct

The correct answer is A. (1). The minimum value of a modulus is (0). Therefore the minimum value of (|2x+4|+1) is (1).

Step 3

Exam Tip

मापांक का न्यूनतम मान (0) होता है। इसलिए (|2x+4|+1) का न्यूनतम मान (1) है।

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Question 3/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|3x-9|) का शीर्ष किस (x) मान पर है?

At which (x)-value is the vertex of (f(x)=|3x-9|)?

Explanation opens after your attempt

Correct Answer

A. (x=3)

Step 1

Concept

The vertex occurs when (3x-9=0). This gives (x=3).

Step 2

Why this answer is correct

The correct answer is A. (x=3). The vertex occurs when (3x-9=0). This gives (x=3).

Step 3

Exam Tip

शीर्ष तब मिलता है जब (3x-9=0)। इससे (x=3) मिलता है।

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Question 4/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=2|x+2|-6) के (x)-अक्ष प्रतिच्छेद कौन से हैं?

What are the (x)-intercepts of (f(x)=2|x+2|-6)?

Explanation opens after your attempt

Correct Answer

A. (x=1) और (x=-5)(x=1) and (x=-5)

Step 1

Concept

From (2|x+2|-6=0), we get (|x+2|=3). So (x=1) and (x=-5).

Step 2

Why this answer is correct

The correct answer is A. (x=1) और (x=-5) / (x=1) and (x=-5). From (2|x+2|-6=0), we get (|x+2|=3). So (x=1) and (x=-5).

Step 3

Exam Tip

(2|x+2|-6=0) से (|x+2|=3) मिलता है। इसलिए (x=1) और (x=-5) हैं।

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Question 5/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=-|x-1|+4) का अधिकतम मान क्या है?

What is the maximum value of (f(x)=-|x-1|+4)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Since \(|x-1|\ge 0\), \(-|x-1|+4\le 4\). The maximum value (4) occurs at (x=1).

Step 2

Why this answer is correct

The correct answer is A. (4). Since \(|x-1|\ge 0\), \(-|x-1|+4\le 4\). The maximum value (4) occurs at (x=1).

Step 3

Exam Tip

क्योंकि \(|x-1|\ge 0\), इसलिए \(-|x-1|+4\le 4\)। अधिकतम मान (4) (x=1) पर मिलता है।

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Question 6/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|x-2|+|x-6|) का (x=4) पर मान क्या है?

What is the value of (f(x)=|x-2|+|x-6|) at (x=4)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(f(4)=|2|+|-2|=2+2=4). Evaluate both modulus parts separately.

Step 2

Why this answer is correct

The correct answer is A. (4). (f(4)=|2|+|-2|=2+2=4). Evaluate both modulus parts separately.

Step 3

Exam Tip

(f(4)=|2|+|-2|=2+2=4)। मापांक के दोनों भाग अलग से निकालें।

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Question 7/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|x+4|-|x-2|) का (x=-1) पर मान क्या है?

What is the value of (f(x)=|x+4|-|x-2|) at (x=-1)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(f(-1)=|3|-|-3|=3-3=0). Take the modulus values before subtracting.

Step 2

Why this answer is correct

The correct answer is A. (0). (f(-1)=|3|-|-3|=3-3=0). Take the modulus values before subtracting.

Step 3

Exam Tip

(f(-1)=|3|-|-3|=3-3=0)। चिन्ह बदलने से पहले मापांक का मान लें।

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Question 8/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=3(x-1)²-12) के (x)-अक्ष प्रतिच्छेद कौन से हैं?

What are the (x)-intercepts of (f(x)=3(x-1)²-12)?

Explanation opens after your attempt

Correct Answer

A. (x=-1) और (x=3)(x=-1) and (x=3)

Step 1

Concept

From (3(x-1)²-12=0), we get ((x-1)²=4). So (x=-1) and (x=3).

Step 2

Why this answer is correct

The correct answer is A. (x=-1) और (x=3) / (x=-1) and (x=3). From (3(x-1)²-12=0), we get ((x-1)²=4). So (x=-1) and (x=3).

Step 3

Exam Tip

(3(x-1)²-12=0) से ((x-1)²=4) मिलता है। इसलिए (x=-1) और (x=3) हैं।

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Question 9/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=x^-2+8x+15) के शून्यक कौन से हैं?

What are the zeros of (f(x)=x^-2+8x+15)?

Explanation opens after your attempt

Correct Answer

A. (x=-3) और (x=-5)(x=-3) and (x=-5)

Step 1

Concept

(x^-2+8x+15=(x+3)(x+5)). Therefore the zeros are (x=-3) and (x=-5).

