Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Expert Quiz

Mathematics Exploring Algebraic Identities Factorisation Expert Class 9 Level 37

Level 37 • 50/50 questions • 25 seconds per question.

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Question 1/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

किसी पौधे की ऊंचाई (t=3) पर (47) सेमी और (t=9) पर (119) सेमी है। यदि वृद्धि रेखीय है तो सही मॉडल क्या होगा?

A plant's height is (47) cm at (t=3) and (119) cm at (t=9). If the growth is linear then what is the correct model?

Explanation opens after your attempt
Correct Answer

A. (H(t)=11+12t)

Step 1

Concept

The rate is \(\frac{119-47}{9-3}=12\). From (47=a+12(3)), (a=11).

Step 2

Why this answer is correct

The correct answer is A. (H(t)=11+12t). The rate is \(\frac{119-47}{9-3}=12\). From (47=a+12(3)), (a=11).

Step 3

Exam Tip

दर \(\frac{119-47}{9-3}=12\) है। (47=a+12(3)) से (a=11) मिलता है।

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Question 2/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

एक टंकी में (t=2) पर (218) लीटर और (t=10) पर (122) लीटर पानी है। रेखीय क्षय मॉडल क्या होगा?

A tank has (218) litres at (t=2) and (122) litres at (t=10). What is the linear decay model?

Explanation opens after your attempt
Correct Answer

B. (W(t)=242-12t)

Step 1

Concept

The rate is \(\frac{122-218}{10-2}=-12\). From (218=a-12(2)), (a=242).

Step 2

Why this answer is correct

The correct answer is B. (W(t)=242-12t). The rate is \(\frac{122-218}{10-2}=-12\). From (218=a-12(2)), (a=242).

Step 3

Exam Tip

दर \(\frac{122-218}{10-2}=-12\) है। (218=a-12(2)) से (a=242) मिलता है।

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Question 3/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

दो मॉडल (A(t)=64+9t) और (B(t)=184-6t) कब बराबर होंगे?

When will the two models (A(t)=64+9t) and (B(t)=184-6t) be equal?

Explanation opens after your attempt
Correct Answer

C. (t=8)

Step 1

Concept

For equality set (64+9t=184-6t). This gives (15t=120) and (t=8).

Step 2

Why this answer is correct

The correct answer is C. (t=8). For equality set (64+9t=184-6t). This gives (15t=120) and (t=8).

Step 3

Exam Tip

बराबरी के लिए (64+9t=184-6t) रखें। इससे (15t=120) और (t=8) मिलता है।

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Question 4/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (P(t)=75+8t) और (Q(t)=219-10t) है तो किस (t) पर (P(t)=Q(t)) होगा?

If (P(t)=75+8t) and (Q(t)=219-10t), at which (t) will (P(t)=Q(t))?

Explanation opens after your attempt
Correct Answer

B. (t=8)

Step 1

Concept

From (75+8t=219-10t), (18t=144). Therefore (t=8) is correct.

Step 2

Why this answer is correct

The correct answer is B. (t=8). From (75+8t=219-10t), (18t=144). Therefore (t=8) is correct.

Step 3

Exam Tip

(75+8t=219-10t) से (18t=144) होता है। इसलिए (t=8) सही है।

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Question 5/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (f(x)=a+15x) और (f(4)=112), तो (f(11)) क्या होगा?

If (f(x)=a+15x) and (f(4)=112), what will (f(11)) be?

Explanation opens after your attempt
Correct Answer

B. (217)

Step 1

Concept

From (a+60=112), (a=52). Then (f(11)=52+165=217).

Step 2

Why this answer is correct

The correct answer is B. (217). From (a+60=112), (a=52). Then (f(11)=52+165=217).

Step 3

Exam Tip

(a+60=112) से (a=52) मिलता है। फिर (f(11)=52+165=217) है।

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Question 6/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (g(x)=b-13x) और (g(5)=116), तो (g(12)) क्या होगा?

If (g(x)=b-13x) and (g(5)=116), what will (g(12)) be?

Explanation opens after your attempt
Correct Answer

A. (25)

Step 1

Concept

From (b-65=116), (b=181). Therefore (g(12)=181-156=25).

Step 2

Why this answer is correct

The correct answer is A. (25). From (b-65=116), (b=181). Therefore (g(12)=181-156=25).

Step 3

Exam Tip

(b-65=116) से (b=181) है। इसलिए (g(12)=181-156=25) है।

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Question 7/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=28+5.25x), तो (x=4) से (x=12) तक (y) में कुल वृद्धि कितनी होगी?

