objective Ques (283 results)
SSC CGL Mains 20241)
138
SSC CGL Mains 20242)Find the value of Y, if X− 2Y + 2Z = 16, X − Y + Z = 9 and 2X − 3Y − Z = 9.
−3
SSC CGL Mains 20243)
44
SSC CGL 20224)If x + y + z = 0 and x2 + y2 + z2 = 40, then what is the value of xy + yz + zx?
-20
SSC CGL 20225)If α, β are the roots of \(6x^2 + 13x + 7 = 0\), then the equation whose roots are \(α^2, β^2\) is:
\(36x^2\) - \(85x\) + 49 = 0
SSC CGL 20226)If x = 222, y = 223 and z = 224, then find the value of x3 + y3 + z3 - 3xyz.
2007
SSC CGL 20227)If \(x^4 + \frac{16}{x^4} \)= 15617, x > 0, then find the value of \(x + \frac{2}{x} \) .
\(\sqrt{129}\)
SSC CGL 20228)If p = 8.15, q = 9.06 and r = -17.21, then the value of p3 + q3 + r3 - 3pqr is:
0
SSC CGL 20229)If \(\frac{x}{8} + \frac{8}{x} = 1\) , then the value of x3 is :
-512
SSC CGL 202210)What is the value of a2 + b2 + c2 - 2ab - 2bc + 2ca ?
(a – b + c)2
SSC CGL 202211)If \({a} + \frac{1}{{{a}}}=5\) , then what is the value of \({a^3} + \frac{1}{{{a^3}}}\)?
110
SSC CGL 202212)If a = 26 and b = 22, then the value of \({{a^3 - b^3} \over a^2 - b^2}-{{3ab} \over a \ + \ b}\) is ______.
\({{1} \over 3}\)
SSC CGL 202213)If \(5x - {{5} \over x} + 6 = 0\), then \( {x^2}+{{1} \over {x^2}}\) is:
\({{86} \over 25}\)
SSC CGL 202214)If \(m + {{1} \over (m \ - \ 2)}= 4\) then find the value of \({(m \ - \ 2)^2}\) + \({{1} \over (m \ - \ 2)^2} \) .
2
SSC CGL 202215)If \(x + \frac{{1}}{{x}}\) = 6, then find the value of\( \frac{{3x}}{{2{x^2} - 5x + 2}}\) .
\(\frac{3}{7}\)
SSC CGL 202216)If K +\( \frac{1}{K}\) + 2 = 0 and K < 0, then what is the value of K11 +\( \frac{1}{K^4}\) ?
0
SSC CGL 202217)Which of the following statement is correct?
I. If x = 12, y = -2 and z = -10, then x + y + z = 360.
II. If x + y = 48 and 4xy = 128, then 4x + 4y = 4480.
Neither I nor II
SSC CGL 202218)A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a, c = 2b, d = 2c. The pin is divisible by ________.
2, 3, 13
SSC CGL 202219)Which of the following statement is correct?
I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 720
II. If x + y = 48 and 4xy = 128, then s the value of 4x2 + 4y2 is 8960
Both I and II
SSC CGL 202220)If 2p + q = 19 and 8p3 + q3 = 361, then find the value of pq.
57
SSC CGL 202221)If a - b = 8 and ab = 9, then the value of a + b is ________.
±10
SSC CGL 202222)Which of the following statement is correct?
I. The value of 1002 - 992 + 982 -972+962-952+942-932+.......+222-212 is 4840.
II. The value of \((k^{2}+ \frac{1}{k^{2}})(k - \frac{1}{k})(k^{4} + \frac{1}{k^{4}})(k + \frac{1}{k})(k^{4} - \frac{1}{k^{4}})\) is \(k^{16}- \frac{1}{k^{16}}\).
Only I
SSC CGL 202223)If \(\frac{a}{b} + \frac{b}{a}\) = -1 and a - b = 2, then the value of a3 - b3 is:
zero
SSC CGL 202224)If, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r3 is:
-2197
SSC CGL 202225)If a = -12, b = -6 and c = 18, then what is the value of (2abc)/9
288
SSC CGL 202226)If a + b + c = 5, a + b3 + c3 = 85 and abc = 25, then find the value of a2 + b2+ c2 - ab - bc - ca.
2
SSC CGL 202227)If \(x = 2 - 2^\frac{1}{3} + 2^\frac{2}{3}\) , then find the value of x3 - 6x2 + 18x.
22
SSC CGL 202228)If P + Q = 6 and PQ = 4, then what is the value of P3 + Q3?
144
SSC CGL 202229)If \({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\) and a + b = 5c, where c > 0, then the value of c is ________________.
8
SSC CGL 202230)If \(y + {1 \over y} = 3\)\(\), then what is the value of \({{1} \over y^3} + y^3 + 2\)?
