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

Question 1/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

रेखा (y=2x-5) का (x)-अक्ष से प्रतिच्छेद बिंदु किसका निर्देशांक होगा?

What will be the intercept point of the line (y=2x-5) on the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. ( \left\(\frac{5}{2},0\right\) )

Step 1

Concept

On the (x)-axis (y=0) so (2x-5=0) gives \(x=\frac{5}{2}\). For an intercept set the other coordinate equal to zero.

Step 2

Why this answer is correct

The correct answer is A. ( \left\(\frac{5}{2},0\right\) ). On the (x)-axis (y=0) so (2x-5=0) gives \(x=\frac{5}{2}\). For an intercept set the other coordinate equal to zero.

Step 3

Exam Tip

(x)-अक्ष पर (y=0) होता है इसलिए (2x-5=0) से \(x=\frac{5}{2}\) मिलता है। ग्राफ में प्रतिच्छेद के लिए दूसरे निर्देशांक को शून्य रखें।

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Question 2/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=|x+3|+|x-1|) का ग्राफ किस अंतराल पर क्षैतिज रहता है?

On which interval is the graph of (y=|x+3|+|x-1|) horizontal?

Explanation opens after your attempt

Correct Answer

A. \(-3\le x\le 1\)

Step 1

Concept

On \(-3\le x\le 1\), the sum ((x+3)+(1-x)=4) is constant. In such modulus sums the graph can be horizontal between the two points.

Step 2

Why this answer is correct

The correct answer is A. \(-3\le x\le 1\). On \(-3\le x\le 1\), the sum ((x+3)+(1-x)=4) is constant. In such modulus sums the graph can be horizontal between the two points.

Step 3

Exam Tip

\(-3\le x\le 1\) पर योग ((x+3)+(1-x)=4) स्थिर रहता है। ऐसे मापांक योग में दोनों बिंदुओं के बीच ग्राफ क्षैतिज हो सकता है।

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Question 3/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=|x-3|) के ग्राफ का शीर्ष बिंदु कौन सा है?

Which point is the vertex of the graph of (f(x)=|x-3|)?

Explanation opens after your attempt

Correct Answer

A. ( \left\(3,0\right\) )

Step 1

Concept

( |x-3| ) is minimum (0) when (x=3). For a modulus graph set the inside expression equal to zero.

Step 2

Why this answer is correct

The correct answer is A. ( \left\(3,0\right\) ). ( |x-3| ) is minimum (0) when (x=3). For a modulus graph set the inside expression equal to zero.

Step 3

Exam Tip

( |x-3| ) न्यूनतम (0) तब होता है जब (x=3)। मापांक ग्राफ का शीर्ष अंदर वाले भाग को शून्य करने से मिलता है।

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Question 4/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\sqrt{x^2-9}\) के ग्राफ का डोमेन क्या है?

What is the domain of the graph of \(y=\sqrt{x^2-9}\)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,-3]\cup[3,\infty\))

Step 1

Concept

For the square root \(x^2-9\ge 0\) is required. This gives \(x\le -3\) or \(x\ge 3\).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-3]\cup[3,\infty\)). For the square root \(x^2-9\ge 0\) is required. This gives \(x\le -3\) or \(x\ge 3\).

Step 3

Exam Tip

वर्गमूल के लिए \(x^2-9\ge 0\) चाहिए। इससे \(x\le -3\) या \(x\ge 3\) मिलता है।

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Question 5/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

परवलय (y=(x+2)²-7) की सममिति अक्ष कौन सी है?

What is the axis of symmetry of the parabola (y=(x+2)²-7)?

Explanation opens after your attempt

Correct Answer

A. (x=-2)

Step 1

Concept

In (y=(x-h)²+k) the axis of symmetry is (x=h). Here (h=-2).

Step 2

Why this answer is correct

The correct answer is A. (x=-2). In (y=(x-h)²+k) the axis of symmetry is (x=h). Here (h=-2).

Step 3

Exam Tip

(y=(x-h)²+k) में सममिति अक्ष (x=h) होती है। यहां (h=-2) है।

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Question 6/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\frac{1}{x^2-4}\) के ग्राफ के ऊर्ध्वाधर आसम्टोट कौन से हैं?

What are the vertical asymptotes of the graph of \(y=\frac{1}{x^2-4}\)?

Explanation opens after your attempt

Correct Answer

A. (x=-2) और (x=2)(x=-2) and (x=2)

Step 1

Concept

Asymptotes are found by making the denominator zero. From \(x^2-4=0\), we get (x=-2,2).

Step 2

Why this answer is correct

The correct answer is A. (x=-2) और (x=2) / (x=-2) and (x=2). Asymptotes are found by making the denominator zero. From \(x^2-4=0\), we get (x=-2,2).

Step 3

Exam Tip

आसम्टोट हर को शून्य करने से मिलते हैं। \(x^2-4=0\) से (x=-2,2) मिलते हैं।

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Question 7/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=-3(x-1)²+4) का अधिकतम मान क्या है?

What is the maximum value of the function (y=-3(x-1)²+4)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The coefficient (-3) is negative so the parabola opens downward. At the vertex (y=4) is the maximum value.

