100 results found for "square-number" in Class 10.
एक धनात्मक संख्या का वर्ग उसके (11) गुने से (60) अधिक है। संख्या क्या है?
The square of a positive number is (60) more than (11) times the number. What is the number?
#quadratic equations
#number application
#square
A (12)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).
Step 2
Why this answer is correct
The correct answer is B. (15). The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).
Step 3
Exam Tip
समीकरण \(x^2=11x+60\) है। \(x^2-11x-60=0\) से धनात्मक हल (x=15) है।
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एक संख्या का वर्ग उसी संख्या के (30) गुने से (2800) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (2800) more than (30) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (56)
B (60)
C (70)
D (80)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).
Step 2
Why this answer is correct
The correct answer is C. (70). The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).
Step 3
Exam Tip
समीकरण \(x^2=30x+2800\) है। \(x^2-30x-2800=0\) से धनात्मक हल (70) है।
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एक संख्या का वर्ग उसी संख्या के (24) गुने से (640) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (640) more than (24) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (32)
B (36)
C (40)
D (44)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).
Step 2
Why this answer is correct
The correct answer is C. (40). The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).
Step 3
Exam Tip
समीकरण \(x^2=24x+640\) है। \(x^2-24x-640=0\) से धनात्मक हल (40) है।
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एक संख्या का वर्ग उसी संख्या के (18) गुने से (432) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (432) more than (18) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).
Step 2
Why this answer is correct
The correct answer is C. (36). The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).
Step 3
Exam Tip
समीकरण \(x^2=18x+432\) है। \(x^2-18x-432=0\) से धनात्मक हल (36) है।
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एक संख्या का वर्ग उसके (15) गुने से (54) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (54) more than (15) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (18)
B (3)
C (15)
D (54)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है।
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एक संख्या का वर्ग उस संख्या के (11) गुने से (42) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (42) more than (11) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (14)
B (3)
C (11)
D (42)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है।
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एक संख्या का वर्ग उसी संख्या के (14) गुने से (240) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (240) more than (14) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (20)
B (24)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).
Step 2
Why this answer is correct
The correct answer is B. (24). The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).
Step 3
Exam Tip
समीकरण \(x^2=14x+240\) है। \(x^2-14x-240=0\) से धनात्मक हल (24) है।
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एक संख्या का वर्ग उसके (10) गुने से (24) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (24) more than (10) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (12)
B (2)
C (10)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=10x+24\)। \(x^2-10x-24=0\) से धनात्मक संख्या (12) है।
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संख्या रेखा पर कौन-सी संख्या \(\sqrt{9.61}\) के बराबर है?
Which number is equal to \(\sqrt{9.61}\) on the number line?
#polynomials
#number-line
#decimal-square-root
#perfect-decimal-square
A (3.1)
B (3.01)
C (3.001)
D (9.61)
Explanation opens after your attempt
Step 1
Concept
Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
Step 2
Why this answer is correct
The correct answer is A. (3.1). Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
Step 3
Exam Tip
क्योंकि \(3.1^2=9.61\), इसलिए \(\sqrt{9.61}=3.1\)। दशमलव वर्गों को सावधानी से गुणा करें।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर है?
Which number is equal to \(\sqrt{9}\) on the number line?
#perfect-square
#square-root
#number-line
A (3)
B (9)
C \(\frac{1}{3}\)
D -(3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है।
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एक धनात्मक संख्या के वर्ग और उसके (5) गुने का योग (84) है। संख्या क्या है?
The sum of the square of a positive number and (5) times the number is (84). What is the number?
#quadratic equations
#number problem
#application
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).
Step 3
Exam Tip
समीकरण \(x^2+5x=84\) है। इससे (x=7) या (x=-12) मिलता है और उत्तर (7) है।
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एक धनात्मक संख्या का वर्ग उसके (3) गुने से (28) अधिक है। संख्या क्या है?
The square of a positive number is (28) more than (3) times the number. What is the number?
#quadratic equations
#number problem
#application
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).
Step 2
Why this answer is correct
The correct answer is C. (7). The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).
Step 3
Exam Tip
समीकरण \(x^2=3x+28\) है। इससे (x=7) या (x=-4) मिलता है और धनात्मक उत्तर (7) है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (9) गुने से (22) अधिक है। संख्या क्या है?
The square of a positive number is (22) more than (9) times the number. What is the number?
#quadratic equations
#number problem
#application
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).
Step 2
Why this answer is correct
The correct answer is B. (11). Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).
Step 3
Exam Tip
संख्या (x) हो, तो \(x^2=9x+22\), यानी \(x^2-9x-22=0\)। धनात्मक मूल (11) है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (8) गुने से (384) अधिक है। संख्या क्या है?
The square of a positive number is (384) more than (8) times the number. What is the number?
#quadratic equations
#number application
#word problem
A (18)
B (20)
C (24)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (24). \(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.
Step 3
Exam Tip
\(x^2=8x+384\) से \(x^2-8x-384=0\), जिससे (x=24) मिलता है। वाक्य को सही क्रम में समीकरण बनाइए।
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एक धनात्मक संख्या का वर्ग उस संख्या के (6) गुने से (187) अधिक है। संख्या क्या है?
The square of a positive number is (187) more than (6) times the number. What is the number?
#quadratic equations
#number problem
#application
A (13)
B (15)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
\(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.
Step 2
Why this answer is correct
The correct answer is C. (17). \(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.
Step 3
Exam Tip
\(x^2=6x+187\) से \(x^2-6x-187=0\), जिसका धनात्मक हल (17) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।
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एक संख्या का वर्ग संख्या के (11) गुने से (60) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (60) more than (11) times the number. What is the positive number?
#quadratic equations
#number application
#word problem
A (12)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.
Step 2
Why this answer is correct
The correct answer is B. (15). \(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.
Step 3
Exam Tip
\(x^2=11x+60\) से \(x^2-11x-60=0\), जिसका धनात्मक हल (15) है। अधिक का अर्थ समीकरण में जोड़ना होता है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (2) गुने से (120) अधिक है। संख्या क्या है?
The square of a positive number is (120) more than (2) times the number. What is the number?
#quadratic equations
#number problem
#word application
A (10)
B (11)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (12). \(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.
Step 3
Exam Tip
\(x^2=2x+120\) से \(x^2-2x-120=0\) और (x=12) मिलता है। वाक्य को सही क्रम में समीकरण में बदलें।
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एक धनात्मक संख्या का वर्ग उस संख्या के (3) गुने से (70) अधिक है। संख्या क्या है?
The square of a positive number is (70) more than (3) times the number. What is the number?
#quadratic equations
#number problem
#application
A (8)
B (10)
C (11)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.
Step 2
Why this answer is correct
The correct answer is B. (10). \(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.
Step 3
Exam Tip
\(x^2=3x+70\) से \(x^2-3x-70=0\) बनता है और धनात्मक हल (10) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल न लें।
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एक संख्या का वर्ग संख्या के (7) गुने से (18) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (18) more than (7) times the number. What is the positive number?
#quadratic equations
#number problem
#application
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.
Step 2
Why this answer is correct
The correct answer is B. (9). \(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.
Step 3
Exam Tip
\(x^2=7x+18\) से \(x^2-7x-18=0\) और धनात्मक हल (9) है। वाक्य में अधिक का अर्थ जोड़ना होता है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (4) गुने से (45) अधिक है। संख्या क्या है?