20
SSC CGL 202231)If x + y = 36, then find (x - 27)3 + (y - 9)3.
0
SSC CGL 202232)If a + b =11 and ab = 35, then what is the value of (a4 + b4)?
151
SSC CGL 202233)Simplify x9 × x5 × x-4 × x0 × x-6
x4
SSC CGL 202234)If \(\left(x+\frac{1}{x}\right)=5 \sqrt{2}\) , then what is the value of (x4 + x - 4)?
2302
SSC CGL 202235)k is a negative number, such that, k + k-1 = -2, then what is the value of \(\frac{k^2+4 k-2}{k^2+k-5}\) ?
1
SSC CGL 202236)If \(x^{2} - 5x + 1 = 0\), then the value of \(\frac{x^{6}+x^{4}+x^{2}+1}{5x^{3}}=?\)
23
SSC CGL 202237)If x4 - 79x2 + 1 = 0, then a value of x + x-1 can be:
9
SSC CGL 202238)If a2 + b2 = 65 and ab = 8, a > b > 0, then find the value of a2 - b2.
63
SSC CGL 202239)If \((a+\frac{1}{a}+3)^2 = 16\), where a is a non-zero real number, then find the value of \(a^2+{1\over a^2}\).
47
SSC CGL 202240)If 4x - 3y = 12 and xy = 5, then find the value of \(\frac{{16{x^2} + 9{y^2}}}{8}\) .
33
SSC CGL 202241)If \(5x - {1\over 4x}= 6\), x > 0, then find the value of \(25x^2-\frac{1}{16x^{2}}\).
\(6 \sqrt{41}\)
SSC CGL 202242)If a + b + c = 6, a2 + b2 + c2 = 32, and a3 + b3 + c3 = 189, then the value of 4abc is:
12
SSC CGL 202243)If (4a - 3b) = 1, ab = \(\frac{1}{2}\) , where a > 0 and b > 0, what is the value of (64a3 + 27b3)?
35
SSC CGL 202244)If 5√3 + √75 = 17.32, then the value of 14√3 + √108 is:
34.64
SSC CGL 202245)If 6√ 6 p3 +2√ 2 q3 = (√ 6p + √ 2q)(Sp2 + Mq2 - Npq), then the positive value of \(\sqrt{S^2+M^2+2N^2}\) is:
8
SSC CGL 202246)If\( \sqrt{x}-{1 \over \sqrt{x}} = \sqrt{5}\) , x ≠ 0, then what is the value of \((x^4+{1\over{x^2}})\over(x^2+1)\)?
46
SSC CGL 202247)If \(x^2+\frac{1}{x^2}=18, x>0\) then find the value of \(x^3+\frac{1}{x^3}\),
\(34 \sqrt{5}\)
SSC CGL 202248)If (x + y)3 - (x - y)3 - 3y(2x2 - 3y2) = ky3, then find the value of k.
11
SSC CGL 202249)If a + b + c = 11 and ab + bc + ca = 28, then find the value of a3 + b3 + c3 - 3abc.
407
SSC CGL 202250)If x2 - 5x - 1 = 0, what is the value of
\( \frac{{{x^6} - {x^4} + {x^2} - 1}}{{{x^3}}}\) ?
135
SSC CGL 202251)If a2 + b2 + 49c2 + 18 = 2(b + 28c - a), then the value of (2a - b + 7c) is:
1
SSC CGL 202252)If x + y + z = 7, xy + yz + zx = 8, then what is the value of x3 + y3 + z3 - 3xyz?
175
SSC CGL 202253)If a3 + b3 = 218 and a + b = 2, then the value of \(\sqrt {1 - ab}\) is:
6
SSC CGL 202254)\(\sqrt{x}-{1\over \sqrt{x}}= \sqrt{3}\), then what is the value of \(x^4+\frac{1}{{{x^4}}} \)?
527
SSC CGL 202255)if \(2 \sqrt{2}x^3- 3 \sqrt{3}y^3\) = \((\sqrt2x-\sqrt3y)\) (Ax2- Bxy+ Cy2), then the value of \(\sqrt {(A^2 + B^2 + C^2)}\) is:
\(\sqrt {19}\)
SSC CGL 202256)If a2 + b2 + 49c2 + 18 = 2(b - 28c - a), then the value of (a - b - 7c) is:
2
SSC CGL 202257)If a + b - c = 5 and ab - bc - ac = 10, then find the value of a2 + b2 + c2.
5
SSC CGL 202258)If x + y + z = 2, xy + yz + zx = -11, and xyz = -12, then what is the value of x3 + y3 + z3?
38
SSC CGL 202259)What is the value of p, if 25(3 + 4p) ÷ 12 of 5 - 3 × 8 = 6?