Step 2

Why this answer is correct

The correct answer is A. (4). The coefficient (-3) is negative so the parabola opens downward. At the vertex (y=4) is the maximum value.

Step 3

Exam Tip

गुणांक (-3) ऋणात्मक है इसलिए परवलय नीचे खुलता है। शीर्ष पर (y=4) अधिकतम मान है।

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Question 8/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\frac{x}{x^-2+1}) के ग्राफ की सममिति कौन सी है?

What is the symmetry of the graph of (f(x)=\frac{x}{x^-2+1})?

Explanation opens after your attempt

Correct Answer

A. मूल बिंदु के सापेक्ष सममितिSymmetry about the origin

Step 1

Concept

(f(-x)=\frac{-x}{x^-2+1}=-f(x)). Therefore it is an odd function and its graph is symmetric about the origin.

Step 2

Why this answer is correct

The correct answer is A. मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin. (f(-x)=\frac{-x}{x^-2+1}=-f(x)). Therefore it is an odd function and its graph is symmetric about the origin.

Step 3

Exam Tip

(f(-x)=\frac{-x}{x^-2+1}=-f(x)) है। इसलिए यह विषम फलन है और ग्राफ मूल बिंदु के सापेक्ष सममित है।

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Question 9/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\sqrt{x+5}) के ग्राफ का डोमेन क्या है?

What is the domain of the graph of (f(x)=\sqrt{x+5})?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

For a square root \(x+5\ge 0\) must hold. Hence \(x\ge -5\).

Step 2

Why this answer is correct

The correct answer is A. \( [-5,\infty\) ). For a square root \(x+5\ge 0\) must hold. Hence \(x\ge -5\).

Step 3

Exam Tip

वर्गमूल के लिए \(x+5\ge 0\) होना चाहिए। इसलिए \(x\ge -5\) है।

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Question 10/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=-|x+2|+5) के ग्राफ का शीर्ष बिंदु कौन सा है?

Which point is the vertex of the graph of (y=-|x+2|+5)?

Explanation opens after your attempt

Correct Answer

A. ((-2,5))

Step 1

Concept

The inside part of the modulus is zero at (x+2=0). Then (y=5), so the vertex is ((-2,5)).

Step 2

Why this answer is correct

The correct answer is A. ((-2,5)). The inside part of the modulus is zero at (x+2=0). Then (y=5), so the vertex is ((-2,5)).

Step 3

Exam Tip

मापांक का अंदरूनी भाग (x+2=0) पर शून्य होता है। तब (y=5) है इसलिए शीर्ष ((-2,5)) है।

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

फलन \(y=\frac{1}{x-4}\) के ग्राफ का ऊर्ध्वाधर आसम्टोट कौन सा है?

What is the vertical asymptote of the graph of \(y=\frac{1}{x-4}\)?

Explanation opens after your attempt

Correct Answer

A. (x=4)

Step 1

Concept

The denominator (x-4) makes the function undefined when it is zero. So the vertical asymptote is (x=4).

Step 2

Why this answer is correct

The correct answer is A. (x=4). The denominator (x-4) makes the function undefined when it is zero. So the vertical asymptote is (x=4).

Step 3

Exam Tip

हर (x-4) शून्य होने पर फलन अपरिभाषित होता है। इसलिए ऊर्ध्वाधर आसम्टोट (x=4) है।

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Question 12/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ (y=|x|) और (y=3-x) किस बिंदु पर मिलते हैं?

At which point do the graphs (y=|x|) and (y=3-x) meet?

Explanation opens after your attempt

Correct Answer

A. (\left\(\frac{3}{2},\frac{3}{2}\right\))

Step 1

Concept

For \(x\ge 0\), put (|x|=x), so (x=3-x) gives \(x=\frac{3}{2}\). Hence the intersection is (\left\(\frac{3}{2},\frac{3}{2}\right\)).

Step 2

Why this answer is correct

The correct answer is A. (\left\(\frac{3}{2},\frac{3}{2}\right\)). For \(x\ge 0\), put (|x|=x), so (x=3-x) gives \(x=\frac{3}{2}\). Hence the intersection is (\left\(\frac{3}{2},\frac{3}{2}\right\)).

Step 3

Exam Tip

\(x\ge 0\) पर (|x|=x) रखकर (x=3-x) से \(x=\frac{3}{2}\) मिलता है। इसलिए प्रतिच्छेद (\left\(\frac{3}{2},\frac{3}{2}\right\)) है।

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Question 13/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\frac{2}{x+1}-3\) के ग्राफ का क्षैतिज आसम्टोट कौन सा है?

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

Explanation opens after your attempt

Correct Answer

A. (y=-3)

Step 1

Concept

The term \(\frac{2}{x+1}\) approaches (0) for large (|x|). Hence the graph approaches (y=-3).

Step 2

Why this answer is correct

The correct answer is A. (y=-3). The term \(\frac{2}{x+1}\) approaches (0) for large (|x|). Hence the graph approaches (y=-3).

Step 3

Exam Tip

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

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Question 14/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\lfloor x \rfloor) के ग्राफ में (x=2.7) पर (y) का मान क्या है?

