Level 5 • 50/50 questions • 35 seconds per question.
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What is the value of \(2^5+2^4\)?
A. 48
(32+16=48)। पहले घात निकालें। / (32+16=48). Evaluate powers first.
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What is the value of \(3^4-3^2\)?
A. 63
(81-9=72)। घात पहले हल करें। / (81-9=72). Solve powers first.
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What is the value of \(4^3 \div 4\)?
B. 16
\(4^{3-1}=4^2=16\)। / \(4^{3-1}=4^2=16\).
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What is the value of \(5^2 \times 5^2\)?
C. 625
\(5^4=625\)। समान आधार पर घात जोड़ें। / \(5^4=625\). Add exponents for same base.
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What is the value of \(6^0+1\)?
D. 2
\(6^0=1\)। इसलिए उत्तर 2 है। / \(6^0=1\). Hence the answer is 2.
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If \(x^2=144\) then what is the positive value of (x)?
A. 12
\(12^2=144\)। वर्गमूल पहचानें। / \(12^2=144\). Recognize perfect squares.
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What is the value of \(7^2+5^2\)?
B. 74
(49+25=74)। / (49+25=74).
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What is the value of \(8^2-2^3\)?
C. 56
(64-8=56)। / (64-8=56).
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What is the value of \(9^2 \div 9^2\)?
D. 1
समान पदों का भाग 1 होता है। / Division of equal terms gives 1.
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What is the value of (\(2^2\)3)?
A. 64
\(2^{6}=64\)। घातों का गुणा करें। / \(2^{6}=64\). Multiply exponents.
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What is the value of \(10^3-10^2\)?
A. 800
(1000-100=900)। / (1000-100=900).
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If \(a^3=216\) then what is (a)?
B. 6
\(6^3=216\)। घनमूल लें। / \(6^3=216\). Take the cube root.
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What is the value of \(11^2+3^2\)?
C. 130
(121+9=130)। / (121+9=130).
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What is the value of \(12^2-4^2\)?
D. 128
(144-16=128)। / (144-16=128).
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What is the value of \(2^7 \div 2^5\)?
A. 4
\(2^{2}=4\)। घात घटाएँ। / \(2^{2}=4\). Subtract exponents.
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What is the value of \(14^2+1\)?
C. 197
(196+1=197)। / (196+1=197).
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What is the value of \(15^2-25\)?
D. 200
(225-25=200)। / (225-25=200).
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Find the value of \((17^2 - 8^2)\).
C. 225
कारण: किसी भी दो संख्याओं के वर्गों का अन्तर नीचे के सूत्र से सरल होता है: \(a^2 - b^2 = (a-b)(a+b)\). यहाँ \(a=17\) और \(b=8\)। इसलिए \((17^2 - 8^2) = (17-8)(17+8) = 9\times25 = 225\). गलत विकल्पों का संक्षिप्त विश्लेषण: विकल्प A (81) आम गलती है जब कोई विद्यार्थी गलती से \((17-8)^2\) निकाल देता है; विकल्प B (353) तब बनता है जब \(17^2 + 8^2\) लिया जाए; विकल्प D (233) एक साधारण अंकगणितीय त्रुटि है (जैसे 289-56 या अशुद्ध घटाव). परीक्षा सुझाव: तेज़ गणना के लिए \(a^2-b^2\) पहचानें और इसे \((a-b)(a+b)\) में बदलकर गुणा करें। / Reason: Use the difference of squares identity \(a^2 - b^2 = (a-b)(a+b)\). With \(a=17\) and \(b=8\), \((17^2 - 8^2) = (17-8)(17+8) = 9\times25 = 225\). Brief notes on wrong options: option A (81) results from the mistake of computing \((17-8)^2\); option B (353) is the sum \(17^2+8^2\); option D (233) is a likely arithmetic subtraction error. Exam tip: Recognise and apply the identity \(a^2-b^2=(a-b)(a+b)\) to simplify such problems quickly and avoid careless subtraction mistakes.
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What is the value of 182 + 192?