\(17\frac{1}{4}\)
SSC CGL 202260)If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then find the value of \(\sqrt[4]{x^3+y^3+z^3+xyz} \)
6
SSC CGL 202261)If 2√2x3 - 3√3y3 = (√2x - √3y)(Ax2 - Bxy + Cy2), then the value of (A2 + B2 + C2) is:
19
SSC CGL 202262)If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then the value of x3 + y3 + z3 + xyz is :
1296
SSC CGL 202263)What is the value of x, if \(5\left( {1 - \frac{x}{5}} \right) - (5 - x) - \frac{1}{{200}}{\rm{of (20 - x) = 0}}{\rm{.08}}\) ?
36
SSC CGL 202264)If 8k6 + 15k3 – 2 = 0, then the positive value of \(\left( {{\rm{k}}\,{\rm{ + }}\,\frac{1}{{\rm{k}}}} \right)\) is :
\(2\frac{1}{2}\)
SSC CGL 202265)If x - y + z = 0, then find the value of \(\frac{{{y^2}}}{{2xz}}\, - \,\frac{{{x^2}}}{{2yz}}\, - \,\frac{{{z^2}}}{{2xy}} \)
\(\frac{3}{2}\)
SSC CGL 202266)If a + b + c = 6, a2 + b2 + c2 = 32, and a3 + b3 + c3 = 189, then the value of abc - 3 is:
0
SSC CGL 202267)If a2 + b2 + 49c2 + 18 = 2(b - 28c - a) then the value of (a + b - 7c) is:
4
SSC CGL 202268)If x + y + z = 11, xy + yz + zx = -6, and x3 + y3 + z3 = 1604, then the value of xyz is:
25
SSC CGL 202269)If a2 + b2 + c2 = 6.25 and (ab + bc + ca) = 0.52, what is the value of (a + b + c), if (a + b + c) < 0?
-2.7
SSC CGL 202270)If \(x = 4 + \sqrt{15}\) , what is the value of \( \left( {{x^2}\, + \,\frac{1}{{{x^2}}}} \right)\)?
62
SSC CGL 202271)If (4x+2y)3+(4x−2y)3=16(Ax3+Bxy2), then what is the value of \({1\over 2 }{(\sqrt{A^2 +B^2})}\)?
5
SSC CGL 202272)Simplify the following expression: \({{{(a^2-4b^2)}^3} + 64 {{(b^2 - 4c^2)}^3} + {{(16c^2 -a^2})^3}} \over {{(a-2b)^3} +{(2b-4c)^3} +{(4c-a)^3}}\)
2(a + 2b) (b + 2c) (4c + a)
SSC CGL 202273)If x + y + 3 = 0, then find the value of x3 + y3 - 9xy + 9.
-18
SSC CGL 202274)If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3 + 216y3)?
224
SSC CPO 202075)If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of \(\sqrt {{x^3} + {y^3} + {z^3} + xyz}\) is:
35
SSC CPO 202076)In a school, 5/12 of the number of students are girls and the rest are boys. 4/7 of the number of boys are below 14 years of age, and 2/5 of the number of girls are 14 years or above 14 years of age. If the number of students below 14 years of age is 1120, then the total number of students in the school is:
1920
SSC CPO 202077)If a2 + b2 = 82 and ab = 9, then a possible value of a3 + b3 is:
730
SSC CPO 202078)If a + b + c = 0, then the value of \(\frac{{a^2}}{{bc}} +\)\(\frac{{b^2}}{{ac}} +\)\(\frac{{c^2}}{{ab}} \) is:
3
SSC CPO 202079)X4 + X-4 = 194, X > 0, then what is the value of X + \(\frac{1}{X}\) + 2 ?
6
SSC CPO 202080)If x + y + z = 19, x2 + y2 + z2 = 133 and xz = y2, x > z > 0, what is the value of (x - z) ?
5
SSC CPO 202081)If (5√5x3 – 3√3y3) ÷ (√5x – √3y) = (Ax2 + By2 + Cxy), then what is the value of (3A – B – √15C) ?