Step 2

Why this answer is correct

The correct answer is A. (x=-3) और (x=-5) / (x=-3) and (x=-5). (x^-2+8x+15=(x+3)(x+5)). Therefore the zeros are (x=-3) and (x=-5).

Step 3

Exam Tip

(x^-2+8x+15=(x+3)(x+5))। इसलिए शून्यक (x=-3) और (x=-5) हैं।

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Question 10/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=x^-2-10x+21) का सममिति अक्ष कौन सा है?

What is the axis of symmetry of (f(x)=x^-2-10x+21)?

Explanation opens after your attempt

Correct Answer

A. (x=5)

Step 1

Concept

The axis of symmetry is \(x=-\frac{b}{2a}\). Here (a=1) and (b=-10), so (x=5).

Step 2

Why this answer is correct

The correct answer is A. (x=5). The axis of symmetry is \(x=-\frac{b}{2a}\). Here (a=1) and (b=-10), so (x=5).

Step 3

Exam Tip

सममिति अक्ष \(x=-\frac{b}{2a}\) होता है। यहां (a=1) और (b=-10), इसलिए (x=5)।

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Question 11/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=2x^-2-8x+1) के आलेख का सममिति अक्ष क्या है?

What is the axis of symmetry of the graph of (f(x)=2x^-2-8x+1)?

Explanation opens after your attempt

Correct Answer

A. (x=2)

Step 1

Concept

Put (a=2) and (b=-8) in \(x=-\frac{b}{2a}\). This gives (x=2).

Step 2

Why this answer is correct

The correct answer is A. (x=2). Put (a=2) and (b=-8) in \(x=-\frac{b}{2a}\). This gives (x=2).

Step 3

Exam Tip

\(x=-\frac{b}{2a}\) में (a=2) और (b=-8) रखें। इससे (x=2) मिलता है।

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Question 12/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=x^-2+2x+5) का न्यूनतम मान क्या है?

What is the minimum value of (f(x)=x^-2+2x+5)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(x^-2+2x+5=(x+1)²+4). Therefore the minimum value is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). (x^-2+2x+5=(x+1)²+4). Therefore the minimum value is (4).

Step 3

Exam Tip

(x^-2+2x+5=(x+1)²+4)। इसलिए न्यूनतम मान (4) है।

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Question 13/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=-x^-2+6x-5) का अधिकतम मान क्या है?

What is the maximum value of (f(x)=-x^-2+6x-5)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(-x^-2+6x-5=-(x-3)²+4). Therefore the maximum value is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). (-x^-2+6x-5=-(x-3)²+4). Therefore the maximum value is (4).

Step 3

Exam Tip

(-x^-2+6x-5=-(x-3)²+4)। इसलिए अधिकतम मान (4) है।

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Question 14/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\sqrt{x+6}-2) का प्रारंभिक बिंदु कौन सा है?

What is the starting point of (f(x)=\sqrt{x+6}-2)?

Explanation opens after your attempt

Correct Answer

A. ((-6,-2))

Step 1

Concept

\(\sqrt{x+6}\) starts at (x=-6), and (-2) is added outside. So the starting point is ((-6,-2)).

Step 2

Why this answer is correct

The correct answer is A. ((-6,-2)). \(\sqrt{x+6}\) starts at (x=-6), and (-2) is added outside. So the starting point is ((-6,-2)).

Step 3

Exam Tip

\(\sqrt{x+6}\) (x=-6) से शुरू होता है और बाहर (-2) जुड़ता है। इसलिए प्रारंभिक बिंदु ((-6,-2)) है।

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Question 15/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=3-\sqrt{x-1}) का अधिकतम मान क्या है?

What is the maximum value of (f(x)=3-\sqrt{x-1})?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

Since \(\sqrt{x-1}\ge 0\), \(3-\sqrt{x-1}\le 3\). The maximum value (3) occurs at (x=1).

Step 2

Why this answer is correct

The correct answer is A. (3). Since \(\sqrt{x-1}\ge 0\), \(3-\sqrt{x-1}\le 3\). The maximum value (3) occurs at (x=1).

Step 3

Exam Tip

\(\sqrt{x-1}\ge 0\), इसलिए \(3-\sqrt{x-1}\le 3\)। अधिकतम मान (3) (x=1) पर मिलता है।

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Question 16/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=2\sqrt{x+1}-5) का परिसर क्या है?

What is the range of (f(x)=2\sqrt{x+1}-5)?