If (y=28+5.25x), what is the total increase in (y) from (x=4) to (x=12)?

Explanation opens after your attempt
Correct Answer

C. (42)

Step 1

Concept

The change in (x) is (12-4=8). The total increase is \(5.25\times8=42\).

Step 2

Why this answer is correct

The correct answer is C. (42). The change in (x) is (12-4=8). The total increase is \(5.25\times8=42\).

Step 3

Exam Tip

(x) में परिवर्तन (12-4=8) है। कुल वृद्धि \(5.25\times8=42\) है।

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Question 8/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=190-7.5x), तो (x=3) से (x=11) तक (y) में कुल कमी कितनी होगी?

If (y=190-7.5x), what is the total decrease in (y) from (x=3) to (x=11)?

Explanation opens after your attempt
Correct Answer

C. (60)

Step 1

Concept

The change in (x) is (11-3=8). The total decrease is \(7.5\times8=60\).

Step 2

Why this answer is correct

The correct answer is C. (60). The change in (x) is (11-3=8). The total decrease is \(7.5\times8=60\).

Step 3

Exam Tip

(x) में परिवर्तन (11-3=8) है। कुल कमी \(7.5\times8=60\) है।

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Question 9/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

एक राशि (x=6) पर (91) और (x=13) पर (189) है। यदि वृद्धि रेखीय है तो प्रति चरण वृद्धि क्या है?

A quantity is (91) at (x=6) and (189) at (x=13). If the growth is linear then what is the increase per step?

Explanation opens after your attempt
Correct Answer

C. (14)

Step 1

Concept

The increase per step is \(\frac{189-91}{13-6}=14\). In a linear model the rate remains constant.

Step 2

Why this answer is correct

The correct answer is C. (14). The increase per step is \(\frac{189-91}{13-6}=14\). In a linear model the rate remains constant.

Step 3

Exam Tip

प्रति चरण वृद्धि \(\frac{189-91}{13-6}=14\) है। रेखीय मॉडल में दर स्थिर रहती है।

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Question 10/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

एक मात्रा (x=5) पर (265) और (x=14) पर (130) है। यदि परिवर्तन रेखीय क्षय है तो प्रति चरण कमी क्या है?

A quantity is (265) at (x=5) and (130) at (x=14). If the change is linear decay then what is the decrease per step?

Explanation opens after your attempt
Correct Answer

C. (15)

Step 1

Concept

The total decrease is (265-130=135) and there are (9) steps. The decrease per step is \(\frac{135}{9}=15\).

Step 2

Why this answer is correct

The correct answer is C. (15). The total decrease is (265-130=135) and there are (9) steps. The decrease per step is \(\frac{135}{9}=15\).

Step 3

Exam Tip

कुल कमी (265-130=135) और चरण (9) हैं। प्रति चरण कमी \(\frac{135}{9}=15\) है।

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Question 11/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (C(t)=55+kt) और (C(12)-C(5)=105), तो (k) क्या है?

If (C(t)=55+kt) and (C(12)-C(5)=105), what is (k)?

Explanation opens after your attempt
Correct Answer

C. (15)

Step 1

Concept

(C(12)-C(5)=k(12-5)=7k). From (7k=105), (k=15).

Step 2

Why this answer is correct

The correct answer is C. (15). (C(12)-C(5)=k(12-5)=7k). From (7k=105), (k=15).

Step 3

Exam Tip

(C(12)-C(5)=k(12-5)=7k) है। (7k=105) से (k=15) मिलता है।

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Question 12/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (D(t)=340-kt) और (D(6)-D(14)=128), तो (k) क्या है?

If (D(t)=340-kt) and (D(6)-D(14)=128), what is (k)?

Explanation opens after your attempt
Correct Answer

C. (16)

Step 1

Concept

(D(6)-D(14)=k(14-6)=8k). From (8k=128), (k=16).

Step 2

Why this answer is correct

The correct answer is C. (16). (D(6)-D(14)=k(14-6)=8k). From (8k=128), (k=16).

Step 3

Exam Tip

(D(6)-D(14)=k(14-6)=8k) है। (8k=128) से (k=16) मिलता है।

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Question 13/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (A(x)=52+9x), तो (A(x+7)-A(x-2)) का मान क्या है?

If (A(x)=52+9x), what is the value of (A(x+7)-A(x-2))?