The square of a positive number is (45) more than (4) times the number. What is the number?
#quadratic equations
#number problem
#word problems
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.
Step 2
Why this answer is correct
The correct answer is C. (9). \(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.
Step 3
Exam Tip
\(x^2=4x+45\) से \(x^2-4x-45=0\) मिलता है और धनात्मक हल (9) है। ऐसे प्रश्न में वाक्य को सीधे समीकरण में बदलें।
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एक धनात्मक संख्या का वर्ग उस संख्या के (5) गुने से (24) अधिक है। संख्या क्या है?
The square of a positive number is (24) more than (5) times the number. What is the number?
#quadratic equations
#number problem
#application
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.
Step 2
Why this answer is correct
The correct answer is C. (8). The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.
Step 3
Exam Tip
समीकरण \(x^2=5x+24\) है, यानी \(x^2-5x-24=0\), जिससे धनात्मक हल (x=8) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।
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एक संख्या के वर्ग में उस संख्या का (9) गुना जोड़ने पर (400) मिलता है। धनात्मक संख्या क्या है?
When (9) times a number is added to its square, the result is (400). What is the positive number?
#quadratic equations
#number problem
#square
A (16)
B (18)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).
Step 2
Why this answer is correct
The correct answer is A. (16). The equation is \(x^2+9x=400\). From \(x^2+9x-400=0\), the positive root is (x=16).
Step 3
Exam Tip
समीकरण \(x^2+9x=400\) है। \(x^2+9x-400=0\) से धनात्मक हल (x=16) है।
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एक धनात्मक संख्या और उसके वर्ग का योग (156) है। संख्या क्या है?
The sum of a positive number and its square is (156). What is the number?
#quadratic equations
#number square
#application
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then \(x^2+x=156\). This gives \(x^2+x-156=0\), so the positive root is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Let the number be (x), then \(x^2+x=156\). This gives \(x^2+x-156=0\), so the positive root is (12).
Step 3
Exam Tip
संख्या (x) हो, तो \(x^2+x=156\)। इससे \(x^2+x-156=0\), इसलिए धनात्मक मूल (12) है।
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एक संख्या के (18) अधिक मान का वर्ग (4096) है। धनात्मक स्थिति में संख्या क्या है?
The square of (18) more than a number is (4096). In the positive case, what is the number?
#quadratic equations
#square expression
#number problem
A (40)
B (46)
C (50)
D (64)
Explanation opens after your attempt
Step 1
Concept
((x+18)2 =4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.
Step 2
Why this answer is correct
The correct answer is B. (46). ((x+18)2 =4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.
Step 3
Exam Tip
((x+18)2 =4096) और (x+18=64), इसलिए (x=46) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।
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एक संख्या के वर्ग में (399) जोड़ने पर (3208) मिलता है। धनात्मक संख्या क्या है?
When (399) is added to the square of a number, the result is (3208). What is the positive number?
#quadratic equations
#number problem
#square
A (47)
B (51)
C (53)
D (57)
Explanation opens after your attempt
Step 1
Concept
\(x^2+399=3208\) gives \(x^2=2809\), so (x=53). First move the constant to the other side.
Step 2
Why this answer is correct
The correct answer is C. (53). \(x^2+399=3208\) gives \(x^2=2809\), so (x=53). First move the constant to the other side.
Step 3
Exam Tip
\(x^2+399=3208\) से \(x^2=2809\), इसलिए (x=53) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ।
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एक संख्या और उसके वर्ग का योग (2352) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (2352). What is the positive number?
#quadratic equations
#number and square
#factoring
A (42)
B (46)
C (48)
D (49)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=2352\) gives \(x^2+x-2352=0\). The positive solution is (48).
Step 2
Why this answer is correct
The correct answer is C. (48). \(x^2+x=2352\) gives \(x^2+x-2352=0\). The positive solution is (48).
Step 3
Exam Tip
\(x^2+x=2352\) से \(x^2+x-2352=0\) मिलता है। धनात्मक हल (48) है।
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एक संख्या के (14) अधिक मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?
The square of (14) more than a number is (2500). In the positive case, what is the number?
#quadratic equations
#square expression
#number problem
A (32)
B (34)
C (36)
D (50)
Explanation opens after your attempt
Step 1
Concept
((x+14)2 =2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.
Step 2
Why this answer is correct
The correct answer is C. (36). ((x+14)2 =2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.
Step 3
Exam Tip
((x+14)2 =2500) और (x+14=50), इसलिए (x=36) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।
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एक संख्या के वर्ग में (444) जोड़ने पर (1900) मिलता है। धनात्मक संख्या क्या है?
When (444) is added to the square of a number, the result is (1900). What is the positive number?
#quadratic equations
#consistency check
#number square
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
\(x^2+444=1900\) gives \(x^2=1456\), which is not a perfect square. Therefore, none of the options can be correct.
Step 2
Why this answer is correct
The correct answer is C. (38). \(x^2+444=1900\) gives \(x^2=1456\), which is not a perfect square. Therefore, none of the options can be correct.
Step 3
Exam Tip
\(x^2+444=1900\) से \(x^2=1456\) नहीं, बल्कि सही घटाव (1900-444=1456) है जो पूर्ण वर्ग नहीं है। इसलिए कोई विकल्प सही नहीं हो सकता।
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एक संख्या और उसके वर्ग का योग (1892) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (1892). What is the positive number?
#quadratic equations
#number and square
#factoring
A (41)
B (42)
C (43)
D (44)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=1892\) gives \(x^2+x-1892=0\). The positive solution is (43).
Step 2
Why this answer is correct
The correct answer is C. (43). \(x^2+x=1892\) gives \(x^2+x-1892=0\). The positive solution is (43).
Step 3
Exam Tip
\(x^2+x=1892\) से \(x^2+x-1892=0\) मिलता है। धनात्मक हल (43) है।
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एक संख्या के (9) अधिक मान का वर्ग (1681) है। धनात्मक स्थिति में संख्या क्या है?
The square of (9) more than a number is (1681). In the positive case, what is the number?
#quadratic equations
#square expression
#number problem
A (30)
B (32)
C (34)
D (41)
Explanation opens after your attempt
Step 1
Concept
((x+9)2 =1681) and (x+9=41), so (x=32). If the positive case is clear, take the positive square root.
Step 2
Why this answer is correct
The correct answer is B. (32). ((x+9)2 =1681) and (x+9=41), so (x=32). If the positive case is clear, take the positive square root.
Step 3
Exam Tip
((x+9)2 =1681) और (x+9=41), इसलिए (x=32) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।
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एक संख्या के वर्ग में (175) जोड़ने पर (1076) मिलता है। धनात्मक संख्या क्या है?
When (175) is added to the square of a number, the result is (1076). What is the positive number?
#quadratic equations
#error spotting
#number square
A (27)
B (29)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(x^2+175=1076\) gives \(x^2=901\), not a perfect square. If the data are inconsistent, do not choose options blindly.
Step 2
Why this answer is correct
The correct answer is C. (30). \(x^2+175=1076\) gives \(x^2=901\), not a perfect square. If the data are inconsistent, do not choose options blindly.
Step 3
Exam Tip
\(x^2+175=1076\) से \(x^2=901\) नहीं बनना चाहिए, इसलिए सही गणना देखें: \(30^2+175=1075\) होता है। दिए गए आंकड़े असंगत हों तो विकल्पों को अंधे रूप से न चुनें।
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एक संख्या और उसके वर्ग का योग (1260) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (1260). What is the positive number?