Explanation opens after your attempt

Correct Answer

A. \([-5,\infty\))

Step 1

Concept

Since \(\sqrt{x+1}\ge 0\), \(2\sqrt{x+1}-5\ge -5\). Hence the range is \([-5,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. \([-5,\infty\)). Since \(\sqrt{x+1}\ge 0\), \(2\sqrt{x+1}-5\ge -5\). Hence the range is \([-5,\infty\)).

Step 3

Exam Tip

\(\sqrt{x+1}\ge 0\), इसलिए \(2\sqrt{x+1}-5\ge -5\)। अतः परिसर \([-5,\infty\)) है।

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Question 17/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{1}{x-5}+2) का ऊर्ध्व आसिम्प्टोट कौन सा है?

What is the vertical asymptote of (f(x)=\frac{1}{x-5}+2)?

Explanation opens after your attempt

Correct Answer

A. (x=5)

Step 1

Concept

The denominator (x-5) cannot be zero. Therefore the vertical asymptote is (x=5).

Step 2

Why this answer is correct

The correct answer is A. (x=5). The denominator (x-5) cannot be zero. Therefore the vertical asymptote is (x=5).

Step 3

Exam Tip

हर (x-5) शून्य नहीं हो सकता। इसलिए ऊर्ध्व आसिम्प्टोट (x=5) है।

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Question 18/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{3}{x+2}-1) का क्षैतिज आसिम्प्टोट कौन सा है?

What is the horizontal asymptote of (f(x)=\frac{3}{x+2}-1)?

Explanation opens after your attempt

Correct Answer

A. (y=-1)

Step 1

Concept

For large (|x|), \(\frac{3}{x+2}\) approaches (0). So the horizontal asymptote is (y=-1).

Step 2

Why this answer is correct

The correct answer is A. (y=-1). For large (|x|), \(\frac{3}{x+2}\) approaches (0). So the horizontal asymptote is (y=-1).

Step 3

Exam Tip

बड़े (|x|) पर \(\frac{3}{x+2}\) (0) के पास जाता है। इसलिए क्षैतिज आसिम्प्टोट (y=-1) है।

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Question 19/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{1}{x+4}+6) का परिसर कौन सा है?

What is the range of (f(x)=\frac{1}{x+4}+6)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,6\)\cup\(6,\infty\))

Step 1

Concept

\(\frac{1}{x+4}\) is never (0). Therefore (f(x)) is never (6).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,6\)\cup\(6,\infty\)). \(\frac{1}{x+4}\) is never (0). Therefore (f(x)) is never (6).

Step 3

Exam Tip

\(\frac{1}{x+4}\) कभी (0) नहीं होता। इसलिए (f(x)) कभी (6) नहीं होता।

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Question 20/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{-2}{x-3}) का आलेख किन चतुर्थांशों में स्थानांतरित आसिम्प्टोट के सापेक्ष होता है?

Relative to its shifted asymptotes, in which branches does (f(x)=\frac{-2}{x-3}) lie?

Explanation opens after your attempt

Correct Answer

A. द्वितीय और चतुर्थ जैसेLike second and fourth

Step 1

Concept

The coefficient in \(\frac{-2}{x-3}\) is negative. So its branches are like \(-\frac{1}{x}\) in opposite quadrants.

Step 2

Why this answer is correct

The correct answer is A. द्वितीय और चतुर्थ जैसे / Like second and fourth. The coefficient in \(\frac{-2}{x-3}\) is negative. So its branches are like \(-\frac{1}{x}\) in opposite quadrants.

Step 3

Exam Tip

\(\frac{-2}{x-3}\) में गुणांक ऋणात्मक है। इसलिए इसकी शाखाएं मूल \(-\frac{1}{x}\) जैसी विपरीत चतुर्थांशों में होती हैं।

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Question 21/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{1}{(x+2)²}) का ऊर्ध्व आसिम्प्टोट कौन सा है?

What is the vertical asymptote of (f(x)=\frac{1}{(x+2)²})?

Explanation opens after your attempt

Correct Answer

A. (x=-2)

Step 1

Concept

The function is not defined when ((x+2)²) is zero. So (x=-2) is the vertical asymptote.

Step 2

Why this answer is correct

The correct answer is A. (x=-2). The function is not defined when ((x+2)²) is zero. So (x=-2) is the vertical asymptote.

Step 3

Exam Tip

हर ((x+2)²) शून्य होने पर फलन परिभाषित नहीं रहता। इसलिए (x=-2) ऊर्ध्व आसिम्प्टोट है।

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Question 22/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{2}{(x-1)²}-3) का परिसर क्या है?

What is the range of (f(x)=\frac{2}{(x-1)²}-3)?

Explanation opens after your attempt

Correct Answer

A. (\(-3,\infty\))

Step 1

Concept

(\frac{2}{(x-1)²}) is always positive but never (0). Therefore the function remains greater than (-3).