Explanation opens after your attempt
Correct Answer

C. (81)

Step 1

Concept

The variable difference is ((x+7)-(x-2)=9). With rate (9), the difference is (81).

Step 2

Why this answer is correct

The correct answer is C. (81). The variable difference is ((x+7)-(x-2)=9). With rate (9), the difference is (81).

Step 3

Exam Tip

चर में अंतर ((x+7)-(x-2)=9) है। दर (9) होने से अंतर (81) है।

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Question 14/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (B(x)=360-14x), तो (B(x-3)-B(x+4)) का मान क्या है?

If (B(x)=360-14x), what is the value of (B(x-3)-B(x+4))?

Explanation opens after your attempt
Correct Answer

C. (98)

Step 1

Concept

Over ((x+4)-(x-3)=7) steps the value decreases by \(14\times7=98\). So the difference is (98).

Step 2

Why this answer is correct

The correct answer is C. (98). Over ((x+4)-(x-3)=7) steps the value decreases by \(14\times7=98\). So the difference is (98).

Step 3

Exam Tip

((x+4)-(x-3)=7) चरणों में मान \(14\times7=98\) घटता है। इसलिए अंतर (98) है।

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Question 15/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

मॉडल (P(t)=p+16t) में (P(4)=125) और (P(s)=221) है। (s) क्या है?

In the model (P(t)=p+16t), (P(4)=125) and (P(s)=221). What is (s)?

Explanation opens after your attempt
Correct Answer

C. (10)

Step 1

Concept

From (P(4)=125), (p=61). From (61+16s=221), (s=10).

Step 2

Why this answer is correct

The correct answer is C. (10). From (P(4)=125), (p=61). From (61+16s=221), (s=10).

Step 3

Exam Tip

(P(4)=125) से (p=61) है। (61+16s=221) से (s=10) मिलता है।

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Question 16/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

मॉडल (R(t)=r-18t) में (R(3)=166) और (R(s)=40) है। (s) क्या है?

In the model (R(t)=r-18t), (R(3)=166) and (R(s)=40). What is (s)?

Explanation opens after your attempt
Correct Answer

B. (10)

Step 1

Concept

From (R(3)=166), (r=220). From (220-18s=40), (s=10).

Step 2

Why this answer is correct

The correct answer is B. (10). From (R(3)=166), (r=220). From (220-18s=40), (s=10).

Step 3

Exam Tip

(R(3)=166) से (r=220) है। (220-18s=40) से (s=10) मिलता है।

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Question 17/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

किस विकल्प में (y) (x) के बढ़ने पर (12) प्रति चरण बढ़ता है और (y(6)=101) है?

Which option makes (y) increase by (12) per step and has (y(6)=101)?

Explanation opens after your attempt
Correct Answer

A. (y=29+12x)

Step 1

Concept

The rate is (12), and (a+12(6)=101) gives (a=29). So (y=29+12x) is correct.

Step 2

Why this answer is correct

The correct answer is A. (y=29+12x). The rate is (12), and (a+12(6)=101) gives (a=29). So (y=29+12x) is correct.

Step 3

Exam Tip

दर (12) है और (a+12(6)=101) से (a=29) मिलता है। इसलिए (y=29+12x) सही है।

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Question 18/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

किस विकल्प में (y) (x) के बढ़ने पर (16) प्रति चरण घटता है और (y(5)=78) है?

Which option makes (y) decrease by (16) per step and has (y(5)=78)?

Explanation opens after your attempt
Correct Answer

B. (y=158-16x)

Step 1

Concept

The rate is (-16), and (a-16(5)=78) gives (a=158). So (y=158-16x) is correct.

Step 2

Why this answer is correct

The correct answer is B. (y=158-16x). The rate is (-16), and (a-16(5)=78) gives (a=158). So (y=158-16x) is correct.

Step 3

Exam Tip

दर (-16) है और (a-16(5)=78) से (a=158) मिलता है। इसलिए (y=158-16x) सही है।

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Question 19/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (M(t)=95+6t) और (N(t)=203-6t), तो (M(t)) कब (N(t)) से (24) अधिक होगा?

If (M(t)=95+6t) and (N(t)=203-6t), when will (M(t)) be (24) more than (N(t))?

Explanation opens after your attempt
Correct Answer

C. (t=11)

Step 1

Concept

The condition is (M(t)=N(t)+24). From (95+6t=227-6t), (12t=132) and (t=11).