#quadratic equations
#number and square
#factoring
A (32)
B (34)
C (35)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=1260\) gives \(x^2+x-1260=0\). The positive solution is (35).
Step 2
Why this answer is correct
The correct answer is C. (35). \(x^2+x=1260\) gives \(x^2+x-1260=0\). The positive solution is (35).
Step 3
Exam Tip
\(x^2+x=1260\) से \(x^2+x-1260=0\) मिलता है। धनात्मक हल (35) है।
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एक संख्या के (4) अधिक मान का वर्ग (900) है। धनात्मक स्थिति में संख्या क्या है?
The square of (4) more than a number is (900). In the positive case, what is the number?
#quadratic equations
#square expression
#number problem
A (22)
B (24)
C (26)
D (30)
Explanation opens after your attempt
Step 1
Concept
((x+4)2 =900) and (x+4=30), so (x=26). If the positive case is clear, take the positive square root.
Step 2
Why this answer is correct
The correct answer is C. (26). ((x+4)2 =900) and (x+4=30), so (x=26). If the positive case is clear, take the positive square root.
Step 3
Exam Tip
((x+4)2 =900) और (x+4=30), इसलिए (x=26) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।
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एक संख्या के वर्ग में (156) जोड़ने पर (1057) मिलता है। धनात्मक संख्या क्या है?
When (156) is added to the square of a number, the result is (1057). What is the positive number?
#quadratic equations
#error spotting
#number square
A (27)
B (29)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(x^2+156=1057\) gives \(x^2=901\), not a listed perfect square, so this is a data-error type question. In exams, check consistency before solving.
Step 2
Why this answer is correct
The correct answer is C. (30). \(x^2+156=1057\) gives \(x^2=901\), not a listed perfect square, so this is a data-error type question. In exams, check consistency before solving.
Step 3
Exam Tip
\(x^2+156=1057\) से \(x^2=901\) नहीं, इसलिए विकल्प जाँच की बजाय समीकरण सुधारें: सही वर्ग के लिए \(x^2+156=1056\) चाहिए।
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एक संख्या और उसके वर्ग का योग (930) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (930). What is the positive number?
#quadratic equations
#number and square
#factoring
A (28)
B (29)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=930\) gives \(x^2+x-930=0\). The positive solution is (30).
Step 2
Why this answer is correct
The correct answer is C. (30). \(x^2+x=930\) gives \(x^2+x-930=0\). The positive solution is (30).
Step 3
Exam Tip
\(x^2+x=930\) से \(x^2+x-930=0\) मिलता है। धनात्मक हल (30) है।
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एक संख्या और उसके वर्ग का योग (72) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (72). What is the positive number?
#quadratic-equations
#word-problems
#number-and-square
A (8)
B (9)
C (7)
D (6)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x^2+x=72\). From \(x^2+x-72=0\), the positive solution is (8).
Step 2
Why this answer is correct
The correct answer is A. (8). Let the number be (x), so \(x^2+x=72\). From \(x^2+x-72=0\), the positive solution is (8).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2+x=72\)। \(x^2+x-72=0\) से धनात्मक हल (8) है।
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एक संख्या के वर्ग में (71) जोड़ने पर (512) मिलता है। धनात्मक संख्या क्या है?
When (71) is added to the square of a number, the result is (512). What is the positive number?
#quadratic equations
#number problem
#square
A (19)
B (20)
C (21)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(x^2+71=512\) gives \(x^2=441\), so (x=21). First move the constant to the other side.
Step 2
Why this answer is correct
The correct answer is C. (21). \(x^2+71=512\) gives \(x^2=441\), so (x=21). First move the constant to the other side.
Step 3
Exam Tip
\(x^2+71=512\) से \(x^2=441\), इसलिए (x=21) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ।
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एक संख्या और उसके वर्ग का योग (342) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (342). What is the positive number?
#quadratic equations
#number and square
#application
A (16)
B (18)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=342\) gives \(x^2+x-342=0\), so (x=18). In sum questions, add both terms directly.
Step 2
Why this answer is correct
The correct answer is B. (18). \(x^2+x=342\) gives \(x^2+x-342=0\), so (x=18). In sum questions, add both terms directly.
Step 3
Exam Tip
\(x^2+x=342\) से \(x^2+x-342=0\), इसलिए (x=18) है। योग वाले प्रश्न में दोनों पद सीधे जोड़ें।
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एक संख्या का वर्ग (6) जोड़ने पर (202) बनता है। संख्या का धनात्मक मान क्या है?
The square of a number becomes (202) after adding (6). What is the positive value of the number?
#quadratic equations
#number problem
#square
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(x^2+6=202\) gives \(x^2=196\), so the positive (x=14). While taking square root, check the condition in the question.
Step 2
Why this answer is correct
The correct answer is C. (14). \(x^2+6=202\) gives \(x^2=196\), so the positive (x=14). While taking square root, check the condition in the question.
Step 3
Exam Tip
\(x^2+6=202\) से \(x^2=196\), इसलिए धनात्मक (x=14) है। वर्गमूल लेते समय प्रश्न की शर्त देखें।
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एक संख्या और उसके वर्ग का योग (156) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (156). What is the positive number?
#quadratic equations
#number and square
#application
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=156\) gives \(x^2+x-156=0\), so (x=12). Write the sum of the number and its square directly.
Step 2
Why this answer is correct
The correct answer is C. (12). \(x^2+x=156\) gives \(x^2+x-156=0\), so (x=12). Write the sum of the number and its square directly.
Step 3
Exam Tip
\(x^2+x=156\) से \(x^2+x-156=0\), इसलिए (x=12) है। संख्या और उसके वर्ग के योग को सीधे लिखें।
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एक संख्या और उसके वर्ग का योग (42) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (42). What is the positive number?
#quadratic equations
#number and square
#word problem
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=42\) gives \(x^2+x-42=0\), so (x=6). Convert the sum of number and square directly into an equation.
Step 2
Why this answer is correct
The correct answer is B. (6). \(x^2+x=42\) gives \(x^2+x-42=0\), so (x=6). Convert the sum of number and square directly into an equation.
Step 3
Exam Tip
\(x^2+x=42\) से \(x^2+x-42=0\), इसलिए (x=6) है। संख्या और वर्ग के योग को सीधे समीकरण में बदलें।
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एक धनात्मक संख्या के वर्ग और संख्या के (40) गुने का अंतर (3825) है। संख्या क्या है?
The difference between the square of a positive number and (40) times the number is (3825). What is the number?
#quadratic equations
#difference
#number problem
A (75)
B (80)
C (85)
D (90)
Explanation opens after your attempt
Step 1
Concept
\(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).
Step 2
Why this answer is correct
The correct answer is C. (85). \(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).
Step 3
Exam Tip
\(x^2-40x=3825\) से \(x^2-40x-3825=0\) बनता है। धनात्मक हल (x=85) है।
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एक धनात्मक संख्या के वर्ग और संख्या के (27) गुने का अंतर (1000) है। संख्या क्या है?
The difference between the square of a positive number and (27) times the number is (1000). What is the number?
#quadratic equations
#difference
#number problem
A (40)
B (45)
C (50)
D (55)
Explanation opens after your attempt
Step 1
Concept
\(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).