-3
SSC CPO 202082)If x + y + z = 13, x2 + y2 + z2 = 133 and x3 + y3 + z3 = 847, then the value of \(\sqrt[3]{{xyz}}\) is:
-6
SSC CPO 202083)If a3 + b3 = 217 and a + b = 7, then the value of ab is:
6
SSC CPO 202084)If a2 + b2 + c2 + 84 = 4(a - 2b + 4c), then \(\sqrt {ab - bc + ca}\) is equal to:
\(2\sqrt {10}\)
SSC CPO 202085)If x2 + 8y2 + 12y - 4xy + 9 = 0, then the value of (7x + 8y) is:
-33
SSC CPO 202086)The students of a class donated a sum of Rs. 2,809 to the Fund. Each student donated as many rupees as the number of students in the class. The number of students in the class is:
53
SSC CPO 202087)If x + y + z = 17, xyz = 171 and xy + yz + zx = 111, then the value of \(\sqrt[3]{{(x^3+y^3+z^3+xyz)}} \) is:
-4
SSC CPO 202088)If x2 – 3x + 1 = 0, then the value of \( (x^4 + \frac{1}{x^2}) \div (x^2+1) \) is:
6
SSC CPO 202089)If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of x3 + y3 + z3 + xyz is:
1225
SSC CPO 202090)If x2 - 5x + 1 = 0, then the value of \(\left(x^4 + \frac 1 {x^2}\right) \)\(\div \left(x^2 + 1\right)\) is:
22
SSC CPO 202091)If x2 + 8y2 - 12y - 4xy + 9 = 0, then the value of (7x - 8y) is:
9
SSC CPO 202092)The students of a class donated a sum of Rs. 2,209. If each student donated as many rupees as the number of students in the class, then the number of students in the class is:
47
SSC CPO 202093)If \(( 5\sqrt 5 x^ 3 − 3\sqrt 3 y^ 3 ) ÷ ( \sqrt 5 x − \sqrt 3 y ) = ( A x ^2 + B y^ 2 + C x y )\) then value of \((3A+ B- \sqrt{15} C)\) is:
3
SSC CPO 202094)If x4 + x-4 = 194, x > 0, then the value of \(x+\dfrac{1}{x} \) is:
4
SSC CPO 202095)If a2 + b 2 + c 2+ 216 = 12 ( a + b − 2 c ), then \(\sqrt{ab-bc+ca} \), is:
6
SSC Selection Post Matric 202296)If \(x+{1\over x}=5\), then find the value of \(x^2+{1\over x^2}\).
23
SSC Selection Post Matric 202297)If \(x+{1\over x}= 1 -\sqrt2\), then find the value of \(x^3+{1\over x^3}\).
\(4 - 2 \sqrt2\)
SSC Selection Post Matric 202298)If x2 + y2 + z2 + 26 = 2(4x + y + 3z), then find the value of x + y + z.
8
SSC Selection Post Matric 202299)If a + b = \(3\over4\) and ab = \(\frac{1}{8}\), then the value of a4 + b4 + ab3 + ba3 is:
\(\frac{27}{256}\)
SSC Selection Post Matric 2022100)If a + b + c = 8 and ab + bc + ca = 11, then what is the value of \(\left(\frac{a^2+b^2+c^2-3abc}{4}\right)\)?
62
SSC Selection Post Matric 2022101)If x - y = 4 and x3 - y3 = 316, y > 0, then the value of x2 - y2 is:
40
SSC Selection Post Matric 2022102)If a + b + c = 8 and ab + bc + ca = 2, then what is the value of a3 + b3 + c3 - 3abc?
464
SSC Selection Post Matric 2022103)If a + b + c = 1, and a3 + b3 + c3 = 55, and ab + bc + ca = -10, then what is the value of 5abc?
40
SSC Selection Post Matric 2022104)If \(x+ {1\over x}=4\), x > 0, then what is the value of \((x^4 + \frac{1}{x^2}) \div (x^2 + 8x + 1)\)?
\(\frac{13}{3}\)
SSC Selection Post Matric 2022105)If (7x - 3)3 + (x + 2)3 + 27(2x + 5)3 = 9(7x - 3) (x + 2) (2x + 5), then (9x + 13) : (5x + 7) = ?
2 : 1
SSC Selection Post Matric 2022106)If 2x2 + 5x - 1 = 0, then what is the value of \(x^3 -\frac{1}{{8{x^3}}}\) ?
\(- \frac{155}{8}\)
SSC Selection Post Matric 2022107)If \( { \sqrt{x}- {1 \over \sqrt{x}}} = \sqrt7\) , then the value of \(x^3 + {1 \over x^3}\) is:
702
SSC Selection Post Matric 2022108)If \({(x+{1\over 2})^3+(3x+{2\over 3})^3+(x−{1\over 6})^3}\) = \({1 \over 12}\) \(( 9 x + 2 ) (2x+1)(6x−1)\), then what is the value of x is ?
\(-{1\over5}\)
SSC Selection Post Matric 2022109)If \( x ^4+{1\over x^4} = 34\) where x > 0 , then find the value of
\( x +{1\over x} \) .
2√2
SSC Selection Post Matric 2022110)If \({x ^ {1 \over 3}} - {y ^ {1 \over 3}} = {z ^ {1 \over 3}}\), then find the value of (x - y - z)3 - 27xyz.