Step 2

Why this answer is correct

The correct answer is C. (t=11). The condition is (M(t)=N(t)+24). From (95+6t=227-6t), (12t=132) and (t=11).

Step 3

Exam Tip

शर्त (M(t)=N(t)+24) है। (95+6t=227-6t) से (12t=132) और (t=11) मिलता है।

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Question 20/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (A(t)=280-13t) और (B(t)=65+5t), तो (A(t)) कब (B(t)) से (17) अधिक होगा?

If (A(t)=280-13t) and (B(t)=65+5t), when will (A(t)) be (17) more than (B(t))?

Explanation opens after your attempt
Correct Answer

B. (t=11)

Step 1

Concept

The condition is (280-13t=65+5t+17). This gives (198=18t) and (t=11).

Step 2

Why this answer is correct

The correct answer is B. (t=11). The condition is (280-13t=65+5t+17). This gives (198=18t) and (t=11).

Step 3

Exam Tip

शर्त (280-13t=65+5t+17) है। इससे (198=18t) और (t=11) मिलता है।

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Question 21/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (F(t)=78+rt) और (F(5)=F(13)-104), तो (r) क्या है?

If (F(t)=78+rt) and (F(5)=F(13)-104), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

(F(13)-F(5)=8r). From (8r=104), (r=13).

Step 2

Why this answer is correct

The correct answer is C. (13). (F(13)-F(5)=8r). From (8r=104), (r=13).

Step 3

Exam Tip

(F(13)-F(5)=8r) है। (8r=104) से (r=13) मिलता है।

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Question 22/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (G(t)=320-rt) और (G(4)=G(13)+144), तो (r) क्या है?

If (G(t)=320-rt) and (G(4)=G(13)+144), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (16)

Step 1

Concept

(G(4)-G(13)=9r). From (9r=144), (r=16).

Step 2

Why this answer is correct

The correct answer is C. (16). (G(4)-G(13)=9r). From (9r=144), (r=16).

Step 3

Exam Tip

(G(4)-G(13)=9r) है। (9r=144) से (r=16) मिलता है।

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Question 23/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

एक वस्तु की कीमत (P(n)=a+30n) है। यदि (P(5)=260), तो (P(13)) क्या है?

The price of an item is (P(n)=a+30n). If (P(5)=260), what is (P(13))?

Explanation opens after your attempt
Correct Answer

C. (500)

Step 1

Concept

From (a+150=260), (a=110). (P(13)=110+390=500).

Step 2

Why this answer is correct

The correct answer is C. (500). From (a+150=260), (a=110). (P(13)=110+390=500).

Step 3

Exam Tip

(a+150=260) से (a=110) है। (P(13)=110+390=500) है।

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Question 24/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

एक मशीन का मूल्य (V(y)=c-4200y) है। यदि (V(4)=53200), तो (V(11)) क्या होगा?

A machine's value is (V(y)=c-4200y). If (V(4)=53200), what will (V(11)) be?

Explanation opens after your attempt
Correct Answer

A. (23800)

Step 1

Concept

From (c-16800=53200), (c=70000). (V(11)=70000-46200=23800).

Step 2

Why this answer is correct

The correct answer is A. (23800). From (c-16800=53200), (c=70000). (V(11)=70000-46200=23800).

Step 3

Exam Tip

(c-16800=53200) से (c=70000) है। (V(11)=70000-46200=23800) है।

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Question 25/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=56+8x), तो (x) का कौन सा मान (y) को (15x) के बराबर बनाता है?

If (y=56+8x), which value of (x) makes (y) equal to (15x)?

Explanation opens after your attempt
Correct Answer

C. (x=8)

Step 1

Concept

The condition is (56+8x=15x). This gives (56=7x) and (x=8).

Step 2

Why this answer is correct

The correct answer is C. (x=8). The condition is (56+8x=15x). This gives (56=7x) and (x=8).

Step 3

Exam Tip

शर्त (56+8x=15x) है। इससे (56=7x) और (x=8) मिलता है।

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Question 26/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=255-14x), तो (x) का कौन सा मान (y) को (3x) के बराबर बनाता है?

If (y=255-14x), which value of (x) makes (y) equal to (3x)?

Explanation opens after your attempt
Correct Answer

B. (x=15)

Step 1

Concept

The condition is (255-14x=3x). This gives (255=17x) and (x=15).

Step 2

Why this answer is correct

The correct answer is B. (x=15). The condition is (255-14x=3x). This gives (255=17x) and (x=15).