Step 2

Why this answer is correct

The correct answer is A. (\(-3,\infty\)). (\frac{2}{(x-1)²}) is always positive but never (0). Therefore the function remains greater than (-3).

Step 3

Exam Tip

(\frac{2}{(x-1)²}) हमेशा धनात्मक है लेकिन (0) नहीं होता। इसलिए फलन (-3) से बड़ा रहता है।

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Question 23/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=-\frac{3}{(x+1)²}+2) का परिसर क्या है?

What is the range of (f(x)=-\frac{3}{(x+1)²}+2)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,2\))

Step 1

Concept

(-\frac{3}{(x+1)²}) is always negative and never becomes (0). So (f(x)) is always less than (2).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,2\)). (-\frac{3}{(x+1)²}) is always negative and never becomes (0). So (f(x)) is always less than (2).

Step 3

Exam Tip

(-\frac{3}{(x+1)²}) हमेशा ऋणात्मक होता है और (0) नहीं बनता। इसलिए (f(x)) हमेशा (2) से कम है।

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Question 24/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\operatorname{sgn}(3x-12)) में (x>4) होने पर मान क्या होगा?

For (f(x)=\operatorname{sgn}(3x-12)), what is the value when (x>4)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

If (x>4), then (3x-12>0). Therefore the signum value is (1).

Step 2

Why this answer is correct

The correct answer is A. (1). If (x>4), then (3x-12>0). Therefore the signum value is (1).

Step 3

Exam Tip

यदि (x>4), तो (3x-12>0)। इसलिए साइनम मान (1) है।

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Question 25/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\operatorname{sgn}(2-x)) में (x>2) होने पर मान क्या होगा?

For (f(x)=\operatorname{sgn}(2-x)), what is the value when (x>2)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

If (x>2), then (2-x<0). Hence (\operatorname{sgn}(2-x)=-1).

Step 2

Why this answer is correct

The correct answer is A. (-1). If (x>2), then (2-x<0). Hence (\operatorname{sgn}(2-x)=-1).

Step 3

Exam Tip

यदि (x>2), तो (2-x<0)। इसलिए (\operatorname{sgn}(2-x)=-1) है।

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Question 26/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\operatorname{sgn}(x+7)) किस (x) पर शून्य होता है?

At which (x)-value does (f(x)=\operatorname{sgn}(x+7)) become zero?

Explanation opens after your attempt

Correct Answer

A. (x=-7)

Step 1

Concept

The signum function is zero when the inside expression is zero. From (x+7=0), we get (x=-7).

Step 2

Why this answer is correct

The correct answer is A. (x=-7). The signum function is zero when the inside expression is zero. From (x+7=0), we get (x=-7).

Step 3

Exam Tip

साइनम फलन शून्य तब होता है जब अंदर की राशि शून्य हो। (x+7=0) से (x=-7) मिलता है।

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Question 27/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\lfloor x-3\rfloor) में (x=5.9) पर मान क्या है?

What is the value of (f(x)=\lfloor x-3\rfloor) at (x=5.9)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

Here (x-3=2.9), and \(\lfloor 2.9\rfloor=2\). First find the inside value.

Step 2

Why this answer is correct

The correct answer is A. (2). Here (x-3=2.9), and \(\lfloor 2.9\rfloor=2\). First find the inside value.

Step 3

Exam Tip

(x-3=2.9) और \(\lfloor 2.9\rfloor=2\)। पहले अंदर का मान निकालें।

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Question 28/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\lfloor 3x\rfloor) में (x=-0.4) पर मान क्या है?

What is the value of (f(x)=\lfloor 3x\rfloor) at (x=-0.4)?

Explanation opens after your attempt

Correct Answer

A. (-2)

Step 1

Concept

Here (3x=-1.2), and \(\lfloor -1.2\rfloor=-2\). For negative decimals, take the lower integer.

Step 2

Why this answer is correct

The correct answer is A. (-2). Here (3x=-1.2), and \(\lfloor -1.2\rfloor=-2\). For negative decimals, take the lower integer.

Step 3

Exam Tip

(3x=-1.2) और \(\lfloor -1.2\rfloor=-2\)। ऋणात्मक दशमलव में नीचे की ओर पूर्णांक लें।

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Question 29/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\left\lfloor\frac{x+2}{3}\right\rfloor) में (x=7.4) पर मान क्या है?

What is the value of (f(x)=\left\lfloor\frac{x+2}{3}\right\rfloor) at (x=7.4)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

\(\frac{7.4+2}{3}=\frac{9.4}{3}\), which is greater than (3) and less than (4). So the greatest integer is (3).

