एक बस मार्ग पर पहले पड़ाव की दूरी (3) किमी है और हर अगला पड़ाव (2.5) किमी आगे है। (18)वें पड़ाव की दूरी क्या होगी?
On a bus route, the first stop is (3) km away and each next stop is (2.5) km farther. What is the distance of the (18)th stop?
#ap
#word-problem
#decimal
#nth-term
A (43.5) किमी / (43.5) km
B (45.5) किमी / (45.5) km
C (47.5) किमी / (47.5) km
D (49.5) किमी / (49.5) km
Explanation opens after your attempt
Correct Answer
B. (45.5) किमी / (45.5) km
Step 1
Concept
(a=3) and (d=2.5) so \(a_{18}=3+17\times2.5=45.5\) km. In word problems, the first value is (a).
Step 2
Why this answer is correct
The correct answer is B. (45.5) किमी / (45.5) km. (a=3) and (d=2.5) so \(a_{18}=3+17\times2.5=45.5\) km. In word problems, the first value is (a).
Step 3
Exam Tip
(a=3) और (d=2.5) हैं इसलिए \(a_{18}=3+17\times2.5=45.5\) किमी। शब्द-प्रश्न में पहला मान (a) होता है।
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एक पौधे की ऊंचाई पहले दिन (25) सेमी है और रोज (1.5) सेमी बढ़ती है। (30)वें दिन ऊंचाई कितनी होगी?
A plant is (25) cm tall on the first day and grows (1.5) cm daily. What will be its height on the (30)th day?
#ap
#word-problem
#decimal
#nth-term
A (66.5) सेमी / (66.5) cm
B (68.5) सेमी / (68.5) cm
C (70) सेमी / (70) cm
D (71.5) सेमी / (71.5) cm
Explanation opens after your attempt
Correct Answer
B. (68.5) सेमी / (68.5) cm
Step 1
Concept
\(a_{30}=25+29\times1.5=68.5\) cm. Treat the first day as \(a_1\), not day (0).
Step 2
Why this answer is correct
The correct answer is B. (68.5) सेमी / (68.5) cm. \(a_{30}=25+29\times1.5=68.5\) cm. Treat the first day as \(a_1\), not day (0).
Step 3
Exam Tip
\(a_{30}=25+29\times1.5=68.5\) सेमी। पहले दिन को \(a_1\) मानें, दिन (0) नहीं।
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किस दशमलव संख्या का स्थान संख्या रेखा पर \(\frac{13}{8}\) के बराबर है?
Which decimal number has the same position as \(\frac{13}{8}\) on the number line?
#polynomials
#number-line
#decimal
#fraction-conversion
A (1.625)
B (1.375)
C (1.75)
D (1.875)
Explanation opens after your attempt
Correct Answer
A. (1.625)
Step 1
Concept
\(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.
Step 2
Why this answer is correct
The correct answer is A. (1.625). \(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.
Step 3
Exam Tip
\(\frac{13}{8}=1.625\), इसलिए दोनों एक ही बिंदु दर्शाते हैं। भिन्न को दशमलव में बदलकर स्थान पहचानें।
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संख्या रेखा पर (2.25) किस भिन्न के बराबर है?
Which fraction is equal to (2.25) on the number line?
#decimal
#fraction
#number-line
A \(\frac{9}{4}\)
B \(\frac{4}{9}\)
C \(\frac{5}{4}\)
D \(\frac{11}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9}{4}\)
Step 1
Concept
\(2.25=\frac{225}{100}=\frac{9}{4}\). Converting a decimal to simplest fraction gives the correct point.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{4}\). \(2.25=\frac{225}{100}=\frac{9}{4}\). Converting a decimal to simplest fraction gives the correct point.
Step 3
Exam Tip
\(2.25=\frac{225}{100}=\frac{9}{4}\)। दशमलव को सरल भिन्न में बदलना सही बिंदु देता है।
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संख्या रेखा पर (3.5) किस भिन्न के बराबर है?
Which fraction is equal to (3.5) on the number line?