For the graph of (f(x)=\lfloor x \rfloor), what is the value of (y) at (x=2.7)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

The greatest integer function gives the largest integer less than or equal to (x). Hence \(\lfloor 2.7 \rfloor=2\).

Step 2

Why this answer is correct

The correct answer is A. (2). The greatest integer function gives the largest integer less than or equal to (x). Hence \(\lfloor 2.7 \rfloor=2\).

Step 3

Exam Tip

महत्तम पूर्णांक फलन (x) से कम या बराबर सबसे बड़ा पूर्णांक देता है। इसलिए \(\lfloor 2.7 \rfloor=2\)।

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Question 15/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\lfloor x \rfloor) के ग्राफ में बिंदु (x=3) पर कौन सा कथन सही है?

Which statement is correct at (x=3) on the graph of (f(x)=\lfloor x \rfloor)?

Explanation opens after your attempt

Correct Answer

A. ग्राफ में छलांग होती हैThe graph has a jump

Step 1

Concept

The greatest integer function changes suddenly at every integer. Therefore a jump occurs at (x=3).

Step 2

Why this answer is correct

The correct answer is A. ग्राफ में छलांग होती है / The graph has a jump. The greatest integer function changes suddenly at every integer. Therefore a jump occurs at (x=3).

Step 3

Exam Tip

महत्तम पूर्णांक फलन हर पूर्णांक पर अचानक बदलता है। इसलिए (x=3) पर छलांग मिलती है।

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Question 16/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\operatorname{sgn}(x)) के ग्राफ में (x=-8) पर मान क्या है?

What is the value of the graph of (f(x)=\operatorname{sgn}(x)) at (x=-8)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

The signum function gives (-1) for negative (x). Therefore (f(-8)=-1).

Step 2

Why this answer is correct

The correct answer is A. (-1). The signum function gives (-1) for negative (x). Therefore (f(-8)=-1).

Step 3

Exam Tip

साइनम फलन ऋणात्मक (x) पर (-1) देता है। इसलिए (f(-8)=-1)।

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Question 17/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\operatorname{sgn}(x-2)) के ग्राफ में छलांग किस (x) पर होगी?

At which (x) will the graph of (f(x)=\operatorname{sgn}(x-2)) have a jump?

Explanation opens after your attempt

Correct Answer

A. (x=2)

Step 1

Concept

A signum graph changes when the inside expression becomes zero. From (x-2=0), we get (x=2).

Step 2

Why this answer is correct

The correct answer is A. (x=2). A signum graph changes when the inside expression becomes zero. From (x-2=0), we get (x=2).

Step 3

Exam Tip

साइनम ग्राफ अंदर की अभिव्यक्ति शून्य होने पर बदलता है। (x-2=0) से (x=2) मिलता है।

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Question 18/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ \(y=x^3\) के बारे में कौन सा कथन सही है?

Which statement is correct about the graph of \(y=x^3\)?

Explanation opens after your attempt

Correct Answer

A. यह मूल बिंदु के सापेक्ष सममित हैIt is symmetric about the origin

Step 1

Concept

\(y=x^3\) is an odd function because (f(-x)=-f(x)). The graph of an odd function is symmetric about the origin.

Step 2

Why this answer is correct

The correct answer is A. यह मूल बिंदु के सापेक्ष सममित है / It is symmetric about the origin. \(y=x^3\) is an odd function because (f(-x)=-f(x)). The graph of an odd function is symmetric about the origin.

Step 3

Exam Tip

\(y=x^3\) विषम फलन है क्योंकि (f(-x)=-f(x))। विषम फलन का ग्राफ मूल बिंदु के सापेक्ष सममित होता है।

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Question 19/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ \(y=x^2-6x+11\) का शीर्ष बिंदु कौन सा है?

What is the vertex of the graph \(y=x^2-6x+11\)?

Explanation opens after your attempt

Correct Answer

A. ( \left\(3,2\right\) )

Step 1

Concept

Completing the square gives (y=(x-3)²+2). Therefore the vertex is (\left\(3,2\right\)).

Step 2

Why this answer is correct

The correct answer is A. ( \left\(3,2\right\) ). Completing the square gives (y=(x-3)²+2). Therefore the vertex is (\left\(3,2\right\)).

Step 3

Exam Tip

पूर्ण वर्ग बनाने पर (y=(x-3)²+2) मिलता है। इसलिए शीर्ष (\left\(3,2\right\)) है।

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Question 20/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=|x+1|+|x-3|) का न्यूनतम मान क्या है?

What is the minimum value of (y=|x+1|+|x-3|)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

It is the sum of distances from (-1) and (3). Between them the sum remains (4).

Step 2

Why this answer is correct

The correct answer is A. (4). It is the sum of distances from (-1) and (3). Between them the sum remains (4).

Step 3

Exam Tip

यह (-1) और (3) से दूरीयों का योग है। इनके बीच योग हमेशा (4) रहता है।

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Question 21/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=|2x-6|) के ग्राफ का (x)-अक्ष से प्रतिच्छेद क्या है?