Step 2

Why this answer is correct

The correct answer is A. (3). \(\frac{7.4+2}{3}=\frac{9.4}{3}\), which is greater than (3) and less than (4). So the greatest integer is (3).

Step 3

Exam Tip

\(\frac{7.4+2}{3}=\frac{9.4}{3}\), जो (3) से बड़ा और (4) से छोटा है। इसलिए ग्रेटेस्ट इंटीजर (3) है।

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Question 30/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\lfloor x\rfloor) के आलेख में \(x\in[-3,-2\)) पर (y) का मान क्या है?

In the graph of (f(x)=\lfloor x\rfloor), what is the value of (y) for \(x\in[-3,-2\))?

Explanation opens after your attempt

Correct Answer

A. (y=-3)

Step 1

Concept

For every \(x\in[-3,-2\)), \(\lfloor x\rfloor=-3\). So on that step, (y=-3).

Step 2

Why this answer is correct

The correct answer is A. (y=-3). For every \(x\in[-3,-2\)), \(\lfloor x\rfloor=-3\). So on that step, (y=-3).

Step 3

Exam Tip

हर \(x\in[-3,-2\)) के लिए \(\lfloor x\rfloor=-3\)। इसलिए उस चरण पर (y=-3) है।

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Question 31/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

भिन्नात्मक भाग फलन (f(x)={x}) में (x=-2.3) पर मान क्या है?

For the fractional part function (f(x)={x}), what is the value at (x=-2.3)?

Explanation opens after your attempt

Correct Answer

A. (0.7)

Step 1

Concept

\({x}=x-\lfloor x\rfloor\), and \(\lfloor -2.3\rfloor=-3\). Therefore ({-2.3}=0.7).

Step 2

Why this answer is correct

The correct answer is A. (0.7). \({x}=x-\lfloor x\rfloor\), and \(\lfloor -2.3\rfloor=-3\). Therefore ({-2.3}=0.7).

Step 3

Exam Tip

\({x}=x-\lfloor x\rfloor\) और \(\lfloor -2.3\rfloor=-3\)। इसलिए ({-2.3}=0.7) है।

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Question 32/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)={2x}) में (x=1.35) पर मान क्या है?

What is the value of (f(x)={2x}) at (x=1.35)?

Explanation opens after your attempt

Correct Answer

A. (0.7)

Step 1

Concept

Here (2x=2.7), and ({2.7}=0.7). The fractional part is obtained by removing the integer part.

Step 2

Why this answer is correct

The correct answer is A. (0.7). Here (2x=2.7), and ({2.7}=0.7). The fractional part is obtained by removing the integer part.

Step 3

Exam Tip

(2x=2.7) और ({2.7}=0.7)। भिन्नात्मक भाग पूर्णांक भाग हटाकर मिलता है।

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Question 33/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

रेखा (3x+2y=12) का (y)-अक्ष प्रतिच्छेद क्या है?

What is the (y)-intercept of the line (3x+2y=12)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

On the (y)-axis, (x=0), so (2y=12) and (y=6). For intercepts, set the other coordinate to zero.

Step 2

Why this answer is correct

The correct answer is A. (6). On the (y)-axis, (x=0), so (2y=12) and (y=6). For intercepts, set the other coordinate to zero.

Step 3

Exam Tip

(y)-अक्ष पर (x=0), इसलिए (2y=12) और (y=6)। प्रतिच्छेद के लिए दूसरे निर्देशांक को शून्य रखें।

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Question 34/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

रेखा (5x-y=10) की ढाल क्या है?

What is the slope of the line (5x-y=10)?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

Write (5x-y=10) as (y=5x-10). So the slope is (5).

Step 2

Why this answer is correct

The correct answer is A. (5). Write (5x-y=10) as (y=5x-10). So the slope is (5).

Step 3

Exam Tip

(5x-y=10) को (y=5x-10) लिखें। इसलिए ढाल (5) है।

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Question 35/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

रेखा (2x-3y=9) का (x)-अक्ष प्रतिच्छेद क्या है?

What is the (x)-intercept of the line (2x-3y=9)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{9}{2}\)

Step 1

Concept

On the (x)-axis, (y=0), so (2x=9). This gives \(x=\frac{9}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{9}{2}\). On the (x)-axis, (y=0), so (2x=9). This gives \(x=\frac{9}{2}\).

Step 3

Exam Tip

(x)-अक्ष पर (y=0), इसलिए (2x=9)। इससे \(x=\frac{9}{2}\) मिलता है।

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Question 36/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

रेखा \(y=-\frac{3}{4}x+2\) के समांतर रेखा की ढाल क्या होगी?