Step 2
Why this answer is correct
The correct answer is C. (50). \(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).
Step 3
Exam Tip
\(x^2-27x=1000\) से \(x^2-27x-1000=0\) बनता है। धनात्मक हल (x=50) है।
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एक धनात्मक संख्या के वर्ग और संख्या के (20) गुने का अंतर (621) है। संख्या क्या है?
The difference between the square of a positive number and (20) times the number is (621). What is the number?
#quadratic equations
#difference
#number problem
A (31)
B (33)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).
Step 2
Why this answer is correct
The correct answer is C. (39). \(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).
Step 3
Exam Tip
\(x^2-20x=621\) से \(x^2-20x-621=0\) बनता है। धनात्मक हल (x=39) है।
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एक धनात्मक संख्या के वर्ग और संख्या के (16) गुने का अंतर (425) है। संख्या क्या है?
The difference between the square of a positive number and (16) times the number is (425). What is the number?
#quadratic equations
#difference
#number problem
A (25)
B (29)
C (31)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(x^2-16x=425\) gives \(x^2-16x-425=0\). The positive solution is (x=29).
Step 2
Why this answer is correct
The correct answer is B. (29). \(x^2-16x=425\) gives \(x^2-16x-425=0\). The positive solution is (x=29).
Step 3
Exam Tip
\(x^2-16x=425\) से \(x^2-16x-425=0\) बनता है। धनात्मक हल (x=29) है।
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एक संख्या के वर्ग और संख्या के (12) गुने का अंतर (589) है। धनात्मक संख्या क्या है?
The difference between the square of a number and (12) times the number is (589). What is the positive number?
#quadratic equations
#difference
#number problem
A (23)
B (27)
C (31)
D (35)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2-12x=589\), or \(x^2-12x-589=0\), giving (x=31). In a difference statement, keep the subtraction order correct.
Step 2
Why this answer is correct
The correct answer is C. (31). The equation is \(x^2-12x=589\), or \(x^2-12x-589=0\), giving (x=31). In a difference statement, keep the subtraction order correct.
Step 3
Exam Tip
समीकरण \(x^2-12x=589\) है, यानी \(x^2-12x-589=0\), जिससे (x=31) मिलता है। अंतर में घटाव का क्रम ध्यान रखें।
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एक संख्या के वर्ग और संख्या के (9) गुने का अंतर (90) है। धनात्मक संख्या क्या है?
The difference between the square of a number and (9) times the number is (90). What is the positive number?
#quadratic equations
#difference
#number problem
A (10)
B (12)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2-9x=90\), or \(x^2-9x-90=0\), which gives (x=15). Keep the subtraction order correct in difference statements.
Step 2
Why this answer is correct
The correct answer is C. (15). The equation is \(x^2-9x=90\), or \(x^2-9x-90=0\), which gives (x=15). Keep the subtraction order correct in difference statements.
Step 3
Exam Tip
समीकरण \(x^2-9x=90\) है, यानी \(x^2-9x-90=0\), जिससे (x=15) मिलता है। अंतर वाले वाक्य में घटाव का क्रम सही रखें।
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एक संख्या के वर्ग और संख्या के (6) गुने का अंतर (16) है। धनात्मक संख्या क्या है?
The difference between the square of a number and (6) times the number is (16). What is the positive number?
#quadratic equations
#number problem
#difference
A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2-6x=16\), or \(x^2-6x-16=0\), giving (x=8). In difference questions, read the order carefully.
Step 2
Why this answer is correct
The correct answer is C. (8). The equation is \(x^2-6x=16\), or \(x^2-6x-16=0\), giving (x=8). In difference questions, read the order carefully.
Step 3
Exam Tip
समीकरण \(x^2-6x=16\) है, यानी \(x^2-6x-16=0\), जिससे (x=8) है। अंतर वाले प्रश्न में क्रम ध्यान से पढ़ें।
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किसी संख्या का वर्ग उस संख्या के (5) गुने से (6) अधिक है। यदि संख्या (x) है तो समीकरण क्या होगा?
The square of a number is (6) more than (5) times the number. If the number is (x), what is the equation?
#quadratic equations
#word problem
#forming equation
A \(x^2=5x+6\)
B \(x^2+5x=6\)
C \(5x^2=x+6\)
D \(x^2=6x+5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2=5x+6\)
Step 1
Concept
The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2=5x+6\). The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 3
Exam Tip
संख्या का वर्ग \(x^2\) और (5) गुने से (6) अधिक (5x+6) है। इसलिए समीकरण \(x^2=5x+6\) बनेगा।
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कौन सी संख्या \( \sqrt{8} \) और (3) के बीच संख्या रेखा पर स्थित है?
Which number lies between \( \sqrt{8} \) and (3) on the number line?
#number-line
#between-numbers
#square-roots
A (2.9)
B (2.7)
C (3.1)
D (2)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.
Step 2
Why this answer is correct
The correct answer is A. (2.9). \( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.
Step 3
Exam Tip
\( \sqrt{8}\approx2.828\), इसलिए (2.9) उसके और (3) के बीच है। पहले अपरिमेय संख्या का अनुमान करें।
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किस संख्या को संख्या रेखा पर \(\sqrt{25}-\sqrt{4}\) के रूप में दर्शाया जा सकता है?
Which number can be represented as \(\sqrt{25}-\sqrt{4}\) on the number line?
#polynomials
#number-line
#simplification
#perfect-square
A (3)
B (7)
C (21)
D \(\sqrt{21}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 3
Exam Tip
\(\sqrt{25}=5\) और \(\sqrt{4}=2\), इसलिए \(\sqrt{25}-\sqrt{4}=3\)। पूर्ण वर्गों को तुरंत सरल करें।
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कौन-सी संख्या रेखा पर \(\sqrt{6}\) के सबसे निकट है?
Which number is closest to \(\sqrt{6}\) on the number line?
#polynomials
#number-line
#approximation
#square-root
A (2.45)
B (2.10)
C (2.90)
D (3.20)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
Step 2
Why this answer is correct
The correct answer is A. (2.45). \(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
Step 3
Exam Tip
\(\sqrt{6}\approx2.449\), इसलिए (2.45) सबसे निकट है। निकटता के लिए अनुमानित मान से अंतर जाँचें।
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संख्या रेखा पर \(-\sqrt{16}\) किस संख्या के बराबर स्थान पर होगा?
On the number line, \(-\sqrt{16}\) will be at the same position as which number?
#polynomials
#number-line
#square-roots
#class-10
A (4)
B (16)
C (-4)
D (-16)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.
Step 2
Why this answer is correct
The correct answer is C. (-4). \(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए \(-\sqrt{16}=-4\) है। परीक्षा में वर्गमूल निकालने के बाद बाहर का ऋण चिह्न लगाएं।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर स्थान पर होगा?
On the number line, \(\sqrt{9}\) will be at the same position as which number?
#polynomials
#number-line
#square-roots
#class-10
A (2)
B (3)
C (9)
D (-3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए इसका स्थान (3) पर होगा। परीक्षा में पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।
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एक संख्या के (22) कम मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?
The square of (22) less than a number is (2500). In the positive case, what is the number?
#quadratic equations
#square expression
#application
A (50)
B (64)
C (72)
D (78)
Explanation opens after your attempt
Step 1
Concept
((x-22)2 =2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.
Step 2
Why this answer is correct
The correct answer is C. (72). ((x-22)2 =2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.