C. 685
182 = 324 और 192 = 361, अतः 324 + 361 = 685। वैकल्पिक रूप से लगातार संख्याओं के लिए सामान्य सूत्र उपयोग करें: \(n^2+(n+1)^2=2n(n+1)+1\)। यहाँ n = 18 है, इसलिए \(2\times18\times19+1=684+1=685\)। सबसे नजदीकी भ्रांतिकर विकल्प (जैसे 675) केवल अंकों की गिनती में त्रुटि से बनता है। परीक्षा टिप: लगातार पूर्णांकों के वर्ग जोड़ने के लिए उपरोक्त सूत्र याद रखें ताकि गलतियाँ कम हों। / 182 = 324 and 192 = 361, so 324 + 361 = 685. Alternatively use the formula for consecutive squares: \(n^2+(n+1)^2=2n(n+1)+1\). With n = 18, \(2\times18\times19+1=684+1=685\). A close distractor like 675 typically arises from an arithmetic slip computing one of the squares. Exam tip: use the consecutive-square formula to avoid calculation errors under time pressure.
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If \(b^2=225\) then what is the positive value of (b)?
A. 15
\(15^2=225\)। / \(15^2=225\).
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What is the value of \(20^2 + 5\)?
B. 405
घात (exponent) पहले किया जाता है: \(20^2=400\)। फिर 5 जोड़ने पर \(400+5=405\) मिलता है। गलत विकल्पों की संभावित गलतियाँ: 395 संभवतः \(400-5\) करने की गलती से आता है; 415 तब आता है जब गलती से 15 जोड़ दिया गया हो; 420 संभवतः \(20\times21\) या कोई बहुगुणा समझकर मिलने वाला उत्तर है। परीक्षा टिप: घात पहले निकालें, फिर जोड़-घटाव करें और सामान्य अंकगणितीय ग़लतियों की जाँच करें। / Apply the exponent first: \(20^2=400\). Adding 5 gives \(400+5=405\). Why other choices are wrong: 395 likely comes from mistakenly subtracting 5 (\(400-5\)); 415 would arise if 15 were added instead of 5; 420 could come from confusing the expression with \(20\times21\). Exam tip: evaluate powers before addition and double-check simple arithmetic to avoid common slip-ups.
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What is the value of \(21^2-41\)?
D. 400
(441-41=400)। / (441-41=400).
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What is the value of \(5^3+5^2\)?
A. 150
(125+25=150)। / (125+25=150).
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What is the value of \(23^2+2^2\)?
C. 533
(529+4=533)। / (529+4=533).
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What is the value of \(24^2-76\)?
D. 500
(576-76=500)। / (576-76=500).
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What is the value of (\(3^2\)2)?
A. 81
\(3^4=81\)। / \(3^4=81\).
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If \(c^3=343\) then what is (c)?
C. 7
\(7^3=343\)। / \(7^3=343\).
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What is the value of \(26^2-100\)?
D. 576
(676-100=576)। / (676-100=576).
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What is the value of \(6^3\div6^2\)?
A. 6
\(6^{1}=6\)। / \(6^{1}=6\).
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What is the value of \(2^8-2^4\)?
C. 240
(256-16=240)। / (256-16=240).
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What is the value of \(28^2-284\)?
D. 500
(784-284=500)। / (784-284=500).
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What is the value of \(30^2+100\)?
C. 1000
(900+100=1000)। / (900+100=1000).
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What is the value of \(31^2-361\)?
D. 600
(961-361=600)। / (961-361=600).
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What is the value of \((9^3-9^2)\)?