What is the slope of a line parallel to \(y=-\frac{3}{4}x+2\)?

Explanation opens after your attempt

Correct Answer

A. \(-\frac{3}{4}\)

Step 1

Concept

Parallel lines have equal slopes. Therefore the slope remains \(-\frac{3}{4}\).

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{3}{4}\). Parallel lines have equal slopes. Therefore the slope remains \(-\frac{3}{4}\).

Step 3

Exam Tip

समांतर रेखाओं की ढाल समान होती है। इसलिए ढाल \(-\frac{3}{4}\) ही रहेगी।

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Question 37/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=x^-3+3) का (y)-अक्ष प्रतिच्छेद क्या है?

What is the (y)-intercept of (f(x)=x^-3+3)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

For the (y)-intercept, put (x=0). Then (f(0)=3).

Step 2

Why this answer is correct

The correct answer is A. (3). For the (y)-intercept, put (x=0). Then (f(0)=3).

Step 3

Exam Tip

(y)-अक्ष प्रतिच्छेद के लिए (x=0) रखें। तब (f(0)=3) मिलता है।

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Question 38/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=(x-2)³+4) का केंद्रीय बिंदु कौन सा है?

What is the central point of (f(x)=(x-2)³+4)?

Explanation opens after your attempt

Correct Answer

A. ((2,4))

Step 1

Concept

The central point of \(y=x^3\) is ((0,0)). This graph shifts (2) right and (4) up.

Step 2

Why this answer is correct

The correct answer is A. ((2,4)). The central point of \(y=x^3\) is ((0,0)). This graph shifts (2) right and (4) up.

Step 3

Exam Tip

\(y=x^3\) का केंद्रीय बिंदु ((0,0)) है। यह आलेख (2) दाईं और (4) ऊपर खिसकता है।

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Question 39/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=x^-3+27) का (x)-अक्ष प्रतिच्छेद क्या है?

What is the (x)-intercept of (f(x)=x^-3+27)?

Explanation opens after your attempt

Correct Answer

A. (x=-3)

Step 1

Concept

On the (x)-axis, \(x^3+27=0\), so \(x^3=-27\). This gives (x=-3).

Step 2

Why this answer is correct

The correct answer is A. (x=-3). On the (x)-axis, \(x^3+27=0\), so \(x^3=-27\). This gives (x=-3).

Step 3

Exam Tip

(x)-अक्ष पर \(x^3+27=0\), इसलिए \(x^3=-27\)। इससे (x=-3) मिलता है।

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Question 40/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=2x^-3) का आलेख \(y=x^3\) की तुलना में कैसा है?

How is the graph of (f(x)=2x^-3) compared with \(y=x^3\)?

Explanation opens after your attempt

Correct Answer

A. ऊर्ध्व रूप से खिंचा हुआVertically stretched

Step 1

Concept

The coefficient (2) multiplies every (y)-value by (2). So the graph is vertically stretched.

Step 2

Why this answer is correct

The correct answer is A. ऊर्ध्व रूप से खिंचा हुआ / Vertically stretched. The coefficient (2) multiplies every (y)-value by (2). So the graph is vertically stretched.

Step 3

Exam Tip

गुणांक (2) हर (y)-मान को (2) गुना करता है। इसलिए आलेख ऊर्ध्व रूप से खिंचता है।

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Question 41/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

कौन सा समीकरण ऊर्ध्व रेखा परीक्षण में असफल होता है?

Which equation fails the vertical line test?

Explanation opens after your attempt

Correct Answer

A. \(y^2=x+1\)

Step 1

Concept

In \(y^2=x+1\), many (x)-values give two (y)-values. So it is not the graph of a function.

Step 2

Why this answer is correct

The correct answer is A. \(y^2=x+1\). In \(y^2=x+1\), many (x)-values give two (y)-values. So it is not the graph of a function.

Step 3

Exam Tip

\(y^2=x+1\) में कई (x)-मानों के लिए दो (y)-मान मिलते हैं। इसलिए यह फलन का आलेख नहीं है।

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Question 42/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

कौन सा फलन \(y=x^2\) को (3) इकाई दाईं ओर और (2) इकाई नीचे खिसकाता है?

Which function shifts \(y=x^2\) (3) units right and (2) units down?

Explanation opens after your attempt

Correct Answer

A. (y=(x-3)²-2)

Step 1

Concept

For (3) units right, use (x-3), and for (2) units down, use outside (-2). So the correct form is (y=(x-3)²-2).

Step 2

Why this answer is correct

The correct answer is A. (y=(x-3)²-2). For (3) units right, use (x-3), and for (2) units down, use outside (-2). So the correct form is (y=(x-3)²-2).