Step 3

Exam Tip

शर्त (255-14x=3x) है। इससे (255=17x) और (x=15) मिलता है।

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Question 27/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (L(t)=7t+41), तो (L(6t)-L(2t)) क्या है?

If (L(t)=7t+41), what is (L(6t)-L(2t))?

Explanation opens after your attempt
Correct Answer

C. (28t)

Step 1

Concept

(L(6t)=42t+41) and (L(2t)=14t+41). The difference is (28t).

Step 2

Why this answer is correct

The correct answer is C. (28t). (L(6t)=42t+41) and (L(2t)=14t+41). The difference is (28t).

Step 3

Exam Tip

(L(6t)=42t+41) और (L(2t)=14t+41) है। अंतर (28t) है।

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Question 28/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (K(t)=350-10t), तो (K(3t)-K(7t)) क्या है?

If (K(t)=350-10t), what is (K(3t)-K(7t))?

Explanation opens after your attempt
Correct Answer

B. (40t)

Step 1

Concept

(K(3t)=350-30t) and (K(7t)=350-70t). The difference is (40t).

Step 2

Why this answer is correct

The correct answer is B. (40t). (K(3t)=350-30t) and (K(7t)=350-70t). The difference is (40t).

Step 3

Exam Tip

(K(3t)=350-30t) और (K(7t)=350-70t) है। अंतर (40t) है।

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Question 29/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (Y(x)=a+10x) रेखीय वृद्धि है और (Y(5)+Y(11)=250), तो (a) क्या है?

If (Y(x)=a+10x) is linear growth and (Y(5)+Y(11)=250), what is (a)?

Explanation opens after your attempt
Correct Answer

B. (45)

Step 1

Concept

(Y(5)+Y(11)=(a+50)+(a+110)=2a+160). From (2a+160=250), (a=45).

Step 2

Why this answer is correct

The correct answer is B. (45). (Y(5)+Y(11)=(a+50)+(a+110)=2a+160). From (2a+160=250), (a=45).

Step 3

Exam Tip

(Y(5)+Y(11)=(a+50)+(a+110)=2a+160) है। (2a+160=250) से (a=45) मिलता है।

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Question 30/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (Z(x)=b-15x) रेखीय क्षय है और (Z(4)+Z(8)=160), तो (b) क्या है?

If (Z(x)=b-15x) is linear decay and (Z(4)+Z(8)=160), what is (b)?

Explanation opens after your attempt
Correct Answer

B. (170)

Step 1

Concept

(Z(4)+Z(8)=(b-60)+(b-120)=2b-180). From (2b-180=160), (b=170).

Step 2

Why this answer is correct

The correct answer is B. (170). (Z(4)+Z(8)=(b-60)+(b-120)=2b-180). From (2b-180=160), (b=170).

Step 3

Exam Tip

(Z(4)+Z(8)=(b-60)+(b-120)=2b-180) है। (2b-180=160) से (b=170) मिलता है।

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Question 31/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (p(x)=60+9x) और (q(x)=14x-10), तो (p(x)) और (q(x)) कब बराबर होंगे?

If (p(x)=60+9x) and (q(x)=14x-10), when will (p(x)) and (q(x)) be equal?

Explanation opens after your attempt
Correct Answer

C. (x=14)

Step 1

Concept

Setting (60+9x=14x-10) gives (70=5x). Therefore (x=14).

Step 2

Why this answer is correct

The correct answer is C. (x=14). Setting (60+9x=14x-10) gives (70=5x). Therefore (x=14).

Step 3

Exam Tip

(60+9x=14x-10) रखने पर (70=5x) मिलता है। इसलिए (x=14) है।

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Question 32/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (p(x)=330-18x) और (q(x)=78+3x), तो (p(x)=q(x)) के लिए (x) क्या है?

If (p(x)=330-18x) and (q(x)=78+3x), what is (x) for (p(x)=q(x))?

Explanation opens after your attempt
Correct Answer

C. (x=12)

Step 1

Concept

From (330-18x=78+3x), (252=21x) and (x=12). Equate the growth and decay models.

Step 2

Why this answer is correct

The correct answer is C. (x=12). From (330-18x=78+3x), (252=21x) and (x=12). Equate the growth and decay models.

Step 3

Exam Tip

(330-18x=78+3x) से (252=21x) और (x=12) है। वृद्धि और क्षय मॉडल को बराबर करें।

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Question 33/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

किस (k) के लिए (y=90+(k-11)x) रेखीय वृद्धि दिखाएगा?