What is the (x)-intercept of the graph of (y=|2x-6|)?

Explanation opens after your attempt

Correct Answer

A. ( \left\(3,0\right\) )

Step 1

Concept

( |2x-6|=0 ) only when (2x-6=0). Hence (x=3).

Step 2

Why this answer is correct

The correct answer is A. ( \left\(3,0\right\) ). ( |2x-6|=0 ) only when (2x-6=0). Hence (x=3).

Step 3

Exam Tip

( |2x-6|=0 ) तभी होगा जब (2x-6=0)। इसलिए (x=3) है।

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Question 22/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

रेखा (3x+2y=12) का ढाल क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(-\frac{3}{2}\)

Step 1

Concept

Write the equation as \(y=-\frac{3}{2}x+6\). The coefficient of (x) is the slope.

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{3}{2}\). Write the equation as \(y=-\frac{3}{2}x+6\). The coefficient of (x) is the slope.

Step 3

Exam Tip

समीकरण को \(y=-\frac{3}{2}x+6\) लिखें। (x) का गुणांक ढाल होता है।

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Question 23/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=5) के ग्राफ के लिए कौन सा कथन सही है?

Which statement is correct for the graph of (y=5)?

Explanation opens after your attempt

Correct Answer

A. यह (x)-अक्ष के समानांतर रेखा हैIt is a line parallel to the (x)-axis

Step 1

Concept

The value of (y) is (5) for every (x). The graph of a constant function is a horizontal line.

Step 2

Why this answer is correct

The correct answer is A. यह (x)-अक्ष के समानांतर रेखा है / It is a line parallel to the (x)-axis. The value of (y) is (5) for every (x). The graph of a constant function is a horizontal line.

Step 3

Exam Tip

(y) का मान हर (x) के लिए (5) है। स्थिर फलन का ग्राफ क्षैतिज रेखा होता है।

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Question 24/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

पहचान फलन (f(x)=x) के ग्राफ पर कौन सा बिंदु स्थित है?

Which point lies on the graph of the identity function (f(x)=x)?

Explanation opens after your attempt

Correct Answer

A. ( \left\(-4,-4\right\) )

Step 1

Concept

In the identity function (y=x). Therefore both coordinates must be equal.

Step 2

Why this answer is correct

The correct answer is A. ( \left\(-4,-4\right\) ). In the identity function (y=x). Therefore both coordinates must be equal.

Step 3

Exam Tip

पहचान फलन में (y=x) होता है। इसलिए दोनों निर्देशांक बराबर होने चाहिए।

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Question 25/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^2\) और (y=2x+3) के ग्राफ किस (x) मान पर प्रतिच्छेद करते हैं?

For which (x) values do the graphs \(y=x^2\) and (y=2x+3) intersect?

Explanation opens after your attempt

Correct Answer

A. (x=-1,3)

Step 1

Concept

For intersection set \(x^2=2x+3\). From \(x^2-2x-3=0\), (x=-1,3).

Step 2

Why this answer is correct

The correct answer is A. (x=-1,3). For intersection set \(x^2=2x+3\). From \(x^2-2x-3=0\), (x=-1,3).

Step 3

Exam Tip

प्रतिच्छेद के लिए \(x^2=2x+3\) रखें। \(x^2-2x-3=0\) से (x=-1,3) मिलते हैं।

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Question 26/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^2\) और (y=|x|) के ग्राफ किन (x) मानों पर मिलते हैं?

At which (x) values do the graphs \(y=x^2\) and (y=|x|) meet?

Explanation opens after your attempt

Correct Answer

A. (x=-1,0,1)

Step 1

Concept

Putting \(x^2=|x|\) gives (x=0) or (|x|=1). Hence (x=-1,0,1).

Step 2

Why this answer is correct

The correct answer is A. (x=-1,0,1). Putting \(x^2=|x|\) gives (x=0) or (|x|=1). Hence (x=-1,0,1).

Step 3

Exam Tip

\(x^2=|x|\) रखने पर (x=0) या (|x|=1) मिलता है। इसलिए (x=-1,0,1) हैं।

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Question 27/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (f(x)=\frac{x}{|x|}) का ग्राफ (x>0) के लिए किस रेखा पर है?

For (x>0), the graph of (f(x)=\frac{x}{|x|}) lies on which line?

Explanation opens after your attempt

Correct Answer

A. (y=1)

Step 1

Concept

For (x>0), (|x|=x). Hence \(\frac{x}{|x|}=1\).

Step 2

Why this answer is correct

The correct answer is A. (y=1). For (x>0), (|x|=x). Hence \(\frac{x}{|x|}=1\).

Step 3

Exam Tip

(x>0) पर (|x|=x) होता है। इसलिए \(\frac{x}{|x|}=1\)।

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Question 28/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=\min(x,-1)) के ग्राफ में (x>-1) के लिए (y) क्या है?

For (x>-1), what is (y) in the graph of (y=\min(x,-1))?

Explanation opens after your attempt

Correct Answer

A. (y=-1)

Step 1

Concept

When (x>-1), the smaller value between (x) and (-1) is (-1). Hence the graph is (y=-1).