0
SSC Selection Post Matric 2022111)If x = 3 - 4y, then \((x^3+64y^3+36xy)\) is equal to:
27
SSC Selection Post Matric 2022112)If a : b = 7 : 4, then find (2a + 7b) : (7b — 2a).
3 : 1
SSC Selection Post Matric 2022113)Find the value of (a — 2x)3 + (b — 2x)3 + (c — 2x)3 — 3(a — 2x)(b— 2x)(c— 2x) given that a + b + c = 6x.
0
SSC Selection Post Matric 2022114)[(4a — 5b)3 + (5b — 3c)3 — (4a — 3c)3] is equal to:
-3(4a - 5b)(5b - 3c)(4a - 3c)
SSC CHSL 2021115)If \(x+{1\over x}=\sqrt{13}\), then one of the values of \(x^3-\frac{1}{x^3}\) is:
36
SSC CHSL 2021116)If x2 + (4 - √3)x - 1 = 0, then what is the value of \(x^2+\frac{1}{x^2} \)?
21 - 8√3
SSC CHSL 2021117)A,B, C and D are four positive numbers such that A is \(\frac{3}{4}\) times of B, B is \(\frac{4}{5}\) times of C, and C is \(\frac{3}{8}\) times of D. If the average of 4 times of A and 7 times of D is 316, then the average of all the four numbers A, B, C and D is:
38
SSC CHSL 2021118)If \(x^2+{1\over x^2}=83\), x > 0, then the value of \(x^3-\frac{1}{x^3}\) is:
756
SSC CHSL 2021119)If (7x - 10y) = 8 and xy = 5, then what is the value of 49x2 + 100y2?
764
SSC CHSL 2021120)If \(a = \frac{\sqrt{5}+2}{\sqrt{5}-2}\) and \(b ={\sqrt5-2\over\sqrt5+2}\), then the value of 2a2 + 2b2 - 5ab is equal to:
639
SSC CHSL 2021121)The value of a3 + b3 + c3 - 3abc, when a = 125, b = 127 and c = 129, is:
4572
SSC CHSL 2021122)If 3x - 2y + 3 = 0, then what will be the value of 27x3 + 54xy + 30 - 8y3 ?
3
SSC CHSL 2021123)Given that 3√3x3 - 8y3 = (√3x + Ay)(3x2 + By2 + Cxy), the value of (A2 + B2 - C2) is:
8
SSC CHSL 2021124)If \(\sqrt x+{1\over\sqrt x}=2\sqrt3\), then what will be the value of \(x^4+\frac{1}{x^4}\) ?
9602
SSC CHSL 2021125)If a + 5b = 25 and ab = 20, then one of the values of (a - 5b) is:
15
SSC CHSL 2021126)If 3a - b = 1 and ab = 4, then the value of (9a2 - b2) is:
7
SSC CHSL 2021127)If x = 555, y = 556 and z = 557, then find the value of x3 + y3 + z3 – 3xyz.
5004
SSC CHSL 2021128)If \(a-{24\over a}=5\), where a > 0, then the value of \(a^2+\frac{64}{a^2} \) is:
65
SSC CHSL 2021129)x, y are two positive numbers such that x > y. If x4 + y4 = 706 and xy = 15, then the value of 2x + 3y is:
19
SSC CHSL 2021130)If a - b = 7 and a2 + b2 = 169 where a, b > 0, then the value of 3a + b is:
41
SSC CHSL 2021131)If x4 + x-4 = 47, x > 0, then the value of (2x - 3)2 is:
5
SSC CHSL 2021132)If a2 + b2 + c2 + 48 = 8(a + b + c), then what is the value of \(\sqrt[3]{a^3-b^3+c^3} \)?
4
SSC CHSL 2021133)If 3x + 5y = 14 and xy = 6, then what is the value of 9x2 + 25y2 ?
16
SSC CHSL 2021134)If (x - 1.5)3 + (x - 4)3 + (x - 3.5)3 = 3(x - 1.5)(x - 4)(x - 3.5), then what is the value of x?
3
SSC CHSL 2021135)If a + b + c = 5, a2 + b2 + c2 = 27, a3 + b3 + c3 = 125, then the value of \(\frac{abc}{5}\) is :
-1
SSC CHSL 2021136)If a + b + c = 11 and ab + bc + ca = 15, then what is the value of a3 + b3 + c3 - 3abc?
836
SSC CHSL 2021137)If 1 + 4x2 + 16x4 = 512 and 1 - 2x + 4x2 = 64, then the value of 1 + 2x + 4x2 is:
8
SSC CHSL 2021138)If \(x+{1\over3x}=5\), then the value of \(27x^3+\frac{1}{x^3}\) will be:
3240
SSC CHSL 2021139)If 2x + 3y + 4z = 11, 8x3 + 27y3 + 64z3 = 105 and xyz = 1, then the value 4x2 + 9y2 + 16z2 - 6xy - 12yz - 8xz is:
3
SSC CHSL 2021140)If x6 - 6√6y6 = (x2 + Ay2)(x4 + Bx2y2 + Cy4), then what will be the value of (A2 - B2 + C2)?
