SSC CGL 20201)\({(4a + 3b +2 c)^2}\) का विस्तार करें।
\({16a^2 + 9b^2 +4c^2+24ab +12bc + 16ca}\)
put a, b, c = 1 in the options
opton C will come out to be 81 as in the \({(4a + 3b +2 c)^2} = {(4 + 3 + 2)^2} = 81\)
SSC CGL 20202)यदि A + B = 12 और AB = 17, तो \({A^3 + B^3}\) का मान क्या है ?
1116
\({(A + B)^3} = {A^3} +B^3 + 3AB(A+B) => {(12)^3 = A^3 +B^3 +3(17)(12)}\)
\(A^3 + B^3 = 1116\)
SSC CGL 20203)\((3a - 4b)^3 \) निम्न में से किसके बराबर है ?
\(27a^3-64b^3-108a^2b+144ab^2\)
instead of solving the question with derivative formula, Solve by elimination method.
put a=1 and b=1 and put the value in question \((3a - 4b)^3 = -1\)
Now check options, this will eliminate option A and D, now check for a = 1 and b =0, \((3a - 4b)^3 = 27\)
this will eliminate option C, the correct answer will be B
SSC CGL 20194)यदि \( {x^8-1442x^4+1}=0\) है, तो (x - \( {1\over x}\)) का संभावित मान है |
6
\(x^8 - 1442 x^4 + 1 = 0; x^4 - 1442 + \frac{1}{x^4} = 0; x^4 + \frac{1}{x^4} = 1442 ; x^4 + \frac{1}{x^4} + 2 = 1442 + 2; (x^2 + \frac{1}{x^2})^2 = (38)^2 ; x^2 + \frac{1}{x^2} = 38 ; x^2 + \frac{1}{x^2} - 2 = 38 - 2 ; (x - \frac{1}{x})^2 = 6^2 ; x - \frac{1}{x} = 6; (\because (a - b)^2 = a^2 - 2ab + b^2);\)
SSC CGL 20195)यदि \({ \sqrt{86-60\sqrt2}}=a-b\sqrt2\) है, तो \( {\sqrt{a^2+b^2} }\) का एक दशमलव स्थान तक सही मान क्या होगा ?
7.8
\(\sqrt{86 - 60\sqrt{2}} = a - b\sqrt{2}; \sqrt{36 + 50 - 2 \times 30\sqrt{2}} = a - b\sqrt{2}; \sqrt{6^2 + (5\sqrt{2})^2 - 2 \times 6 \times 5\sqrt{2}} = a - b\sqrt{2}; \sqrt{(6 - 5\sqrt{2})^2 } = a - b\sqrt{2}; 6 - 5\sqrt{2} = a - b\sqrt{2}; \)
solve a = 6, b = 5, ans is 7.8
SSC CGL 20196)यदि \({a^2+b^2+c^2+96}=8(a+b-2c)\),तो \({\sqrt {ab-bc+ca}}\) निम्न में से किसके बराबर है ?
4
\(a^2 + b^2 + c^2 + 96 = 8(a + b - 2c)\);
\(a^2 + b^2 + c^2 + 96 - 8a - 8b + 16c = 0;\)
\((a^2 - 8a + 16) + (b^2 - 8b + 16) + (c^2 + 16c + 64) = 0; \) \((a - 4)^2 + (b - 4)^2 + (c + 8)^2 = 0;\)
\((a - 4)^2 = 0, (b - 4)^2 = 0, (c + 8)^2 = 0;\)
a = 4,
b = 4,
c = -8;
\(\sqrt{ab - bc + ca} = \sqrt{4 \times 4 + 4 \times 8 - 4 \times 8 } = \sqrt{16 + 32 - 32 } = 4\)
SSC CGL 20197)एक विद्यालय में, छात्रों की कुल संख्या का \({4 \over 9}\) लडकियां और शेष लड़के हैं । लड़कों की कुल संख्या का \({3 \over 5}\), 12 वर्ष से कम हैं, और लडकियों की संख्या का \({5 \over 12}\), 12 वर्ष या उससे अधिक है । यदि 12 वर्ष से कम आयु के छात्रों की संख्या 480 है, तो स्कूल में छात्रों की कुल संख्या का \({5 \over 18}\) निम्न में से किसके बराबर है ?
225
Let the total student be x.
Number of girls = 4x/9;
Number of boys = x - 4x/9 = 5x/9;
Number of boys below 12 years = \(5x/9 \times 3/5 \)= x/3;
Number of girls are 12 years or above 12 years of age =\( 4x/9 \times 5/12 \)= 5x/27;
Number of girls below 12 years =\( \frac{4x}{9} - \frac{5x}{27}\) = 7x/27;
The number of students below 12 years of age = 480;
Number of boys below 12 years + number of girls below 12 years = 480;
\(\frac{x}{3} +\frac{7x}{27} \)= 480;
16x/27 = 480;
x = 810;
\(\frac{5}{18} \)of the total number of students in the school =\( 810 \times \frac{5}{18}\) = 225
SSC CGL 20198)यदि x + y + z =11, \({x^2 + y^2 + z^2 = 133}\) और \({x^3 + y^3 + z^3 = 881}\), तो \(\sqrt[3]{xyz}\) का मान है |
-6
\((x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz);\)
\((11)^2 = 133 + 2(xy + yz + xz);\)
2(xy + yz + xz) = -12;
xy + yz + xz = -6;
\(x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - (xy + yz + xz)); \)
881 - 3(xyz) = 11(133 + 6);
3xyz = 648;
xyz = -216;
\(\sqrt[3]{xyz} \) = -6
SSC CGL 20199)\({(253)^3+(247)^3}\over {25.3\times25.3-624.91+24.7\times24.7}\) का मान \({50\times10^k}\) है, जहां k का मान है |
3
\(\frac{(253)^3 + (247)^3}{25.3 \times 25.3 - 624.91 + 24.7 \times 24.7} = 50 \times 10^k;\)
\(\frac{(253 + 247)(253)^2 + (247)^2 - 253 \times 247)}{\frac{1}{100}[(253)^2 - 253 \times 247 + (247)^2] } = 50 \times 10^k;\)
\(50000 = 50 \times 10^k;\)
\(50 \times 10^3 = 50 \times 10^k;\)
k = 3
SSC CGL 201910)यदि \({(\sqrt2+\sqrt5-\sqrt3)\times k=-12}\), तो k का मान क्या होगा ?
\({(\sqrt2+\sqrt5+\sqrt3)(2-\sqrt10)}\)
\(\left(\sqrt{2} + \sqrt{5} - \sqrt{3}\right) \times k\) = -12;
\((1.414 + 2.236 - 1.732) \times k \)= -12;
By the option B,
\((1.414 + 2.236 - 1.732) \times \left(\sqrt{2} + \sqrt{5} + \sqrt{3}\right)\left(2 - \sqrt{10}\right) \)= -12;
(1.414 + 2.236 - 1.732) x (1.414 + 2.236 + 1.732)(2 - 3.16) = -12;
\(1.9 \times 5.3 \times (-1.16) \)= -12;
-12 = -12