Step 3
Exam Tip
((x-22)2 =2500) और (x-22=50), इसलिए (x=72) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।
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एक संख्या के वर्ग में (975) घटाने पर (2625) मिलता है। धनात्मक संख्या क्या है?
When (975) is subtracted from the square of a number, the result is (2625). What is the positive number?
#quadratic equations
#number application
#square
A (50)
B (55)
C (60)
D (65)
Explanation opens after your attempt
Step 1
Concept
\(x^2-975=2625\) gives \(x^2=3600\), so (x=60). Write the subtraction sign carefully.
Step 2
Why this answer is correct
The correct answer is C. (60). \(x^2-975=2625\) gives \(x^2=3600\), so (x=60). Write the subtraction sign carefully.
Step 3
Exam Tip
\(x^2-975=2625\) से \(x^2=3600\), इसलिए (x=60) है। घटाव के चिन्ह को ध्यान से लिखें।
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एक संख्या के (15) कम मान का वर्ग (2209) है। धनात्मक स्थिति में संख्या क्या है?
The square of (15) less than a number is (2209). In the positive case, what is the number?
#quadratic equations
#square expression
#application
A (47)
B (55)
C (62)
D (70)
Explanation opens after your attempt
Step 1
Concept
((x-15)2 =2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.
Step 2
Why this answer is correct
The correct answer is C. (62). ((x-15)2 =2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.
Step 3
Exam Tip
((x-15)2 =2209) और (x-15=47), इसलिए (x=62) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।
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एक संख्या के (11) कम मान का वर्ग (1156) है। धनात्मक स्थिति में संख्या क्या है?
The square of (11) less than a number is (1156). In the positive case, what is the number?
#quadratic equations
#square expression
#application
A (34)
B (39)
C (45)
D (47)
Explanation opens after your attempt
Step 1
Concept
((x-11)2 =1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.
Step 2
Why this answer is correct
The correct answer is C. (45). ((x-11)2 =1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.
Step 3
Exam Tip
((x-11)2 =1156) और (x-11=34), इसलिए (x=45) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।
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एक संख्या के वर्ग में (256) घटाने पर (1040) मिलता है। धनात्मक संख्या क्या है?
When (256) is subtracted from the square of a number, the result is (1040). What is the positive number?
#quadratic equations
#number application
#square
A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
\(x^2-256=1040\) gives \(x^2=1296\), so (x=36). Write the subtraction sign carefully.
Step 2
Why this answer is correct
The correct answer is C. (36). \(x^2-256=1040\) gives \(x^2=1296\), so (x=36). Write the subtraction sign carefully.
Step 3
Exam Tip
\(x^2-256=1040\) से \(x^2=1296\), इसलिए (x=36) है। घटाव के चिन्ह को ध्यान से लिखें।
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एक संख्या के (6) कम मान का वर्ग (784) है। धनात्मक स्थिति में संख्या क्या है?
The square of (6) less than a number is (784). In the positive case, what is the number?
#quadratic equations
#square expression
#application
A (28)
B (30)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
((x-6)2 =784) and (x-6=28), so (x=34). After taking square root, choose the sign according to the condition.
Step 2
Why this answer is correct
The correct answer is C. (34). ((x-6)2 =784) and (x-6=28), so (x=34). After taking square root, choose the sign according to the condition.
Step 3
Exam Tip
((x-6)2 =784) और (x-6=28), इसलिए (x=34) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।
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एक संख्या के वर्ग में (119) घटाने पर (457) मिलता है। धनात्मक संख्या क्या है?
When (119) is subtracted from the square of a number, the result is (457). What is the positive number?
#quadratic equations
#number application
#square
A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
\(x^2-119=457\) gives \(x^2=576\), so (x=24). Write the subtraction sign carefully.
Step 2
Why this answer is correct
The correct answer is C. (24). \(x^2-119=457\) gives \(x^2=576\), so (x=24). Write the subtraction sign carefully.
Step 3
Exam Tip
\(x^2-119=457\) से \(x^2=576\), इसलिए (x=24) है। घटाव के चिन्ह को ध्यान से लिखें।
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किसी संख्या में (11) घटाने पर प्राप्त संख्या का वर्ग (196) है। धनात्मक स्थिति में मूल संख्या क्या है?
When (11) is subtracted from a number, the square of the result is (196). In the positive case, what is the original number?
#quadratic equations
#number problem
#square
A (14)
B (21)
C (25)
D (29)
Explanation opens after your attempt
Step 1
Concept
((x-11)2 =196) and (x-11=14), so (x=25). While taking square root, check the given condition.
Step 2
Why this answer is correct
The correct answer is C. (25). ((x-11)2 =196) and (x-11=14), so (x=25). While taking square root, check the given condition.
Step 3
Exam Tip
((x-11)2 =196) और (x-11=14), इसलिए (x=25) है। वर्गमूल लेते समय दी हुई स्थिति देखें।
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किसी संख्या में (9) जोड़ने पर प्राप्त संख्या का वर्ग (676) है। धनात्मक मूल के अनुसार मूल संख्या क्या है?
When (9) is added to a number, the square of the result is (676). According to the positive root, what is the original number?
#quadratic equations
#square
#number problem
A (15)
B (17)
C (19)
D (26)
Explanation opens after your attempt
Step 1
Concept
((x+9)2 =676) and (x+9=26), so (x=17). If positive root is stated, take (26).
Step 2
Why this answer is correct
The correct answer is B. (17). ((x+9)2 =676) and (x+9=26), so (x=17). If positive root is stated, take (26).
Step 3
Exam Tip
((x+9)2 =676) और (x+9=26), इसलिए (x=17) है। धनात्मक मूल लिखा हो तो (26) लें।
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एक संख्या के वर्ग में (25) घटाने पर (119) मिलता है। धनात्मक संख्या क्या है?
When (25) is subtracted from the square of a number, the result is (119). What is the positive number?
#quadratic equations
#number application
#square
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(x^2-25=119\) gives \(x^2=144\), so (x=12). In subtraction questions, place the sign carefully.
Step 2
Why this answer is correct
The correct answer is B. (12). \(x^2-25=119\) gives \(x^2=144\), so (x=12). In subtraction questions, place the sign carefully.
Step 3
Exam Tip
\(x^2-25=119\) से \(x^2=144\), इसलिए (x=12) है। घटाने वाले प्रश्नों में चिन्ह ध्यान से लगाएँ।
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किसी संख्या में (7) घटाने पर प्राप्त संख्या का वर्ग (100) है। धनात्मक स्थिति में मूल संख्या क्या है?
When (7) is subtracted from a number, the square of the result is (100). In the positive case, what is the original number?
#quadratic equations
#number problem
#square
A (10)
B (15)
C (17)
D (20)
Explanation opens after your attempt
Step 1
Concept
((x-7)2 =100) and (x-7=10), so (x=17). In square-based questions, read the condition carefully.
Step 2
Why this answer is correct
The correct answer is C. (17). ((x-7)2 =100) and (x-7=10), so (x=17). In square-based questions, read the condition carefully.
Step 3
Exam Tip
((x-7)2 =100) और (x-7=10), इसलिए (x=17) है। वर्ग वाले प्रश्नों में शर्त ध्यान से पढ़ें।
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किसी संख्या में (5) जोड़ने पर प्राप्त संख्या का वर्ग (225) है। धनात्मक मूल के अनुसार मूल संख्या क्या है?