For which (k) will (y=90+(k-11)x) show linear growth?

Explanation opens after your attempt
Correct Answer

C. (k>11)

Step 1

Concept

For linear growth the coefficient of (x) must be positive. From (k-11>0), (k>11).

Step 2

Why this answer is correct

The correct answer is C. (k>11). For linear growth the coefficient of (x) must be positive. From (k-11>0), (k>11).

Step 3

Exam Tip

रेखीय वृद्धि के लिए (x) का गुणांक धनात्मक होना चाहिए। (k-11>0) से (k>11) मिलता है।

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Question 34/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

किस (k) के लिए (y=410-(k-8)x) रेखीय क्षय दिखाएगा?

For which (k) will (y=410-(k-8)x) show linear decay?

Explanation opens after your attempt
Correct Answer

A. (k>8)

Step 1

Concept

For decay the effective coefficient must be negative. From (-(k-8)<0), (k>8).

Step 2

Why this answer is correct

The correct answer is A. (k>8). For decay the effective coefficient must be negative. From (-(k-8)<0), (k>8).

Step 3

Exam Tip

क्षय के लिए प्रभावी गुणांक ऋणात्मक चाहिए। (-(k-8)<0) से (k>8) मिलता है।

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Question 35/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (R(x)=140+mx) और (R(14)-R(7)=126), तो (R(0)) क्या है?

If (R(x)=140+mx) and (R(14)-R(7)=126), what is (R(0))?

Explanation opens after your attempt
Correct Answer

C. (140)

Step 1

Concept

Here (R(0)=140) is directly the initial value. The difference gives (m=18), but the initial value remains the same.

Step 2

Why this answer is correct

The correct answer is C. (140). Here (R(0)=140) is directly the initial value. The difference gives (m=18), but the initial value remains the same.

Step 3

Exam Tip

यहां (R(0)=140) सीधे आरंभिक मान है। अंतर से (m=18) मिलता है पर आरंभिक मान वही रहता है।

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Question 36/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (S(x)=s-13x) और (S(6)-S(15)=117), तो कौन सा निष्कर्ष सही है?

If (S(x)=s-13x) and (S(6)-S(15)=117), which conclusion is correct?

Explanation opens after your attempt
Correct Answer

A. हर (s) के लिए शर्त सही हैThe condition is true for every (s)

Step 1

Concept

(S(6)-S(15)=(s-78)-(s-195)=117). Therefore (s) can be any value.

Step 2

Why this answer is correct

The correct answer is A. हर (s) के लिए शर्त सही है / The condition is true for every (s). (S(6)-S(15)=(s-78)-(s-195)=117). Therefore (s) can be any value.

Step 3

Exam Tip

(S(6)-S(15)=(s-78)-(s-195)=117) है। इसलिए (s) कोई भी हो सकता है।

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Question 37/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (A(t)=72+8t) और (B(t)=111+15t), तो (B(t)-A(t)) किस प्रकार बदलता है?

If (A(t)=72+8t) and (B(t)=111+15t), how does (B(t)-A(t)) change?

Explanation opens after your attempt
Correct Answer

A. हर चरण (7) बढ़ता हैIt increases by (7) each step

Step 1

Concept

(B(t)-A(t)=39+7t). Its coefficient is (7), so the difference increases.

Step 2

Why this answer is correct

The correct answer is A. हर चरण (7) बढ़ता है / It increases by (7) each step. (B(t)-A(t)=39+7t). Its coefficient is (7), so the difference increases.

Step 3

Exam Tip

(B(t)-A(t)=39+7t) है। इसका गुणांक (7) है इसलिए अंतर बढ़ता है।

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Question 38/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (C(t)=390-11t) और (D(t)=270-22t), तो (C(t)-D(t)) किस प्रकार बदलता है?

If (C(t)=390-11t) and (D(t)=270-22t), how does (C(t)-D(t)) change?

Explanation opens after your attempt
Correct Answer

A. हर चरण (11) बढ़ता हैIt increases by (11) each step

Step 1

Concept

(C(t)-D(t)=120+11t). Therefore the difference of the two decay models increases.

Step 2

Why this answer is correct

The correct answer is A. हर चरण (11) बढ़ता है / It increases by (11) each step. (C(t)-D(t)=120+11t). Therefore the difference of the two decay models increases.