#decimal
#fraction
#number-line
A \(\frac{7}{2}\)
B \(\frac{5}{3}\)
C \(\frac{3}{5}\)
D \(\frac{2}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{2}\)
Step 1
Concept
\(3.5=\frac{35}{10}=\frac{7}{2}\). Convert the decimal to a simplest fraction to fix its position.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{2}\). \(3.5=\frac{35}{10}=\frac{7}{2}\). Convert the decimal to a simplest fraction to fix its position.
Step 3
Exam Tip
\(3.5=\frac{35}{10}=\frac{7}{2}\)। दशमलव को सरल भिन्न में बदलकर सही स्थान तय करें।
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संख्या रेखा पर \(-\frac{5}{2}\) का स्थान किसके बीच होगा?
Between which points will \(-\frac{5}{2}\) lie on the number line?
#negative-fraction
#decimal
#number-line
A -(3) और (-2) / (-3) and (-2)
B -(2) और (-1) / (-2) and (-1)
C (2) और (3) / (2) and (3)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. -(3) और (-2) / (-3) and (-2)
Step 1
Concept
-\(\frac{5}{2}=-2.5\), so it lies between (-3) and (-2). Place negative values to the left of (0).
Step 2
Why this answer is correct
The correct answer is A. -(3) और (-2) / (-3) and (-2). -\(\frac{5}{2}=-2.5\), so it lies between (-3) and (-2). Place negative values to the left of (0).
Step 3
Exam Tip
-\(\frac{5}{2}=-2.5\), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक मान को (0) के बाईं ओर रखें।
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संख्या रेखा पर \(\frac{5}{2}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\frac{5}{2}\) lie on the number line?
#fraction
#decimal
#number-line
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
\( \frac{5}{2}=2.5\), so it lies between (2) and (3). Converting a fraction to decimal is an easy method.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). \( \frac{5}{2}=2.5\), so it lies between (2) and (3). Converting a fraction to decimal is an easy method.
Step 3
Exam Tip
\(\frac{5}{2}=2.5\), इसलिए यह (2) और (3) के बीच है। भिन्न को दशमलव रूप में बदलना आसान तरीका है।
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संख्या रेखा पर (0.2) किस भिन्न के बराबर है?
Which fraction is equal to (0.2) on the number line?
#decimal
#fraction
#number-line
A \(\frac{1}{5}\)
B \(\frac{1}{2}\)
C \(\frac{2}{5}\)
D \(\frac{5}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{5}\)
Step 1
Concept
\(0.2=\frac{2}{10}=\frac{1}{5}\). Use decimal place value to form the simplest fraction.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{5}\). \(0.2=\frac{2}{10}=\frac{1}{5}\). Use decimal place value to form the simplest fraction.
Step 3
Exam Tip
\(0.2=\frac{2}{10}=\frac{1}{5}\)। दशमलव स्थान देखकर सरल भिन्न बनाइए।
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संख्या रेखा पर (1.25) किस भिन्न के बराबर है?
Which fraction is equal to (1.25) on the number line?
#decimal
#fraction
#number-line
A \(\frac{5}{4}\)
B \(\frac{4}{5}\)
C \(\frac{3}{4}\)
D \(\frac{7}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{4}\)
Step 1
Concept
\(1.25=\frac{125}{100}=\frac{5}{4}\). Convert a decimal to a fraction to locate the point correctly.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{4}\). \(1.25=\frac{125}{100}=\frac{5}{4}\). Convert a decimal to a fraction to locate the point correctly.
Step 3
Exam Tip
\(1.25=\frac{125}{100}=\frac{5}{4}\)। दशमलव को भिन्न में बदलकर सही बिंदु पहचानें।
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संख्या रेखा पर (2) और (3) के बीच कौन-सी संख्या आती है?
Which number lies between (2) and (3) on the number line?
#between-numbers
#decimal
#number-line
A (2.5)
B (3.5)
C (1.5)
D (4.5)
Explanation opens after your attempt
Step 1
Concept
(2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.