When (5) is added to a number, the square of the result is (225). According to the positive root, what is the original number?
#quadratic equations
#square
#number problem
A (8)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
((x+5)2 =225) and (x+5=15), so (x=10). If the positive root is given, do not take the negative root.
Step 2
Why this answer is correct
The correct answer is B. (10). ((x+5)2 =225) and (x+5=15), so (x=10). If the positive root is given, do not take the negative root.
Step 3
Exam Tip
((x+5)2 =225) और (x+5=15), इसलिए (x=10) है। धनात्मक मूल दिया हो तो ऋणात्मक मूल नहीं लेना है।
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किसी संख्या में (3) जोड़ने पर प्राप्त संख्या का वर्ग (100) है। धनात्मक मूल के अनुसार संख्या क्या है?
When (3) is added to a number, the square of the result is (100). According to the positive root, what is the number?
#quadratic equations
#number problem
#square
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
((x+3)2 =100) gives (x+3=10), so (x=7). If the question says positive root, take (10).
Step 2
Why this answer is correct
The correct answer is C. (7). ((x+3)2 =100) gives (x+3=10), so (x=7). If the question says positive root, take (10).
Step 3
Exam Tip
((x+3)2 =100) से (x+3=10), इसलिए (x=7) है। प्रश्न में धनात्मक मूल कहा हो तो (10) लें।
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संख्या रेखा पर \(-\frac{17}{5}\) किस मिश्र संख्या के बराबर स्थान पर होगा?
At which mixed number position will \(-\frac{17}{5}\) lie on the number line?
#polynomials
#number-line
#negative-mixed-number
#medium
A \(3+\frac{2}{5}\)
B \(-3-\frac{2}{5}\)
C \(-4-\frac{2}{5}\)
D \(-2-\frac{3}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(-3-\frac{2}{5}\)
Step 1
Concept
\(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
Step 2
Why this answer is correct
The correct answer is B. \(-3-\frac{2}{5}\). \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
Step 3
Exam Tip
\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें।
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संख्या रेखा पर \(\frac{13}{4}\) को किस मिश्र संख्या के रूप में दिखाया जाएगा?
How will \(\frac{13}{4}\) be shown as a mixed number on the number line?
#polynomials
#number-line
#mixed-number
#medium
A \(3+\frac{1}{4}\)
B \(3+\frac{3}{4}\)
C \(4+\frac{1}{3}\)
D \(2+\frac{3}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(3+\frac{1}{4}\)
Step 1
Concept
\(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
Step 2
Why this answer is correct
The correct answer is A. \(3+\frac{1}{4}\). \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
Step 3
Exam Tip
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें।
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संख्या रेखा पर \(\frac{5}{4}\) को मिश्र संख्या के रूप में कहां रखा जाएगा?
Where will \(\frac{5}{4}\) be placed as a mixed number on the number line?
#polynomials
#number-line
#mixed-number
#class-10
A \(1+\frac{1}{4}\)
B \(1+\frac{3}{4}\)
C \(2+\frac{1}{4}\)
D \(\frac{4}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(1+\frac{1}{4}\)
Step 1
Concept
\(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
Step 2
Why this answer is correct
The correct answer is A. \(1+\frac{1}{4}\). \(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
Step 3
Exam Tip
\(\frac{5}{4}=1+\frac{1}{4}\), इसलिए यह (1) के बाद एक चौथाई भाग पर है। परीक्षा में अपूर्ण भिन्न को मिश्र रूप में बदलें।
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एक दो अंकों की संख्या में अंकों का योग (12) है। उस संख्या और उलटी संख्या का गुणनफल (4032) है। मूल संख्या कौन-सी हो सकती है?
A two-digit number has digit sum (12). The product of the number and its reversed number is (4032). Which can be the original number?
#quadratic equations
#digit problem
#reverse number
A (39)
B (48)
C (57)
D (66)
Explanation opens after your attempt
Step 1
Concept
The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.
Step 2
Why this answer is correct
The correct answer is B. (48). The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.
Step 3
Exam Tip
(48) की उलटी संख्या (84) है और \(48 \times 84=4032\)। अंकों की समस्याओं में उलटी संख्या भी जाँचना जरूरी है।
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यदि \( \sqrt{x}=7.9 \), तो संख्या रेखा पर (x) किस बिंदु से जुड़ा है?
If \( \sqrt{x}=7.9 \), with which point is (x) associated on the number line?
#number-line
#square-root-equation
#decimal-square
A (60.41)
B (61.41)
C (62.41)
D (63.41)
Explanation opens after your attempt
Correct Answer
C. (62.41)
Step 1
Concept
\(x=7.9^2=62.41\). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is C. (62.41). \(x=7.9^2=62.41\). Square both sides to remove the square root.
Step 3
Exam Tip
\(x=7.9^2=62.41\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें।
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यदि \( \sqrt{x}=6.8 \), तो संख्या रेखा पर (x) किस बिंदु से जुड़ा है?
If \( \sqrt{x}=6.8 \), with which point is (x) associated on the number line?
#number-line
#square-root-equation
#decimal-square
A (44.24)
B (45.24)
C (46.24)
D (47.24)
Explanation opens after your attempt
Correct Answer
C. (46.24)
Step 1
Concept
\(x=6.8^2=46.24\). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is C. (46.24). \(x=6.8^2=46.24\). Square both sides to remove the square root.
Step 3
Exam Tip
\(x=6.8^2=46.24\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें।
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यदि \( \sqrt{x}=4.7 \), तो (x) संख्या रेखा पर किस मान से संबंधित है?
If \( \sqrt{x}=4.7 \), then (x) corresponds to which value on the number line?
#number-line
#square-root-equation
#decimal-square
A (20.09)
B (21.09)
C (22.09)
D (23.09)
Explanation opens after your attempt
Correct Answer
C. (22.09)
Step 1
Concept
\(x=4.7^2=22.09\). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is C. (22.09). \(x=4.7^2=22.09\). Square both sides to remove the square root.
Step 3
Exam Tip
\(x=4.7^2=22.09\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें।
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यदि \( \sqrt{x}=3.9 \), तो संख्या रेखा पर (x) किस बिंदु से जुड़ा है?
If \( \sqrt{x}=3.9 \), with which point is (x) associated on the number line?
#number-line
#square-root-equation
#decimal-square
A (15.21)
B (7.8)
C (12.21)
D (3.09)
Explanation opens after your attempt
Correct Answer
A. (15.21)
Step 1
Concept
\(x=3.9^2=15.21\). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is A. (15.21). \(x=3.9^2=15.21\). Square both sides to remove the square root.
Step 3
Exam Tip
\(x=3.9^2=15.21\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें।
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संख्या रेखा पर \(\sqrt{0.49}\) का सही स्थान कौन सा है?
What is the correct position of \(\sqrt{0.49}\) on the number line?
#number-line
#decimal-square-root
#perfect-square
#position
A (0.07)
B (0.7)
C (4.9)
D (7)
Explanation opens after your attempt
Step 1
Concept
Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 2
Why this answer is correct
The correct answer is B. (0.7). Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 3
Exam Tip
\(0.7^2=0.49\), इसलिए \(\sqrt{0.49}=0.7\) है। दशमलव वर्गों में स्थान मान सावधानी से देखें।
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संख्या रेखा पर \(\sqrt{9}\) किस बिंदु के समान है?