Step 3

Exam Tip

दाईं ओर (3) इकाई के लिए (x-3) और नीचे (2) इकाई के लिए बाहर (-2) होता है। इसलिए सही रूप (y=(x-3)²-2) है।

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Question 43/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

कौन सा फलन \(y=\sqrt{x}\) को (4) इकाई बाईं ओर और (5) इकाई ऊपर खिसकाता है?

Which function shifts \(y=\sqrt{x}\) (4) units left and (5) units up?

Explanation opens after your attempt

Correct Answer

A. \(y=\sqrt{x+4}+5\)

Step 1

Concept

For (4) units left, use inside (x+4), and for (5) units up, use outside (+5).

Step 2

Why this answer is correct

The correct answer is A. \(y=\sqrt{x+4}+5\). For (4) units left, use inside (x+4), and for (5) units up, use outside (+5).

Step 3

Exam Tip

बाईं ओर (4) इकाई के लिए अंदर (x+4) और ऊपर (5) इकाई के लिए बाहर (+5) होता है।

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Question 44/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{1}{x}) का \(y=\frac{1}{x+3}-4\) बनने पर कौन सा परिवर्तन हुआ?

What transformation changes (f(x)=\frac{1}{x}) into \(y=\frac{1}{x+3}-4\)?

Explanation opens after your attempt

Correct Answer

A. (3) इकाई बाईं ओर और (4) इकाई नीचे(3) units left and (4) units down

Step 1

Concept

The inside term (x+3) shifts the graph (3) units left, and outside (-4) shifts it (4) units down.

Step 2

Why this answer is correct

The correct answer is A. (3) इकाई बाईं ओर और (4) इकाई नीचे / (3) units left and (4) units down. The inside term (x+3) shifts the graph (3) units left, and outside (-4) shifts it (4) units down.

Step 3

Exam Tip

अंदर (x+3) होने से (3) इकाई बाईं ओर और बाहर (-4) होने से (4) इकाई नीचे खिसकाव होता है।

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Question 45/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=-(x-4)³+2) का केंद्रीय बिंदु कौन सा है?

What is the central point of (f(x)=-(x-4)³+2)?

Explanation opens after your attempt

Correct Answer

A. ((4,2))

Step 1

Concept

The central point of \(y=x^3\) is ((0,0)) and it shifts (4) right and (2) up. The negative sign changes direction but the central point remains ((4,2)).

Step 2

Why this answer is correct

The correct answer is A. ((4,2)). The central point of \(y=x^3\) is ((0,0)) and it shifts (4) right and (2) up. The negative sign changes direction but the central point remains ((4,2)).

Step 3

Exam Tip

\(y=x^3\) का केंद्रीय बिंदु ((0,0)) होता है और यह (4) दाईं ओर तथा (2) ऊपर खिसकता है। ऋण चिह्न दिशा बदलता है लेकिन केंद्रीय बिंदु ((4,2)) ही रहता है।

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Question 46/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\frac{4}{(x-3)²}+1) का क्षैतिज आसिम्प्टोट कौन सा है?

What is the horizontal asymptote of (f(x)=\frac{4}{(x-3)²}+1)?

Explanation opens after your attempt

Correct Answer

A. (y=1)

Step 1

Concept

For large (|x|), (\frac{4}{(x-3)²}) approaches (0). So the horizontal asymptote is (y=1).

Step 2

Why this answer is correct

The correct answer is A. (y=1). For large (|x|), (\frac{4}{(x-3)²}) approaches (0). So the horizontal asymptote is (y=1).

Step 3

Exam Tip

बड़े (|x|) पर (\frac{4}{(x-3)²}) (0) के पास जाता है। इसलिए क्षैतिज आसिम्प्टोट (y=1) है।

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Question 47/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\left\lfloor x+1\right\rfloor) के आलेख में \(x\in[2,3\)) पर (y) का मान क्या है?

In the graph of (f(x)=\left\lfloor x+1\right\rfloor), what is the value of (y) for \(x\in[2,3\))?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

If \(x\in[2,3\)), then \(x+1\in[3,4\)). Hence \(\left\lfloor x+1\right\rfloor=3\).

Step 2

Why this answer is correct

The correct answer is A. (3). If \(x\in[2,3\)), then \(x+1\in[3,4\)). Hence \(\left\lfloor x+1\right\rfloor=3\).

Step 3

Exam Tip

यदि \(x\in[2,3\)), तो \(x+1\in[3,4\))। इसलिए \(\left\lfloor x+1\right\rfloor=3\) है।

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Question 48/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)={x-2}) में (x=5.75) पर मान क्या है?