Step 2

Why this answer is correct

The correct answer is A. (y=-1). When (x>-1), the smaller value between (x) and (-1) is (-1). Hence the graph is (y=-1).

Step 3

Exam Tip

जब (x>-1) हो तो (x) और (-1) में छोटा मान (-1) है। इसलिए ग्राफ (y=-1) है।

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Question 29/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ (y=|x-2|+1) की रेंज क्या है?

What is the range of the graph (y=|x-2|+1)?

Explanation opens after your attempt

Correct Answer

A. \( [1,\infty\) )

Step 1

Concept

The minimum value of (|x-2|) is (0). Therefore the minimum value of (y) is (1).

Step 2

Why this answer is correct

The correct answer is A. \( [1,\infty\) ). The minimum value of (|x-2|) is (0). Therefore the minimum value of (y) is (1).

Step 3

Exam Tip

(|x-2|) का न्यूनतम मान (0) है। इसलिए (y) का न्यूनतम मान (1) है।

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Question 30/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ (y=-(x+4)²+9) की रेंज क्या है?

What is the range of the graph (y=-(x+4)²+9)?

Explanation opens after your attempt

Correct Answer

A. ( \(-\infty,9] \)

Step 1

Concept

The parabola opens downward and its vertex has (y=9). Hence the range is ( \(-\infty,9] \).

Step 2

Why this answer is correct

The correct answer is A. ( \(-\infty,9] \). The parabola opens downward and its vertex has (y=9). Hence the range is ( \(-\infty,9] \).

Step 3

Exam Tip

परवलय नीचे खुलता है और शीर्ष पर (y=9) है। इसलिए रेंज ( \(-\infty,9] \) है।

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Question 31/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\sqrt{4-x}\) के ग्राफ का डोमेन क्या है?

What is the domain of the graph \(y=\sqrt{4-x}\)?

Explanation opens after your attempt

Correct Answer

A. ( \(-\infty,4] \)

Step 1

Concept

For the square root \(4-x\ge 0\) is required. Therefore \(x\le 4\).

Step 2

Why this answer is correct

The correct answer is A. ( \(-\infty,4] \). For the square root \(4-x\ge 0\) is required. Therefore \(x\le 4\).

Step 3

Exam Tip

वर्गमूल के लिए \(4-x\ge 0\) चाहिए। इसलिए \(x\le 4\) है।

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Question 32/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ \(y=\frac{x+2}{x-1}\) में कौन सा (x) मान डोमेन में नहीं है?

Which (x) value is not in the domain of the graph \(y=\frac{x+2}{x-1}\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The denominator (x-1) cannot be zero. From (x-1=0), (x=1) is excluded.

Step 2

Why this answer is correct

The correct answer is A. (1). The denominator (x-1) cannot be zero. From (x-1=0), (x=1) is excluded.

Step 3

Exam Tip

हर (x-1) शून्य नहीं हो सकता। (x-1=0) से (x=1) निषिद्ध है।

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Question 33/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^4\) के ग्राफ के बारे में कौन सा कथन सही है?

Which statement is correct about the graph of \(y=x^4\)?

Explanation opens after your attempt

Correct Answer

A. यह (y)-अक्ष के सापेक्ष सममित हैIt is symmetric about the (y)-axis

Step 1

Concept

(f(-x)=(-x)⁴=x^-4=f(x)). Therefore it is an even function and is symmetric about the (y)-axis.

Step 2

Why this answer is correct

The correct answer is A. यह (y)-अक्ष के सापेक्ष सममित है / It is symmetric about the (y)-axis. (f(-x)=(-x)⁴=x^-4=f(x)). Therefore it is an even function and is symmetric about the (y)-axis.

Step 3

Exam Tip

(f(-x)=(-x)⁴=x^-4=f(x)) है। इसलिए यह सम फलन है और (y)-अक्ष के सापेक्ष सममित है।

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

फलन (y=-|x|) के ग्राफ की रेंज क्या है?

What is the range of the graph (y=-|x|)?

Explanation opens after your attempt

Correct Answer

A. ( \(-\infty,0] \)

Step 1

Concept

Since \(|x|\ge 0\), we have \(-|x|\le 0\). The maximum value is (0).

Step 2

Why this answer is correct

The correct answer is A. ( \(-\infty,0] \). Since \(|x|\ge 0\), we have \(-|x|\le 0\). The maximum value is (0).

Step 3

Exam Tip

\(|x|\ge 0\) होने से \(-|x|\le 0\) होता है। अधिकतम मान (0) है।

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

फलन (y=|x+2|-|x-2|) का (x>2) के लिए मान क्या होगा?

For (x>2), what is the value of (y=|x+2|-|x-2|)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

For (x>2), (|x+2|=x+2) and (|x-2|=x-2). Their difference is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). For (x>2), (|x+2|=x+2) and (|x-2|=x-2). Their difference is (4).

Step 3

Exam Tip

(x>2) पर (|x+2|=x+2) और (|x-2|=x-2) है। अंतर (4) मिलता है।

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Question 36/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\frac{1}{x^2}\) के ग्राफ के बारे में कौन सा कथन सही है?