Step 3

Exam Tip

(C(t)-D(t)=120+11t) है। इसलिए दोनों क्षय मॉडलों का अंतर बढ़ता है।

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Question 39/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=96+24x), तो (x) में कितनी वृद्धि करने पर (y) (192) बढ़ेगा?

If (y=96+24x), by how much must (x) increase for (y) to increase by (192)?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

The total increase is \(24\Delta x\). From \(24\Delta x=192\), \(\Delta x=8\).

Step 2

Why this answer is correct

The correct answer is C. (8). The total increase is \(24\Delta x\). From \(24\Delta x=192\), \(\Delta x=8\).

Step 3

Exam Tip

कुल वृद्धि \(24\Delta x\) होगी। \(24\Delta x=192\) से \(\Delta x=8\) मिलता है।

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Question 40/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=480-30x), तो (y) में (210) की कमी के लिए (x) कितना बढ़ना चाहिए?

If (y=480-30x), by how much should (x) increase for (y) to decrease by (210)?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

The total decrease is \(30\Delta x\). From \(30\Delta x=210\), \(\Delta x=7\).

Step 2

Why this answer is correct

The correct answer is C. (7). The total decrease is \(30\Delta x\). From \(30\Delta x=210\), \(\Delta x=7\).

Step 3

Exam Tip

कुल कमी \(30\Delta x\) होगी। \(30\Delta x=210\) से \(\Delta x=7\) मिलता है।

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Question 41/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (f(x)=12x+50), तो (f(5x)-f(2x)) कब (180) होगा?

If (f(x)=12x+50), when will (f(5x)-f(2x)) be (180)?

Explanation opens after your attempt
Correct Answer

B. (x=5)

Step 1

Concept

(f(5x)-f(2x)=(60x+50)-(24x+50)=36x). From (36x=180), (x=5).

Step 2

Why this answer is correct

The correct answer is B. (x=5). (f(5x)-f(2x)=(60x+50)-(24x+50)=36x). From (36x=180), (x=5).

Step 3

Exam Tip

(f(5x)-f(2x)=(60x+50)-(24x+50)=36x) है। (36x=180) से (x=5) है।

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Question 42/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (g(x)=420-14x), तो (g(2x)-g(6x)) कब (224) होगा?

If (g(x)=420-14x), when will (g(2x)-g(6x)) be (224)?

Explanation opens after your attempt
Correct Answer

B. (x=4)

Step 1

Concept

(g(2x)-g(6x)=(420-28x)-(420-84x)=56x). From (56x=224), (x=4).

Step 2

Why this answer is correct

The correct answer is B. (x=4). (g(2x)-g(6x)=(420-28x)-(420-84x)=56x). From (56x=224), (x=4).

Step 3

Exam Tip

(g(2x)-g(6x)=(420-28x)-(420-84x)=56x) है। (56x=224) से (x=4) है।

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Question 43/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (P(t)=90+8t), तो (P(7)+P(19)) किस एक (P(k)) के दोगुने के बराबर है?

If (P(t)=90+8t), (P(7)+P(19)) is equal to twice which (P(k))?

Explanation opens after your attempt
Correct Answer

C. (P(13))

Step 1

Concept

In a linear model the midpoint of (7) and (19) is (13). Therefore (P(7)+P(19)=2P(13)).

Step 2

Why this answer is correct

The correct answer is C. (P(13)). In a linear model the midpoint of (7) and (19) is (13). Therefore (P(7)+P(19)=2P(13)).

Step 3

Exam Tip

रेखीय मॉडल में (7) और (19) का मध्य (13) है। इसलिए (P(7)+P(19)=2P(13)) होता है।

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Question 44/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (Q(t)=420-12t), तो (Q(6)+Q(18)) किस एक (Q(k)) के दोगुने के बराबर है?

If (Q(t)=420-12t), (Q(6)+Q(18)) is equal to twice which (Q(k))?

Explanation opens after your attempt
Correct Answer

C. (Q(12))

Step 1

Concept

In a linear model the midpoint of (6) and (18) is (12). Therefore (Q(6)+Q(18)=2Q(12)).

Step 2

Why this answer is correct

The correct answer is C. (Q(12)). In a linear model the midpoint of (6) and (18) is (12). Therefore (Q(6)+Q(18)=2Q(12)).

Step 3

Exam Tip

रेखीय मॉडल में (6) और (18) का मध्य (12) है। इसलिए (Q(6)+Q(18)=2Q(12)) होता है।

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Question 45/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=220+ax) में (x=9) से (x=17) तक (y) (144) बढ़ता है, तो (a) क्या है?