Step 2
Why this answer is correct
The correct answer is A. (2.5). (2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.
Step 3
Exam Tip
(2.5), (2) और (3) के बीच आता है। बीच की संख्या दोनों सिरों से छोटी-बड़ी तुलना करके पहचानें।
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कौन सा विकल्प (0.2020020002...) के बारे में सही है?
Which option is correct about (0.2020020002...)?
#non-repeating-decimal
#irrational-number
#decimal
A यह अपरिमेय संख्या है / It is an irrational number
B यह सांत दशमलव है / It is a terminating decimal
C यह आवर्ती दशमलव है / It is a repeating decimal
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय संख्या है / It is an irrational number
Step 1
Concept
It has no fixed repeating block and the decimal is infinite. So it is irrational.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय संख्या है / It is an irrational number. It has no fixed repeating block and the decimal is infinite. So it is irrational.
Step 3
Exam Tip
इसमें कोई निश्चित आवर्ती समूह नहीं है और दशमलव अनंत है। इसलिए यह अपरिमेय है।
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कौन सा दशमलव अपरिमेय संख्या दिखाता है?
Which decimal shows an irrational number?
#irrational-decimal
#non-repeating
#decimal
A (0.3030030003...)
B (0.303030...)
C (0.303)
D (0.3000...)
Explanation opens after your attempt
Correct Answer
A. (0.3030030003...)
Step 1
Concept
The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.
Step 2
Why this answer is correct
The correct answer is A. (0.3030030003...). The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.
Step 3
Exam Tip
पहला दशमलव अनंत और अनावर्ती है। अनंत अनावर्ती दशमलव अपरिमेय होता है।
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कौन सा विकल्प सांत दशमलव है?
Which option is a terminating decimal?
#terminating-decimal
#rational-numbers
#decimal
A (7.03125)
B (7.030303...)
C (7.031031003...)
D \(\pi\)
Explanation opens after your attempt
Correct Answer
A. (7.03125)
Step 1
Concept
(7.03125) ends after a finite number of digits. A terminating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (7.03125). (7.03125) ends after a finite number of digits. A terminating decimal is rational.
Step 3
Exam Tip
(7.03125) कुछ अंकों के बाद समाप्त हो जाता है। सांत दशमलव परिमेय होता है।
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कौन सा विकल्प अनंत लेकिन आवर्ती दशमलव है?
Which option is a non terminating but repeating decimal?
#repeating-decimal
#rational-numbers
#decimal
A (4.565656...)
B (4.567891011...)
C (4.56)
D \(\sqrt{4}\)
Explanation opens after your attempt
Correct Answer
A. (4.565656...)
Step 1
Concept
The block (56) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (4.565656...). The block (56) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(56) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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दशमलव (3.272727...) किस प्रकार की संख्या है?
What type of number is the decimal (3.272727...)?
#recurring-decimal
#rational-numbers
#decimal
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्णांक / Integer
D अवास्तविक संख्या / Non real number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The block (27) repeats so it is a recurring decimal. Every recurring decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The block (27) repeats so it is a recurring decimal. Every recurring decimal is rational.
Step 3
Exam Tip
इसमें (27) बार-बार दोहरता है इसलिए यह आवर्ती दशमलव है। हर आवर्ती दशमलव परिमेय होता है।
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यदि किसी संख्या का दशमलव विस्तार समाप्त हो जाता है तो वह कैसी संख्या होती है?
If the decimal expansion of a number terminates then what type of number is it?
#terminating-decimal
#rational-numbers
#decimal
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D सिर्फ प्राकृतिक संख्या / Natural number only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
A terminating decimal can be written as a fraction. Hence it is a rational number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. A terminating decimal can be written as a fraction. Hence it is a rational number.
Step 3
Exam Tip
सांत दशमलव को भिन्न के रूप में लिखा जा सकता है। इसलिए यह परिमेय संख्या होती है।
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\(0.\overline{7}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{7}\)?