What is the value of (f(x)={x-2}) at (x=5.75)?

Explanation opens after your attempt

Correct Answer

A. (0.75)

Step 1

Concept

Here (x-2=3.75) and ({3.75}=0.75). Remove the integer part to get the fractional part.

Step 2

Why this answer is correct

The correct answer is A. (0.75). Here (x-2=3.75) and ({3.75}=0.75). Remove the integer part to get the fractional part.

Step 3

Exam Tip

(x-2=3.75) और ({3.75}=0.75)। भिन्नात्मक भाग पाने के लिए पूर्णांक भाग हटाएं।

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Question 49/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=|2x-8|+3) का शीर्ष कौन सा है?

What is the vertex of (f(x)=|2x-8|+3)?

Explanation opens after your attempt

Correct Answer

A. ((4,3))

Step 1

Concept

For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).

Step 2

Why this answer is correct

The correct answer is A. ((4,3)). For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).

Step 3

Exam Tip

शीर्ष के लिए (2x-8=0) रखें जिससे (x=4) मिलता है। बाहर (+3) होने से शीर्ष ((4,3)) है।

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Question 50/50 Medium Mathematics Relations and Functions Graphs of standard functions Class 11 Level 35

फलन (f(x)=\sqrt{16-x^-2}) का वास्तविक डोमेन क्या है?

What is the real domain of (f(x)=\sqrt{16-x^-2})?

Explanation opens after your attempt

Correct Answer

A. ([-4,4])

Step 1

Concept

For a real square root, \(16-x^2\ge 0\) is required. This gives \(x^2\le 16\) and the domain ([-4,4]).

Step 2

Why this answer is correct

The correct answer is A. ([-4,4]). For a real square root, \(16-x^2\ge 0\) is required. This gives \(x^2\le 16\) and the domain ([-4,4]).

Step 3

Exam Tip

वास्तविक वर्गमूल के लिए \(16-x^2\ge 0\) चाहिए। इससे \(x^2\le 16\) और डोमेन ([-4,4]) मिलता है।

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Class 11 Mathematics - Relations And Functions - Algebra of real functions Medium Quiz

फलन (f(x)=|x-5|-2) के आलेख का शीर्ष कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=|2x+4|+1) का न्यूनतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=|3x-9|) का शीर्ष किस (x) मान पर है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=2|x+2|-6) के (x)-अक्ष प्रतिच्छेद कौन से हैं?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=-|x-1|+4) का अधिकतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=|x-2|+|x-6|) का (x=4) पर मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=|x+4|-|x-2|) का (x=-1) पर मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=3(x-1)2-12) के (x)-अक्ष प्रतिच्छेद कौन से हैं?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=x-2+8x+15) के शून्यक कौन से हैं?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=x-2-10x+21) का सममिति अक्ष कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=2x-2-8x+1) के आलेख का सममिति अक्ष क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=x-2+2x+5) का न्यूनतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=-x-2+6x-5) का अधिकतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\sqrt{x+6}-2) का प्रारंभिक बिंदु कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=3-\sqrt{x-1}) का अधिकतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=2\sqrt{x+1}-5) का परिसर क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\frac{1}{x-5}+2) का ऊर्ध्व आसिम्प्टोट कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\frac{3}{x+2}-1) का क्षैतिज आसिम्प्टोट कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\frac{1}{x+4}+6) का परिसर कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\frac{-2}{x-3}) का आलेख किन चतुर्थांशों में स्थानांतरित आसिम्प्टोट के सापेक्ष होता है?

Concept

Why this answer is correct

फलन (f(x)=3(x-1)²-12) के (x)-अक्ष प्रतिच्छेद कौन से हैं?

फलन (f(x)=x^-2+8x+15) के शून्यक कौन से हैं?

फलन (f(x)=x^-2-10x+21) का सममिति अक्ष कौन सा है?

फलन (f(x)=2x^-2-8x+1) के आलेख का सममिति अक्ष क्या है?

फलन (f(x)=x^-2+2x+5) का न्यूनतम मान क्या है?

फलन (f(x)=-x^-2+6x-5) का अधिकतम मान क्या है?

फलन (f(x)=\frac{1}{(x+2)²}) का ऊर्ध्व आसिम्प्टोट कौन सा है?

फलन (f(x)=\frac{2}{(x-1)²}-3) का परिसर क्या है?

फलन (f(x)=-\frac{3}{(x+1)²}+2) का परिसर क्या है?

फलन (f(x)=x^-3+3) का (y)-अक्ष प्रतिच्छेद क्या है?

फलन (f(x)=(x-2)³+4) का केंद्रीय बिंदु कौन सा है?