On the number line \(\sqrt{9}\) is the same as which point?
#number-line
#square-root
#perfect-square
#easy
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।
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संख्या रेखा पर \(\sqrt{16}\) का स्थान कौन-सा है?
What is the position of \(\sqrt{16}\) on the number line?
#perfect-square
#number-line
#square-root
A (4)
B (8)
C (16)
D -(4)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 2
Why this answer is correct
The correct answer is A. (4). \(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए इसका स्थान (4) है। पूर्ण वर्गों के वर्गमूल सीधे पहचाने जा सकते हैं।
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एक संख्या और उसके वर्ग का योग (506) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (506). What is the positive number?
#quadratic equations
#number problem
#factoring
A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=506\) gives \(x^2+x-506=0\), whose positive solution is (22). While factoring, check factors of (506).
Step 2
Why this answer is correct
The correct answer is C. (22). \(x^2+x=506\) gives \(x^2+x-506=0\), whose positive solution is (22). While factoring, check factors of (506).
Step 3
Exam Tip
\(x^2+x=506\) से \(x^2+x-506=0\), जिसका धनात्मक हल (22) है। गुणनखंड बनाते समय (506) के गुणनखंड देखें।
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एक संख्या के वर्ग में (39) जोड़ने पर (208) मिलता है। धनात्मक संख्या क्या है?
When (39) is added to the square of a number, the result is (208). What is the positive number?
#quadratic equations
#number problem
#application
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(x^2+39=208\) gives \(x^2=169\), so (x=13). First move the constant number to the other side.
Step 2
Why this answer is correct
The correct answer is C. (13). \(x^2+39=208\) gives \(x^2=169\), so (x=13). First move the constant number to the other side.
Step 3
Exam Tip
\(x^2+39=208\) से \(x^2=169\), इसलिए (x=13) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ।
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एक संख्या और उसके वर्ग का योग (210) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (210). What is the positive number?
#quadratic equations
#number problem
#factoring
A (12)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=210\) gives \(x^2+x-210=0\), whose positive solution is (14). While factoring, check factors of (210).
Step 2
Why this answer is correct
The correct answer is B. (14). \(x^2+x=210\) gives \(x^2+x-210=0\), whose positive solution is (14). While factoring, check factors of (210).
Step 3
Exam Tip
\(x^2+x=210\) से \(x^2+x-210=0\), जिसका धनात्मक हल (14) है। गुणनखंड बनाते समय (210) के गुणनखंड देखें।
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एक संख्या और उसके वर्ग का योग (110) है। धनात्मक संख्या क्या है?
The sum of a number and its square is (110). What is the positive number?
#quadratic equations
#number problem
#factoring
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(x^2+x=110\) gives \(x^2+x-110=0\), whose positive solution is (10). While factoring, check factors of (110).
Step 2
Why this answer is correct
The correct answer is C. (10). \(x^2+x=110\) gives \(x^2+x-110=0\), whose positive solution is (10). While factoring, check factors of (110).
Step 3
Exam Tip
\(x^2+x=110\) से \(x^2+x-110=0\), जिसका धनात्मक हल (10) है। गुणनखंड बनाते समय (110) के गुणनखंड देखें।
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संख्या रेखा पर \(\sqrt{5}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{5}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच है। पूर्ण वर्गों से अंतराल जल्दी मिल जाता है।
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संख्या रेखा पर \(\sqrt{2}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{2}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (1) और (2) / (1) and (2)
B (0) और (1) / (0) and (1)
C (2) और (3) / (2) and (3)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 3
Exam Tip
क्योंकि \(1^2<2<2^2\), इसलिए \(1<\sqrt{2}<2\)। वर्गों की तुलना करके वर्गमूल का स्थान पहचानें।
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यदि \(1,4,7,\ldots\) के प्रत्येक पद में पद संख्या का वर्ग जोड़ा जाए तो नया अनुक्रम कैसा होगा?
If the square of the term number is added to each term of \(1,4,7,\ldots\), what type will the new sequence be?
#ap
#term number square
#not ap
#hard
A अंकगणितीय श्रेणी क्योंकि मूल अनुक्रम अंकगणितीय है / Arithmetic progression because the original sequence is arithmetic
B अंकगणितीय श्रेणी क्योंकि वर्ग जोड़े गए हैं / Arithmetic progression because squares are added
C अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगे / Not an arithmetic progression because new differences will not be equal
D (d=4) वाली अंकगणितीय श्रेणी / Arithmetic progression with (d=4)
Explanation opens after your attempt
Correct Answer
C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगे / Not an arithmetic progression because new differences will not be equal
Step 1
Concept
The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.
Step 2
Why this answer is correct
The correct answer is C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगे / Not an arithmetic progression because new differences will not be equal. The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.
Step 3
Exam Tip
नए पद \(2,8,16,\ldots\) मिलते हैं और अंतर \(6,8,\ldots\) हैं, जो समान नहीं हैं। पद संख्या के वर्ग जोड़ने से समान अंतर नहीं बचता।
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यदि \(7, 11, 15,\ldots\) में हर पद में उसकी पद संख्या का वर्ग जोड़ा जाए, तो क्या नया अनुक्रम अंकगणितीय श्रेणी होगा?
If the square of its term number is added to each term of \(7, 11, 15,\ldots\), will the new sequence be an arithmetic progression?
#ap
#term number square
#not ap
#expert
A हां, (d=4) रहेगा / Yes, (d=4) remains
B हां, (d=5) होगा / Yes, (d=5)
C नहीं, क्योंकि नए अंतर समान नहीं होंगे / No, because new differences will not be equal
D हां, क्योंकि मूल अनुक्रम अंकगणितीय है / Yes, because the original sequence is arithmetic
Explanation opens after your attempt
Correct Answer
C. नहीं, क्योंकि नए अंतर समान नहीं होंगे / No, because new differences will not be equal
Step 1
Concept
The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.
Step 2
Why this answer is correct
The correct answer is C. नहीं, क्योंकि नए अंतर समान नहीं होंगे / No, because new differences will not be equal. The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.
Step 3
Exam Tip
नए जोड़े गए वर्ग \(1,4,9,\ldots\) के अंतर \(3,5,\ldots\) समान नहीं हैं, इसलिए नया अनुक्रम अंकगणितीय नहीं रहेगा। पद संख्या के वर्ग से समान अंतर नहीं बनता।
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एक संख्या के वर्ग में (17) घटाने पर (127) मिलता है। धनात्मक संख्या क्या है?
When (17) is subtracted from the square of a number, the result is (127). What is the positive number?
#quadratic-equations
#word-problems
#square-root
A (12)
B (10)
C (14)
D (8)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2-17=127\)। इससे \(x^2=144\), इसलिए धनात्मक संख्या (12) है।
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एक संख्या के वर्ग में (11) घटाने पर (85) मिलता है। धनात्मक संख्या क्या है?
When (11) is subtracted from the square of a number, the result is (85). What is the positive number?
