Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 311-320 of 600 questions.
If \(2^{x+1}=32\), what is the value of (x)?
A. (,4,)
क्योंकि \(32=2^5\), इसलिए (x+1=5) और (x=4)। परीक्षा में पहले दोनों पक्षों का आधार समान बनाएं। / Since \(32=2^5\), we get (x+1=5) and (x=4). In exams, first make the bases the same on both sides.
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If \(3^a=9\) and \(2^b=8\), what is the value of (a+b)?
A. (,5,)
\(9=3^2\) से (a=2) और \(8=2^3\) से (b=3), इसलिए (a+b=5)। परीक्षा में छोटे powers को याद रखना तेज समाधान देता है। / From \(9=3^2\), (a=2), and from \(8=2^3\), (b=3), so (a+b=5). In exams, remembering small powers gives faster solutions.
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If (a>0), what is the simplified form of (\dfrac{\(a^{\frac{1}{2}}\times a^{\frac{3}{2}}\)2}{a-3})?
A. (,a,)
अंदर \(a^{\frac{1}{2}}a^{\frac{3}{2}}=a^2\), इसलिए (\dfrac{\(a^2\)2}{a-3}=a)। परीक्षा में fractional exponents को भी सामान्य घात नियम से हल करें। / Inside, \(a^{\frac{1}{2}}a^{\frac{3}{2}}=a^2\), so (\dfrac{\(a^2\)2}{a-3}=a). In exams, solve fractional exponents using the usual exponent rules.
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If \(x \neq y\), what is the simplified form of \(\dfrac{x^2-y^2}{x-y}\)?
A. (,x+y,)
क्योंकि (x-2-y-2=(x-y)(x+y)), इसलिए सरल रूप (x+y) है। परीक्षा में difference of squares पहचानना बहुत उपयोगी है। / Because (x-2-y-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.
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What is the simplified form of ((p+q)2-(p-q)2)?
A. (,4pq,)
विस्तार करने पर ((p+q)2=p-2+2pq+q-2) और ((p-q)2=p-2-2pq+q-2), इसलिए अंतर (4pq) है। परीक्षा में standard identities सीधे लगाएं। / On expansion, ((p+q)2=p-2+2pq+q-2) and ((p-q)2=p-2-2pq+q-2), so the difference is (4pq). In exams, apply standard identities directly.
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What is the product of (\(2x^2y\)\(-3xy^2\))?
A. \(,-6x^3y^3,\)
गुणांक (2) और (-3) का गुणनफल (-6) है, और समान चरों की घातें जुड़ती हैं। परीक्षा में sign और exponents दोनों ध्यान से देखें। / The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.
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If \(a \neq 0\) and \(b \neq 0\), what is the simplified form of \(\dfrac{6a^3b^2}{2ab^{-1}}\)?
A. \(,3a^2b^3,\)
गुणांक \(\dfrac{6}{2}=3\), \(a^{3-1}=a^2\) और \(b^{2-(-1)}=b^3\) है। परीक्षा में हर के ऋणात्मक घातांक को घटाते समय sign बदलता है। / The coefficient is \(\dfrac{6}{2}=3\), \(a^{3-1}=a^2\), and \(b^{2-(-1)}=b^3\). In exams, the sign changes when subtracting a negative exponent.
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If \(x \neq 0\), what is the simplified form of (\dfrac{\(x^3\)2}{x^{-1}x-4})?
A. \(,x^3,\)
ऊपर (\(x^3\)2=x-6) और नीचे \(x^{-1}x^4=x^3\), इसलिए उत्तर \(x^3\) है। परीक्षा में हर step पर exponent law अलग से लगाएं। / The numerator is (\(x^3\)2=x-6) and the denominator is \(x^{-1}x^4=x^3\), so the answer is \(x^3\). In exams, apply an exponent law at each step.
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What is the value of \(\dfrac{0.00032}{10^{-5}}\)?
A. (,32,)
क्योंकि \(0.00032=3.2\times 10^{-4}\), इसलिए \(\dfrac{3.2\times 10^{-4}}{10^{-5}}=3.2\times 10^1=32\)। परीक्षा में decimal को scientific notation में बदलना मदद करता है। / Since \(0.00032=3.2\times 10^{-4}\), \(\dfrac{3.2\times 10^{-4}}{10^{-5}}=3.2\times 10^1=32\). In exams, converting decimals to scientific notation helps.
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If \(5^n=\dfrac{1}{125}\), what is the value of (n)?
A. (,-3,)
क्योंकि \(125=5^3\), इसलिए \(\dfrac{1}{125}=5^{-3}\) और (n=-3)। परीक्षा में reciprocal को negative exponent से जोड़ें। / Since \(125=5^3\), \(\dfrac{1}{125}=5^{-3}\), so (n=-3). In exams, connect a reciprocal with a negative exponent.
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