36
SSC CHSL 2021141)If \(x+{1\over15x}=3\), then the value of \(9x^3+\frac{1}{375x^3}\) will be:
237.6
SSC CHSL 2021142)Simplify the given expression.
\(\left(x-\frac{2}{x}\right)^3-\left(x+\frac{2}{x}\right)^3\)
\(-4\left(3x+\frac{4}{x^3}\right)\)
SSC CHSL 2021143)If \((2x+{1\over2x})= 5\), then what is the value of \(\left(8x^3 + \frac{1}{8x^3}\right)\)?
110
SSC CHSL 2021144)If 3x + y = 12 and xy = 9, then the value of (3x - y) is:
6
SSC CHSL 2021145)If a2 + b2 + c2 = 576 and (ab + bc + ca) = 50, then what is the value of (a + b + c), if (a + b + c) < 0?
-26
SSC CHSL 2021146)If x ∶ y = 4 ∶ 5, then the value of (8x - 6y) ∶ (9x - 7y) is:
2 : 1
SSC CHSL 2021147)If x + y = 27 and x2 + y2 = 425, then the value of (x - y)2 will be:
121
SSC CHSL 2021148)If \(x^4+{1\over x^4}=1154\), x > 0, then what will be the value of \(x+\frac{1}{x}\)?
6
SSC CHSL 2021149)If x + 2y = 19 and x3 + 8y3 = 361, then xy is equal to:
57
SSC CHSL 2021150)If 27x3 - 64y3 = (Ax + By)(Cx2 + Dy2 - Exy), then value of (A - B + C - D + E) will be:
-12
SSC CHSL 2021151)If (3x + 2y)3 + (3x - 2y)3 = 3kx(3x2 + 4y2), then the value of k will be:
6
SSC CHSL 2021152)If \(x+{81\over x}= 18\) where x > 0, then the value of \(x^2+\frac{162}{x^2}\) is:
83
SSC CHSL 2021153)If \({x-{1\over x}}=2\sqrt2\), then what will be the value of \( x^3-\frac{1}{x^3}\) ?
22√2
SSC CHSL 2021154)If x4 - 12x2 + 1 = 0, then what will be the value of \(x^4+\frac{1}{x^4} \)?
142
SSC CHSL 2021155)If a + b + c = 2 and ab + bc + ca = -1, then the value of a3 + b3 + c3 - 3 abc is:
14
SSC CHSL 2021156)If \((x^2+{1\over49x^2})=15{5\over7}\), then what is the value of \( \left(x+\frac{1}{7x}\right)\)?
± 4
SSC CHSL 2021157)If (2a + 3b) (2c - 3d) = (2a - 3b) (2c + 3d), then:
\(\frac{a}{b}=\frac{c}{d}\)
SSC CHSL 2021158)If x - y = 4 and xy = 3, then what is the value of x3 - y3?
100
SSC CHSL 2021159)If a + b - c = 0, then what is the value of \(\frac{(b-c)^2}{4bc}\frac{(c-a)^2}{4ca}\frac{(a+b)^2}{4ab}\)?
\(\frac{1}{64}\)
SSC CHSL 2021160)Simplify the following expression.
(2a - b - 3c)(4a2 + b2 + 9c2 + 2ab + 6ac - 3bc)
8a3 - b3 - 27c3 - 18abc
SSC CHSL 2021161)If x - y = 4 and x3 - y3 = 316, then the value of x4 + y4 is:
2482
SSC CHSL 2021162)What is the coefficient of y2 in the expansion of (√2y2 - 5√3)3?
225√2
SSC CHSL 2021163)If a + b = 24 and a2 + b2 = 306, where a > b, then the value of 4a - 5b is:
15
SSC CHSL 2021164)If 9x2 - 6x + 1 = 0, then the value of 27x3 + (27x3)-1 will be:
2
SSC CHSL 2021165)If 9a2 + 4b2 + 49c2 + 18 = 2(2b + 28c - 3a), then the value of (a + 2b - c) will be:
\(\frac{2}{21}\)
SSC CHSL 2021166)If (4X - 5)3 + (X - 2)3 + 27(2X - 5)3 = 9(4X - 5)(X - 2)(2X - 5), then the value of \(\left(x+\frac{3}{2}\right)\) will be:
\(\frac{7}{2}\)
SSC CHSL 2021167)If x2 + 4y2 + 3z2 +\(\frac{19}{4}=2\sqrt{3}\)\((x+y+z)\) , then the value of (x - 4y + 3z) is:
\(\sqrt{3}\)
SSC CHSL 2021168)If x + y + z = 13, x2 + y2 + z2 = 91 and xz = y2, then the difference between z and x is:
8
SSC CHSL 2021169)The value of \({5\over4}\times2{2\over3}\div{5\over9}\)\(of\space 1{1\over5}+{2\over25}\times\)\(4{1\over6}\div{2\over7}\)\(of\space2 \frac{1}{3}\) is:
\(5\frac{1}{2}\)
SSC CHSL 2021170)The coefficient of x3 y in (x - 2y) × (5x + y)3 is:
-175
SSC CHSL 2021171)If \(x^2 – 3\sqrt2x+ 1 = 0,\) then what is the value of \({x^3} + \left( {\frac{1}{{{x^3}}}} \right)\)?