If in (y=220+ax), (y) increases by (144) from (x=9) to (x=17), what is (a)?

Explanation opens after your attempt
Correct Answer

C. (18)

Step 1

Concept

The change in (x) is (8). From (8a=144), (a=18).

Step 2

Why this answer is correct

The correct answer is C. (18). The change in (x) is (8). From (8a=144), (a=18).

Step 3

Exam Tip

(x) में परिवर्तन (8) है। (8a=144) से (a=18) मिलता है।

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Question 46/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (y=420-bx) में (x=8) से (x=16) तक (y) (152) घटता है, तो (b) क्या है?

If in (y=420-bx), (y) decreases by (152) from (x=8) to (x=16), what is (b)?

Explanation opens after your attempt
Correct Answer

C. (19)

Step 1

Concept

The change in (x) is (8). The total decrease is (8b=152), so (b=19).

Step 2

Why this answer is correct

The correct answer is C. (19). The change in (x) is (8). The total decrease is (8b=152), so (b=19).

Step 3

Exam Tip

(x) में परिवर्तन (8) है। कुल कमी (8b=152) है इसलिए (b=19) है।

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Question 47/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (A(t)=70+9t) और (B(t)=118+5t), तो किस (t) पर (A(t)) (B(t)) से (8) अधिक होगा?

If (A(t)=70+9t) and (B(t)=118+5t), at what (t) will (A(t)) be (8) more than (B(t))?

Explanation opens after your attempt
Correct Answer

C. (t=14)

Step 1

Concept

The condition is (70+9t=118+5t+8). This gives (4t=56) and (t=14).

Step 2

Why this answer is correct

The correct answer is C. (t=14). The condition is (70+9t=118+5t+8). This gives (4t=56) and (t=14).

Step 3

Exam Tip

शर्त (70+9t=118+5t+8) है। इससे (4t=56) और (t=14) मिलता है।

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Question 48/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (C(t)=350-14t) और (D(t)=80+4t), तो किस (t) पर (C(t)) (D(t)) से (18) कम होगा?

If (C(t)=350-14t) and (D(t)=80+4t), at what (t) will (C(t)) be (18) less than (D(t))?

Explanation opens after your attempt
Correct Answer

C. (t=16)

Step 1

Concept

The condition is (350-14t=80+4t-18). This gives (288=18t) and (t=16).

Step 2

Why this answer is correct

The correct answer is C. (t=16). The condition is (350-14t=80+4t-18). This gives (288=18t) and (t=16).

Step 3

Exam Tip

शर्त (350-14t=80+4t-18) है। इससे (288=18t) और (t=16) मिलता है।

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Question 49/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (f(t)=a+9t) और (f(3), f(7), f(11)) का योग (279) है, तो (a) क्या है?

If (f(t)=a+9t) and the sum of (f(3), f(7), f(11)) is (279), what is (a)?

Explanation opens after your attempt
Correct Answer

B. (36)

Step 1

Concept

The sum is ((a+27)+(a+63)+(a+99)=3a+189). From (3a+189=279), (a=30), so option (A) is correct.

Step 2

Why this answer is correct

The correct answer is B. (36). The sum is ((a+27)+(a+63)+(a+99)=3a+189). From (3a+189=279), (a=30), so option (A) is correct.

Step 3

Exam Tip

योग ((a+27)+(a+63)+(a+99)=3a+189) है। (3a+189=279) से (a=30) नहीं बल्कि विकल्प (A) है।

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Question 50/50 Expert Mathematics Introduction to Polynomials Linear growth and decay Class 9 Level 37

यदि (g(t)=b-8t) और (g(5), g(9), g(13)) का योग (288) है, तो (b) क्या है?

If (g(t)=b-8t) and the sum of (g(5), g(9), g(13)) is (288), what is (b)?

Explanation opens after your attempt
Correct Answer

A. (144)

Step 1

Concept

The sum is ((b-40)+(b-72)+(b-104)=3b-216). From (3b-216=288), (b=168), so option (D) is correct.

Step 2

Why this answer is correct

The correct answer is A. (144). The sum is ((b-40)+(b-72)+(b-104)=3b-216). From (3b-216=288), (b=168), so option (D) is correct.

Step 3

Exam Tip

योग ((b-40)+(b-72)+(b-104)=3b-216) है। (3b-216=288) से (b=168) नहीं बल्कि विकल्प (D) है।

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