A. समांतर श्रेणी है और \(d=\sqrt{3}\)/It is an AP and \(d=\sqrt{3}\)
Step 1
Concept
The terms become \(\sqrt{3},2\sqrt{3},3\sqrt{3},4\sqrt{3}\). In exams, simplify radicals before finding differences.
Step 2
Why this answer is correct
The correct answer is A. समांतर श्रेणी है और \(d=\sqrt{3}\) / It is an AP and \(d=\sqrt{3}\). The terms become \(\sqrt{3},2\sqrt{3},3\sqrt{3},4\sqrt{3}\). In exams, simplify radicals before finding differences.
Step 3
Exam Tip
पद \(\sqrt{3},2\sqrt{3},3\sqrt{3},4\sqrt{3}\) बनते हैं। परीक्षा में मूलों को सरल करके ही अंतर निकालें।
A. समांतर श्रेणी है, \(d=\sqrt{2}\)/It is an AP, \(d=\sqrt{2}\)
Step 1
Concept
The terms become \(\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2}\), so the difference is \(\sqrt{2}\). In exams, simplify radicals first.
Step 2
Why this answer is correct
The correct answer is A. समांतर श्रेणी है, \(d=\sqrt{2}\) / It is an AP, \(d=\sqrt{2}\). The terms become \(\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2}\), so the difference is \(\sqrt{2}\). In exams, simplify radicals first.
Step 3
Exam Tip
पद \(\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2}\) बनते हैं, इसलिए अंतर \(\sqrt{2}\) है। परीक्षा में मूलों को पहले सरल करें।
The first equation becomes (2x+y=19), and substituting (y=x-5) gives (3x-5=19). Simplifying the equation first saves time.
Step 2
Why this answer is correct
The correct answer is D. (x=8,\ y=3). The first equation becomes (2x+y=19), and substituting (y=x-5) gives (3x-5=19). Simplifying the equation first saves time.
Step 3
Exam Tip
पहला समीकरण (2x+y=19) बनता है और (y=x-5) रखने पर (3x-5=19)। समीकरण को पहले सरल करना समय बचाता है।
The first equation becomes (x+y=8); adding it with (x-y=2) gives (2x=10). Simplifying an equation first makes solving easier.
Step 2
Why this answer is correct
The correct answer is C. (x=5,\ y=3). The first equation becomes (x+y=8); adding it with (x-y=2) gives (2x=10). Simplifying an equation first makes solving easier.
Step 3
Exam Tip
पहला समीकरण (x+y=8) बनता है; इसे (x-y=2) से जोड़ने पर (2x=10)। पहले समीकरण को सरल करने से हल आसान होता है।
\( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{300}=10\sqrt{3} \) और \( \sqrt{147}=7\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें।
\( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{192}=8\sqrt{3} \) और \( \sqrt{75}=5\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें।
\( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{3}\). \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए योग \(5\sqrt{3}\) है। पहले मूलों को सरल करें।
\( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3} \). \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \( \sqrt{3} \) है। पहले मूलों को सरल करें।
Here \(\sqrt{363}=11\sqrt{3}\), \(2\sqrt{147}=14\sqrt{3}\), and \(3\sqrt{75}=15\sqrt{3}\). The numerator is \(12\sqrt{3}\), so the value should be (12).
Step 2
Why this answer is correct
The correct answer is C. (15). Here \(\sqrt{363}=11\sqrt{3}\), \(2\sqrt{147}=14\sqrt{3}\), and \(3\sqrt{75}=15\sqrt{3}\). The numerator is \(12\sqrt{3}\), so the value should be (12).
Step 3
Exam Tip
\(\sqrt{363}=11\sqrt{3}\), \(2\sqrt{147}=14\sqrt{3}\), और \(3\sqrt{75}=15\sqrt{3}\)। अंश \(12\sqrt{3}\) है, इसलिए मान (12) होना चाहिए।
Here \(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\), and \(\sqrt{108}=6\sqrt{3}\). The numerator is \(12\sqrt{3}\), so the value is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Here \(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\), and \(\sqrt{108}=6\sqrt{3}\). The numerator is \(12\sqrt{3}\), so the value is (12).
Step 3
Exam Tip
\(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\), और \(\sqrt{108}=6\sqrt{3}\)। अंश \(12\sqrt{3}\) है, इसलिए मान (12) है।
We have \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). The total is \(4\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(4\sqrt{2}\). We have \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). The total is \(4\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{72}=6\sqrt{2}\)। कुल \(4\sqrt{2}\) मिलता है।
Here \(\sqrt{192}=8\sqrt{3}\), \(2\sqrt{48}=8\sqrt{3}\), and \(3\sqrt{12}=6\sqrt{3}\). The numerator is \(6\sqrt{3}\), so the value is (6).
Step 2
Why this answer is correct
The correct answer is C. (12). Here \(\sqrt{192}=8\sqrt{3}\), \(2\sqrt{48}=8\sqrt{3}\), and \(3\sqrt{12}=6\sqrt{3}\). The numerator is \(6\sqrt{3}\), so the value is (6).
Step 3
Exam Tip
\(\sqrt{192}=8\sqrt{3}\), \(2\sqrt{48}=8\sqrt{3}\), और \(3\sqrt{12}=6\sqrt{3}\)। अंश \(6\sqrt{3}\) है, इसलिए मान (6) है।
Here \(\sqrt{108}=6\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The numerator is \(9\sqrt{3}\), so the value is (9).
Step 2
Why this answer is correct
The correct answer is C. (9). Here \(\sqrt{108}=6\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The numerator is \(9\sqrt{3}\), so the value is (9).
Step 3
Exam Tip
\(\sqrt{108}=6\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), और \(\sqrt{12}=2\sqrt{3}\)। अंश \(9\sqrt{3}\) है, इसलिए मान (9) है।