#repeating-decimal
#rational-number
#decimal
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 3
Exam Tip
\(0.\overline{7}\) आवर्ती दशमलव है। हर आवर्ती दशमलव परिमेय होता है।
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कौन सा दशमलव परिमेय संख्या दिखाता है?
Which decimal represents a rational number?
#repeating-decimal
#rational-numbers
#decimal
A (2.454545...)
B (1.010010001...)
C (3.14159265...) बिना आवर्तन / (3.14159265...) without repetition
D (0.1234567891011...)
Explanation opens after your attempt
Correct Answer
A. (2.454545...)
Step 1
Concept
The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (2.454545...). The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(45) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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यदि ग्राफ (x)-अक्ष को (2.5) पर काटता है तो सही शून्यक कौन सा है?
If a graph cuts the (x)-axis at (2.5), which is the correct zero?
#zero-vs-point
#decimal
#graph
A (2.5)
B ((2.5,0))
C (0)
D ((0,2.5))
Explanation opens after your attempt
Step 1
Concept
A zero is a number not a point. The point is ((2.5,0)) but the zero is (2.5).
Step 2
Why this answer is correct
The correct answer is A. (2.5). A zero is a number not a point. The point is ((2.5,0)) but the zero is (2.5).
Step 3
Exam Tip
शून्यक संख्या होता है बिंदु नहीं। बिंदु ((2.5,0)) है लेकिन शून्यक (2.5) है।
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कौन-सा विकल्प \(\sqrt{5}\) की अपरिमेयता के लिए केवल अधूरा संकेत है, पूर्ण प्रमाण नहीं?
Which option is only an incomplete hint for the irrationality of \(\sqrt{5}\), not a full proof?
#real-numbers
#root5
#decimal
#proof-quality
A \(\sqrt{5}\) का दशमलव समाप्त नहीं दिखता / The decimal of \(\sqrt{5}\) does not seem to terminate
B मानें \(\sqrt{5}=\frac{p}{q}\) / Assume \(\sqrt{5}=\frac{p}{q}\)
C \(p^2=5q^2\)
D (p) और (q) दोनों (5) से विभाज्य निकलते हैं / Both (p) and (q) turn out divisible by (5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\) का दशमलव समाप्त नहीं दिखता / The decimal of \(\sqrt{5}\) does not seem to terminate
Step 1
Concept
Looking at the decimal only gives an idea.
Step 2
Why this answer is correct
A complete proof assumes rationality and shows the common-factor contradiction.
Step 3
Exam Tip
In exams, write a proof, not a guess. चरण 1: दशमलव को देखकर केवल अनुमान बनता है। चरण 2: पूर्ण प्रमाण में परिमेय मानकर साझा गुणनखंड का विरोधाभास दिखाते हैं। चरण 3: परीक्षा में अनुमान नहीं, प्रमाण लिखें।
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कौन-सा विकल्प अपरिमेय संख्या की सही पहचान बताता है?
Which option gives the correct identification of an irrational number?
#real-numbers
#irrational-definition
#decimal
A जिसका दशमलव समाप्त हो / Its decimal terminates
B जिसका दशमलव आवर्ती हो / Its decimal recurs
C जिसका दशमलव अनवसानी और अनावर्ती हो / Its decimal is non-terminating and non-recurring
D जो हमेशा ऋणात्मक हो / It is always negative
Explanation opens after your attempt
Correct Answer
C. जिसका दशमलव अनवसानी और अनावर्ती हो / Its decimal is non-terminating and non-recurring
Step 1
Concept
The decimal of an irrational number does not terminate.
Step 2
Why this answer is correct
It also does not repeat in a fixed pattern.
Step 3
Exam Tip
Decimal expansion is a useful way to identify irrational numbers. चरण 1: अपरिमेय संख्या का दशमलव खत्म नहीं होता। चरण 2: उसमें कोई निश्चित दोहराव भी नहीं होता। चरण 3: दशमलव विस्तार देखकर अपरिमेय संख्या पहचानना आसान हो जाता है।
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