Which statement is correct about the graph of \(y=\frac{1}{x^2}\)?

Explanation opens after your attempt

Correct Answer

A. यह (y)-अक्ष के सापेक्ष सममित हैIt is symmetric about the (y)-axis

Step 1

Concept

(f(-x)=\frac{1}{(-x)²}=\frac{1}{x^-2}). Hence the graph is symmetric about the (y)-axis.

Step 2

Why this answer is correct

The correct answer is A. यह (y)-अक्ष के सापेक्ष सममित है / It is symmetric about the (y)-axis. (f(-x)=\frac{1}{(-x)²}=\frac{1}{x^-2}). Hence the graph is symmetric about the (y)-axis.

Step 3

Exam Tip

(f(-x)=\frac{1}{(-x)²}=\frac{1}{x^-2}) है। इसलिए ग्राफ (y)-अक्ष के सापेक्ष सममित है।

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Question 37/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\frac{1}{x}\) के ग्राफ के बारे में कौन सा कथन सही है?

Which statement is correct about the graph of \(y=\frac{1}{x}\)?

Explanation opens after your attempt

Correct Answer

A. यह मूल बिंदु के सापेक्ष सममित हैIt is symmetric about the origin

Step 1

Concept

(f(-x)=-\frac{1}{x}=-f(x)). Therefore it is an odd function and symmetric about the origin.

Step 2

Why this answer is correct

The correct answer is A. यह मूल बिंदु के सापेक्ष सममित है / It is symmetric about the origin. (f(-x)=-\frac{1}{x}=-f(x)). Therefore it is an odd function and symmetric about the origin.

Step 3

Exam Tip

(f(-x)=-\frac{1}{x}=-f(x)) है। इसलिए यह विषम फलन है और मूल बिंदु के सापेक्ष सममित है।

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Question 38/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^2-4\) का ग्राफ (x)-अक्ष को किन बिंदुओं पर काटता है?

At which points does the graph of \(y=x^2-4\) cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. ( \left\(-2,0\right\),\left\(2,0\right\) )

Step 1

Concept

Set (y=0) on the (x)-axis. From \(x^2-4=0\), \(x=\pm 2\).

Step 2

Why this answer is correct

The correct answer is A. ( \left\(-2,0\right\),\left\(2,0\right\) ). Set (y=0) on the (x)-axis. From \(x^2-4=0\), \(x=\pm 2\).

Step 3

Exam Tip

(x)-अक्ष पर (y=0) रखें। \(x^2-4=0\) से \(x=\pm 2\) मिलता है।

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Question 39/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=(x-5)²) का ग्राफ \(y=x^2\) से कैसे प्राप्त होगा?

How is the graph of (y=(x-5)²) obtained from \(y=x^2\)?

Explanation opens after your attempt

Correct Answer

A. (5) इकाई दाईं ओर खिसकाकरBy shifting (5) units right

Step 1

Concept

Replacing (x) by (x-5) shifts the graph (5) units right. In horizontal shift read the sign oppositely.

Step 2

Why this answer is correct

The correct answer is A. (5) इकाई दाईं ओर खिसकाकर / By shifting (5) units right. Replacing (x) by (x-5) shifts the graph (5) units right. In horizontal shift read the sign oppositely.

Step 3

Exam Tip

(x) की जगह (x-5) आने पर ग्राफ दाईं ओर (5) इकाई खिसकता है। क्षैतिज खिसकाव में संकेत उल्टा पढ़ें।

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Question 40/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=(x+3)²) का ग्राफ \(y=x^2\) से कैसे प्राप्त होगा?

How is the graph of (y=(x+3)²) obtained from \(y=x^2\)?

Explanation opens after your attempt

Correct Answer

A. (3) इकाई बाईं ओर खिसकाकरBy shifting (3) units left

Step 1

Concept

(x+3) means (x-(-3)). Therefore the graph shifts (3) units left.

Step 2

Why this answer is correct

The correct answer is A. (3) इकाई बाईं ओर खिसकाकर / By shifting (3) units left. (x+3) means (x-(-3)). Therefore the graph shifts (3) units left.

Step 3

Exam Tip

(x+3) का अर्थ (x-(-3)) है। इसलिए ग्राफ बाईं ओर (3) इकाई खिसकता है।

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Question 41/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^2+6\) का ग्राफ \(y=x^2\) से कैसे प्राप्त होगा?

How is the graph of \(y=x^2+6\) obtained from \(y=x^2\)?

Explanation opens after your attempt

Correct Answer

A. (6) इकाई ऊपर खिसकाकरBy shifting (6) units up

Step 1

Concept

Adding (+6) outside the function increases every (y)-value by (6). Hence the graph moves up.

Step 2

Why this answer is correct

The correct answer is A. (6) इकाई ऊपर खिसकाकर / By shifting (6) units up. Adding (+6) outside the function increases every (y)-value by (6). Hence the graph moves up.

Step 3

Exam Tip

फलन के बाहर (+6) जुड़ने से सभी (y)-मान (6) बढ़ते हैं। इसलिए ग्राफ ऊपर जाता है।

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Question 42/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=-\sqrt{x}\) का ग्राफ \(y=\sqrt{x}\) से कैसे संबंधित है?