\(45\sqrt 2\)
SSC CHSL 2021172)If x2 + 1 – 2x = 0, x > 0, then x2 (x2 - 2) = ________.
–1
SSC CHSL 2021173)If a + b + c = 7 and a3 + b3 + c3 – 3abc = 301, then ab + bc + ca = ?
2
SSC CHSL 2021174)If \(x-{2\over x}=4\), then what will be the value of \( x^2 + \frac{4}{x^2}\)?
20
SSC CHSL 2021175)If \(x^4+{1\over x^4}=3842\), then the positive value of \( x + \frac{1}{x}\) will be:
8
SSC CHSL 2021176)If \(\sqrt x+{1\over\sqrt x}=\sqrt6\), then the value of \(x^6 + \frac{1}{x^6}\) will be:
2702
SSC CHSL 2021177)Using algebraic identities, simplify the following expression.
\(\frac{(x^4 + x^2 + 1)}{(x^2 + x + 1)}\)
(x2 - x + 1)
SSC CHSL 2021178)If \((x+{1\over x})^3=27\), then what is the value of \(\left( x^2 + \frac{1}{x^2} \right) \)? Given that x is real.
7
SSC CHSL 2021179)If a + b = p, ab = q, then (a4 + b4) is equal to
p4 - 4p2q + 2q2
SSC CHSL 2021180)If x8 – 2599x4 + 1 = 0, then the positive value of \(x-\frac{1}{x}\) will be:
7
SSC CHSL 2021181)If a2 + 49b2 + c2 + 18 = 2(28b - c - a) then the value of (a + 7b - c) is:
4
SSC CHSL 2021182)If a + b + c = 4, ab + bc + ca = -14 and abc = -18, then the value of \(\sqrt{4a^3+4b^3+4c^3-36}\) will be:
26
SSC CHSL 2021183)If x2 - 5√2x - 1 = 0, then what will be the value of \(x^3 - \frac{1}{x^3}\) ?
265√2
SSC CHSL 2021184)If a4 + b4 + a2b2 = 133 and a2 + b2 - ab = 19, then the value of ab will be:
-6
SSC CHSL 2021185)If \(x - y ={7\over4}\) and \(\frac{1}{x}-\frac{1}{y}=\frac{14}{3}\), then x3 - y3 is equal to:
\(\frac{217}{64}\)
SSC CHSL 2021186)If \(x+{1\over x}= \sqrt7\), then what is the value of \((x^2 + 1)\div\left[x^4+\left(\frac{1}{x^2}\right)\right]\)?
\(\frac{1}{4}\)
SSC CHSL 2021187)If 4√3x2 + 5x -2√3 = (Ax + 2)(Bx + C). then what is the value of (A + B + C)?(A>0)
4
SSC CHSL 2021188)If x + y + z = 3, x2 + y2 + z2 = 45 and x3 + y3 + z3 = 69 then what is the value of xyz?
-40
SSC CHSL 2021189)If a3 + b3 + c3 - 3abc = 250 and a + b + c = 10, then what will be the value of \(\frac{1}{5}(ab+bc+ca)\) ?
5
SSC CHSL 2021190)If x2 + y2 = 45 and x - y = 5 then what is the value of x3 - y3?
275
SSC CHSL 2021191)If \(x+{1\over x}=7\), then \(x^3 + \dfrac{1}{x^3}\) is equal to:
322
SSC CHSL 2021192)If x + y + z = 4, xy + yz + zx = 1 and x3 + y3 + z3 = 34 , then what is the value of 2xyz ?
-12
SSC CHSL 2021193)If a2 + 4b2 + 25c2 + 18 = 2 (a - 2b + 20c), then what is the value of (a + 2b + 5c) ?
4
SSC CHSL 2021194)If \(x-3={1\over2x}\), then what is the value of \(( x^4 + \frac{1}{16x^4})\) ?
\(99 \frac{1}{2}\)
SSC CHSL 2021195)If \(({x\over y}+1)=4\), then what is the value of \(( \frac{x^2 + y^2}{y^2})\) ?