#quadratic-equations
#word-problems
#square-root
A \(4\sqrt{6}\)
B \(6\sqrt{4}\)
C (9)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{6}\)
Step 1
Concept
Let the number be (x), so \(x^2-11=85\). This gives \(x^2=96\), so the positive number is \(4\sqrt{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{6}\). Let the number be (x), so \(x^2-11=85\). This gives \(x^2=96\), so the positive number is \(4\sqrt{6}\).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2-11=85\)। इससे \(x^2=96\), इसलिए धनात्मक संख्या \(4\sqrt{6}\) है।
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पूर्ण वर्ग विधि में \(x^2+24x+17=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+24x+17=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (144)
B (24)
C (12)
D (17)
Explanation opens after your attempt
Step 1
Concept
Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (144). Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(24) का आधा (12) है और \(12^2=144\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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पूर्ण वर्ग विधि में \(x^2+20x+13=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+20x+13=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (100)
B (20)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (100). Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(20) का आधा (10) है और \(10^2=100\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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पूर्ण वर्ग विधि में \(x^2+16x+11=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+16x+11=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (64)
B (16)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (64). Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(16) का आधा (8) है और \(8^2=64\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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पूर्ण वर्ग विधि में \(x^2+12x+7=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+12x+7=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (36)
B (12)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (36). Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(12) का आधा (6) है और \(6^2=36\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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पूर्ण वर्ग विधि में \(x^2-10x+7=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2-10x+7=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (25)
B (10)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (25). Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(-10) का आधा (-5) है और ((-5)2 =25) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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किस संख्या का वर्ग (2) होता है और वह अपरिमेय है?
Which number has square (2) and is irrational?
#square
#irrational-number
#sqrt2
A \(\sqrt{2}\)
B (2)
C \(\frac{1}{2}\)
D (4)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\)
Step 1
Concept
(\(\sqrt{2}\)2 =2) and \(\sqrt{2}\) is irrational. This is an important basic example.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}\). (\(\sqrt{2}\)2 =2) and \(\sqrt{2}\) is irrational. This is an important basic example.
Step 3
Exam Tip
(\(\sqrt{2}\)2 =2) और \(\sqrt{2}\) अपरिमेय है। यह एक महत्वपूर्ण मूल उदाहरण है।
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यदि कोई संख्या (12q+5) या (12q+7) रूप में है, तो उसके वर्ग को 12 से भाग देने पर शेषफल क्या होगा?
If a number is of the form (12q+5) or (12q+7), what is the remainder when its square is divided by 12?
#euclids-division-lemma
#number-forms
#square-remainder
A 1
B 5
C 7
D 11
Explanation opens after your attempt
Step 1
Concept
The remainders in the two forms are 5 and 7.
Step 2
Why this answer is correct
\(5^2=25\) and \(7^2=49\), and both leave remainder 1 when divided by 12.
Step 3
Exam Tip
In form-based questions, work only with the remainder. चरण 1: दोनों रूपों में शेषफल 5 या 7 है। चरण 2: \(5^2=25\) और \(7^2=49\), दोनों को 12 से भाग देने पर शेषफल 1 है। चरण 3: रूप आधारित प्रश्नों में केवल शेषफल पर काम करें।
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यदि कोई संख्या (10q+3) या (10q+7) रूप में है, तो उसके वर्ग को 10 से भाग देने पर शेषफल क्या होगा?
If a number is of the form (10q+3) or (10q+7), what is the remainder when its square is divided by 10?
#euclids-division-lemma
#number-forms
#square-remainder
A 1
B 3
C 7
D 9
Explanation opens after your attempt
Step 1
Concept
The remainders in the two forms are 3 and 7.
Step 2
Why this answer is correct
\(3^2=9\) and \(7^2=49\), and both leave remainder 9 when divided by 10.
Step 3
Exam Tip
In form-based questions, work only with the remainder. चरण 1: दोनों रूपों में शेषफल 3 या 7 है। चरण 2: \(3^2=9\) और \(7^2=49\), दोनों को 10 से भाग देने पर शेषफल 9 है। चरण 3: रूप आधारित प्रश्नों में केवल शेषफल पर काम करें।
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यदि कोई संख्या (8q+3) या (8q+5) रूप में है, तो उसके वर्ग को 8 से भाग देने पर शेषफल क्या होगा?
If a number is of the form (8q+3) or (8q+5), what is the remainder when its square is divided by 8?
#euclids-division-lemma
#number-forms
#square-remainder
A 0
B 1
C 3
D 5
Explanation opens after your attempt
Step 1
Concept
The remainders in the two forms are 3 and 5.
Step 2
Why this answer is correct
\(3^2=9\) and \(5^2=25\), and both leave remainder 1 on division by 8.
Step 3
Exam Tip
Checking squares of odd remainders modulo 8 is a quick method. चरण 1: दोनों रूपों में शेषफल 3 या 5 है। चरण 2: \(3^2=9\) और \(5^2=25\), दोनों को 8 से भाग देने पर शेषफल 1 है। चरण 3: विषम शेषफलों के वर्ग को 8 से जांचना तेज तरीका है।
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यदि कोई संख्या (6q+1) या (6q+5) रूप में है, तो उसके वर्ग को 6 से भाग देने पर शेषफल क्या होगा?
If a number is of the form (6q+1) or (6q+5), what is the remainder when its square is divided by 6?
#euclids-division-lemma
#square-remainder
#number-forms
A 0
B 1
C 3
D 5
Explanation opens after your attempt
Step 1
Concept
The possible remainders are 1 and 5.
Step 2
Why this answer is correct
\(1^2=1\) and \(5^2=25=6\times4+1\), so the remainder is 1 in both cases.
Step 3
Exam Tip
In such forms, work only with the remainder, not the whole number. चरण 1: संभावित शेषफल 1 और 5 हैं। चरण 2: \(1^2=1\) और \(5^2=25=6\times4+1\), इसलिए दोनों स्थितियों में शेषफल 1 है। चरण 3: ऐसे रूपों में पूरी संख्या नहीं, केवल शेषफल पर काम करें।
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एक वर्गाकार मैदान की भुजा (4) मीटर बढ़ाने पर क्षेत्रफल (96) वर्ग मीटर बढ़ जाता है। मूल भुजा कितनी थी?
When the side of a square field is increased by (4) m, its area increases by (96) square m. What was the original side?
#quadratic equations
#square
#area increase
A (8) मीटर / (8) m
B (10) मीटर / (10) m
C (12) मीटर / (12) m
D (14) मीटर / (14) m
Explanation opens after your attempt
Correct Answer
B. (10) मीटर / (10) m
Step 1
Concept
If the original side is (x), then ((x+4)2 -x-2 =96). Thus (8x+16=96), giving (x=10).
Step 2
Why this answer is correct
The correct answer is B. (10) मीटर / (10) m. If the original side is (x), then ((x+4)2 -x-2 =96). Thus (8x+16=96), giving (x=10).
Step 3
Exam Tip
मूल भुजा (x) हो तो ((x+4)2 -x-2 =96)। इससे (8x+16=96) और (x=10) मिलता है।
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एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (60) मीटर भुजा का बचता है। बाहरी भुजा (92) मीटर है। (x) क्या है?
Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (60) m. The outer side is (92) m. What is (x)?
#quadratic equations
#square border
#application
A (12) मीटर / (12) m
B (14) मीटर / (14) m
C (16) मीटर / (16) m
D (18) मीटर / (18) m
Explanation opens after your attempt
Correct Answer
C. (16) मीटर / (16) m
Step 1
Concept
The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.
Step 2
Why this answer is correct
The correct answer is C. (16) मीटर / (16) m. The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.
Step 3
Exam Tip
अंदर की भुजा (92-2x) है और (92-2x=60), इसलिए (x=16) है। सीमा दोनों तरफ से घटती है।
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