How is the graph of \(y=-\sqrt{x}\) related to \(y=\sqrt{x}\)?

Explanation opens after your attempt

Correct Answer

A. (x)-अक्ष में परावर्तनReflection in the (x)-axis

Step 1

Concept

A negative sign outside the function makes every (y)-value negative. So it is a reflection in the (x)-axis.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष में परावर्तन / Reflection in the (x)-axis. A negative sign outside the function makes every (y)-value negative. So it is a reflection in the (x)-axis.

Step 3

Exam Tip

फलन के बाहर ऋण चिह्न सभी (y)-मानों को ऋणात्मक कर देता है। इसलिए (x)-अक्ष में परावर्तन होता है।

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Question 43/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=2|x|) का ग्राफ (y=|x|) से कैसे बदलेगा?

How does the graph of (y=2|x|) change from (y=|x|)?

Explanation opens after your attempt

Correct Answer

A. ऊर्ध्वाधर खिंचाव (2) गुनाVertical stretch by factor (2)

Step 1

Concept

Multiplying outside by (2) doubles all (y)-values. So it is a vertical stretch.

Step 2

Why this answer is correct

The correct answer is A. ऊर्ध्वाधर खिंचाव (2) गुना / Vertical stretch by factor (2). Multiplying outside by (2) doubles all (y)-values. So it is a vertical stretch.

Step 3

Exam Tip

बाहर (2) से गुणा होने पर सभी (y)-मान दुगुने होते हैं। इसलिए ऊर्ध्वाधर खिंचाव होता है।

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Question 44/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=|2x|) का ग्राफ (y=|x|) से कैसे बदलेगा?

How does the graph of (y=|2x|) change from (y=|x|)?

Explanation opens after your attempt

Correct Answer

A. क्षैतिज संपीड़न (2) गुनाHorizontal compression by factor (2)

Step 1

Concept

Having (2x) inside makes the graph shrink toward the (y)-axis. This is horizontal compression.

Step 2

Why this answer is correct

The correct answer is A. क्षैतिज संपीड़न (2) गुना / Horizontal compression by factor (2). Having (2x) inside makes the graph shrink toward the (y)-axis. This is horizontal compression.

Step 3

Exam Tip

अंदर (2x) होने से ग्राफ (y)-अक्ष की ओर सिमटता है। यह क्षैतिज संपीड़न है।

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Question 45/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ (y=|x-1|+|x+1|) की रेंज क्या है?

What is the range of the graph (y=|x-1|+|x+1|)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

It is the sum of distances from (1) and (-1). The minimum sum of distances is (2).

Step 2

Why this answer is correct

The correct answer is A. \( [2,\infty\) ). It is the sum of distances from (1) and (-1). The minimum sum of distances is (2).

Step 3

Exam Tip

यह (1) और (-1) से दूरीयों का योग है। न्यूनतम दूरी योग (2) है।

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Question 46/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=x^3-1\) का ग्राफ \(y=x^3\) से कैसे प्राप्त होगा?

How is the graph of \(y=x^3-1\) obtained from \(y=x^3\)?

Explanation opens after your attempt

Correct Answer

A. (1) इकाई नीचे खिसकाकरBy shifting (1) unit down

Step 1

Concept

The outside (-1) decreases every (y)-value by (1). Hence the graph shifts down.

Step 2

Why this answer is correct

The correct answer is A. (1) इकाई नीचे खिसकाकर / By shifting (1) unit down. The outside (-1) decreases every (y)-value by (1). Hence the graph shifts down.

Step 3

Exam Tip

फलन के बाहर (-1) सभी (y)-मानों को (1) घटाता है। इसलिए ग्राफ नीचे खिसकता है।

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Question 47/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन (y=(x-2)³) का ग्राफ \(y=x^3\) से कैसे प्राप्त होगा?

How is the graph of (y=(x-2)³) obtained from \(y=x^3\)?

Explanation opens after your attempt

Correct Answer

A. (2) इकाई दाईं ओर खिसकाकरBy shifting (2) units right

Step 1

Concept

Replacing (x) by (x-2) moves the graph (2) units right. The same rule applies to the cubic function.

Step 2

Why this answer is correct

The correct answer is A. (2) इकाई दाईं ओर खिसकाकर / By shifting (2) units right. Replacing (x) by (x-2) moves the graph (2) units right. The same rule applies to the cubic function.

Step 3

Exam Tip

(x) की जगह (x-2) आने से ग्राफ दाईं ओर (2) इकाई जाता है। घन फलन में भी यही नियम लागू होता है।

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Question 48/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

फलन \(y=\frac{1}{|x|}\) के ग्राफ की रेंज क्या है?

What is the range of the graph \(y=\frac{1}{|x|}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(|x|>0) when \(x\ne 0\), and \(\frac{1}{|x|}\) is always positive. It never becomes (0).

Step 2

Why this answer is correct

The correct answer is A. ( \(0,\infty\) ). (|x|>0) when \(x\ne 0\), and \(\frac{1}{|x|}\) is always positive. It never becomes (0).