C. 648
पहले गणना करें: \(9^3=729\) और \(9^2=81\)। अतः \(9^3-9^2=729-81=648\)। वैकल्पिक तरीक़ा: सामान्य गुणक निकालें — \(9^2(9-1)=81\times8=648\)। निकटतम विकल्प 658 सिर्फ एक अंक की गणना त्रुटि का परिणाम है; 729 केवल \(9^3\) है (घटाना भूल जाना), और 81 केवल \(9^2\) है। परीक्षीय सुझाव: बड़े घातों के योग-घटाव में सामान्य गुणक निकाल लेना तेज और भरोसेमंद तरीका है। / Compute the powers first: \(9^3=729\) and \(9^2=81\). So \(9^3-9^2=729-81=648\). Alternate method: factor out \(9^2\): \(9^2(9-1)=81\times8=648\). The closest distractor 658 is a simple arithmetic slip (off by 10); 729 would be the result of forgetting to subtract, and 81 is just \(9^2\). Exam tip: factor the common power \(a^n(a-1)\) or compute powers then subtract to avoid mistakes.
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What is the value of \(33^2-489\)?
D. 600
(1089-489=600)। / (1089-489=600).
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If \(d^2=324\) then what is the positive value of (d)?
A. 18
\(18^2=324\)। / \(18^2=324\).
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What is the value of \(35^2+25\)?
C. 1250
(1225+25=1250)। / (1225+25=1250).
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What is the value of \(36^2-696\)?
D. 600
(1296-696=600)। / (1296-696=600).
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What is the value of \(2^6+3^3\)?
A. 81
(64+27=91)। पहले घातों का मान निकालें। / (64+27=91). Evaluate powers first.
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If \(x^3=512\) then what is the value of (x)?
C. 8
\(8^3=512\)। घनमूल पहचानें। / \(8^3=512\). Recognize perfect cubes.
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What is the value of \(38^2-444\)?
D. 1000
(1444-444=1000)। / (1444-444=1000).
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What is the value of \(7^4 \div 7^2\)?
A. 49
\(7^{4-2}=7^2=49\)। भाग में घात घटती है। / \(7^{4-2}=7^2=49\). Subtract exponents in division.
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What is the value of \(40^2-600\)?
D. 1000
(1600-600=1000)। / (1600-600=1000).
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If \(y^2=441\) then what is the positive value of (y)?
A. 21
\(21^2=441\)। वर्गमूल पहचानें। / \(21^2=441\). Recognize perfect squares.
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What is the value of \((4^5-4^2)\)?
A. 1008
गणना करें: \(4^5=1024\) और \(4^2=16\)। इसलिए \(1024-16=1008\)। निकटतम भ्रमित विकल्पों की व्याख्या: 1024 वह संख्या है जिसे आप तब चुनेंगे जब घटाना भूल जाएँ; 16 तब चुना जा सकता है जब केवल \(4^2\) लिया गया हो; 1000 केवल एक मोटा अनुमान है। परीक्षा युक्ति: व्यवहारिक रूप से इसे इस तरह भी करें: \(4^5-4^2=4^2(4^3-1)=16\times(64-1)=16\times63=1008\)। / Compute powers: \(4^5=1024\) and \(4^2=16\), so \(1024-16=1008\). Why other options are wrong: 1024 corresponds to forgetting the subtraction step; 16 is just \(4^2\) alone; 1000 is a rounded estimate. Exam tip: factor out \(4^2\): \(4^5-4^2=4^2(4^3-1)=16(64-1)=16\times63=1008\), which helps avoid large subtraction errors.
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What is the value of \(42^2-764\)?
D. 1000
(1764-764=1000)। / (1764-764=1000).
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What is the value of \(9^4 \div 9^2\)?
A. 81
\(9^{4-2}=9^2=81\)। भाग में घातें घटती हैं। / \(9^{4-2}=9^2=81\). Subtract exponents in division.
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If \(z^3=729\) then what is the value of (z)?
C. 9
\(9^3=729\)। पूर्ण घनों को याद रखें। / \(9^3=729\). Remember perfect cubes.
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What is the value of \(44^2-936\)?
D. 1000
(1936-936=1000)। / (1936-936=1000).
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What is the value of \(2^3 \times 3^2\)?
A. 72
\(2^3=8\) और \(3^2=9\)। \(8\times9=72\)। / \(2^3=8\) and \(3^2=9\). \(8\times9=72\).
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