Step 3

Exam Tip

(|x|>0) जब \(x\ne 0\) होता है और \(\frac{1}{|x|}\) हमेशा धनात्मक है। यह (0) को कभी नहीं लेता।

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Question 49/50 Expert Mathematics Relations and Functions Graphs of standard functions Class 11 Level 34

ग्राफ \(y=x^2\) और रेखा (y=4) से घिरा क्षेत्र किन (x) मानों के बीच है?

Between which (x) values is the region bounded by \(y=x^2\) and the line (y=4)?

Explanation opens after your attempt

Correct Answer

A. \(-2\le x\le 2\)

Step 1

Concept

The boundaries come from intersections. From \(x^2=4\), (x=-2,2).

Step 2

Why this answer is correct

The correct answer is A. \(-2\le x\le 2\). The boundaries come from intersections. From \(x^2=4\), (x=-2,2).

Step 3

Exam Tip

सीमाएं प्रतिच्छेद से मिलती हैं। \(x^2=4\) से (x=-2,2) मिलते हैं।

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

फलन (y=|x|+|x-4|) का ग्राफ किस अंतराल पर क्षैतिज रहता है?

On which interval is the graph of (y=|x|+|x-4|) horizontal?

Explanation opens after your attempt

Correct Answer

A. \(0\le x\le 4\)

Step 1

Concept

For \(0\le x\le 4\), the sum is (x+(4-x)=4), which is constant. Hence the graph is horizontal.

Step 2

Why this answer is correct

The correct answer is A. \(0\le x\le 4\). For \(0\le x\le 4\), the sum is (x+(4-x)=4), which is constant. Hence the graph is horizontal.

Step 3

Exam Tip

\(0\le x\le 4\) पर योग (x+(4-x)=4) स्थिर है। इसलिए ग्राफ क्षैतिज रहता है।

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Class 11 Mathematics - Relations And Functions - Graphs of standard functions Expert Quiz

रेखा (y=2x-5) का (x)-अक्ष से प्रतिच्छेद बिंदु किसका निर्देशांक होगा?

Concept

Why this answer is correct

Exam Tip

फलन (y=|x+3|+|x-1|) का ग्राफ किस अंतराल पर क्षैतिज रहता है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=|x-3|) के ग्राफ का शीर्ष बिंदु कौन सा है?

Concept

Why this answer is correct

Exam Tip

फलन \(y=\sqrt{x^2-9}\) के ग्राफ का डोमेन क्या है?

Concept

Why this answer is correct

Exam Tip

परवलय (y=(x+2)2-7) की सममिति अक्ष कौन सी है?

Concept

Why this answer is correct

Exam Tip

फलन \(y=\frac{1}{x^2-4}\) के ग्राफ के ऊर्ध्वाधर आसम्टोट कौन से हैं?

Concept

Why this answer is correct

Exam Tip

फलन (y=-3(x-1)2+4) का अधिकतम मान क्या है?

Concept

Why this answer is correct

Exam Tip

फलन (f(x)=\frac{x}{x-2+1}) के ग्राफ की सममिति कौन सी है?

Concept

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फलन (f(x)=\sqrt{x+5}) के ग्राफ का डोमेन क्या है?

Concept

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Exam Tip

फलन (y=-|x+2|+5) के ग्राफ का शीर्ष बिंदु कौन सा है?

Concept

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Exam Tip

फलन \(y=\frac{1}{x-4}\) के ग्राफ का ऊर्ध्वाधर आसम्टोट कौन सा है?

Concept

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ग्राफ (y=|x|) और (y=3-x) किस बिंदु पर मिलते हैं?

Concept

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Exam Tip

फलन \(y=\frac{2}{x+1}-3\) के ग्राफ का क्षैतिज आसम्टोट कौन सा है?

Concept

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Exam Tip

फलन (f(x)=\lfloor x \rfloor) के ग्राफ में (x=2.7) पर (y) का मान क्या है?

Concept

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Exam Tip

फलन (f(x)=\lfloor x \rfloor) के ग्राफ में बिंदु (x=3) पर कौन सा कथन सही है?

Concept

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फलन (f(x)=\operatorname{sgn}(x)) के ग्राफ में (x=-8) पर मान क्या है?

Concept

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Exam Tip

फलन (f(x)=\operatorname{sgn}(x-2)) के ग्राफ में छलांग किस (x) पर होगी?

Concept

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Exam Tip

ग्राफ \(y=x^3\) के बारे में कौन सा कथन सही है?

Concept

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Exam Tip

ग्राफ \(y=x^2-6x+11\) का शीर्ष बिंदु कौन सा है?

Concept

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Exam Tip

फलन (y=|x+1|+|x-3|) का न्यूनतम मान क्या है?

Concept

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परवलय (y=(x+2)²-7) की सममिति अक्ष कौन सी है?

फलन (y=-3(x-1)²+4) का अधिकतम मान क्या है?

फलन (f(x)=\frac{x}{x^-2+1}) के ग्राफ की सममिति कौन सी है?

ग्राफ (y=-(x+4)²+9) की रेंज क्या है?