10
SSC CHSL 2021196)If \((x+{2\over x})=7\), then what is the value of \(( 2x^2 + \frac{8}{x^2} )\) ?
90
SSC CHSL 2021197)If \(x^4+{16\over x^4}=27217\), x > 0, then the value of \(\rm x + \frac{2}{x}\) is:
13
SSC CHSL 2021198)If 8a3 + b3 = 16 and 2a + b = 4, then find the value of 16a4 + b4.
32
SSC CHSL 2021199)If \(x-{1\over2x}=4\), then the value of \(\rm8x^3 - \frac{1}{x^3}\) will be :
560
SSC CHSL 2021200)If (3p - 5m) = 5 and pm = 6, then what is the value of (9p2 - 25 m2)?
±5√385
SSC CHSL 2021201)If x + y = 5 and x2 + y2 = 17 then the value of \((x-y)^2\) is equal to:
9
SSC CHSL 2021202)If (7x + 3)3 + (x - 2)3 + 27(2x - 5)3 = 9(7x + 3) × (x - 2) × (2x - 5) then the value of 5x + 3 is:
8
SSC CHSL 2021203)If 49a2 + 25b2 = 30 and ab = 1, a, b > 0, then the value of (7a + 5b) is:
10
SSC CHSL 2021204)If x + y = 5 and \(\rm \frac{1}{x}+\frac{1}{y}=\frac{20}{9} \), then the value of (x3 + y3) will be:
\(\rm \frac{365}{4}\)
SSC CHSL 2021205)If x + y + z = 5, \(\rm \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\) , xyz = 12, and x3 + y3 + z3 = 151 then the value of (x2 + y2 + z2) is:
23
SSC CHSL 2021206)If a2 + b2 + c2 + 170 = 2 (8a + 5b - 9c), then the value of \(\rm \sqrt {4a + 8b -c}\) will be:
9
SSC CHSL 2021207)If x3 + y3 = 468 and x + y = 12, then the value of x4 + y4 will be:
3026
SSC CHSL 2021208)If then \( \rm k - \frac{3}{k} = 5\) what is the value of \( \rm k^2 + \frac{9}{k^2} \)?
31
SSC CHSL 2021209)Given that (2x + y)3 - (x + 2y)3 = (x - y) [A(x2 + y2) + Bxy], the value of (2A - B) is:
1
SSC CHSL 2021210)If a2 + b2 = 25, x2 + y2 = 17 and ax + by = 8, then what is the value of (ay - bx)?
19
SSC CHSL 2021211)If x4 - 142x2 + 1 = 0, then the value of \(x^3+1/x^3\) is
1692
SSC CHSL 2021212)If 2x2 - 6x = 1, then x2 + \(\frac{1}{4x^2}\)=?
10
SSC CHSL 2021213)If 3u + 2v = 7 and uv = 2, then the value of (3u - 2v) is:
1
SSC CHSL 2021214)If a + b + c = 5 and a3 + b3 + c3 - 3abc = 185, then the value of ab + bc + ac lies between:
-7 and -3
SSC CHSL 2021215)If x2 - 3x + 1 = 0, then the value of \(\rm 2(x^8+\frac{1}{x^8}) - 5(x^2+\frac{1}{x^2})\) is:
4379
SSC CHSL 2021216)The value of \(\left(4\frac{3}{5}+7\frac{2}{5}\right) + \left(7\frac{1}{6}-2\frac{1}{3}\right)\) of is:
8
SSC CHSL 2021217)If x - y - z = 0, then the value of (x2 + y2 + z2) ÷ (y2 + xz) is:
2
SSC CHSL 2021218)If \(\rm x^4-\frac{1}{x^4} = 6887\), then the positive value of \(\rm x-\frac{1}{x} \) is:
9
SSC CHSL 2021219)If (a + b + c) = 0 and (abc) = 12, then what is the value of (a3 + b3 + c3)?
36
SSC CHSL 2021220)If x4 + y4 + x2y2 = 117 and x2 + y2 - xy = 3(4 + √3), then the value of (x2 + y2) will be:
12
SSC CHSL 2021221)If \(x^2- 6√3 x + 1 = 0\), then the value of \(\rm x^3 + \frac{1}{x^3}\) will be :
630√3
SSC CHSL 2021222)Simplify the following expression. (2x - 3y)3 - 18xy (2x - 3y)
8x3 - 72x2y + 108xy2 - 27y3
SSC CGL 2020223)If \(P={x^3+y^3\over (x-y)^2+3xy}\) , \(Q={(x+y)^2-3xy\over x^3-y^3}\) and \(R={(x+y)^2+(x-y)^2\over x^2-y^2}\), then what is the value of \((P\div Q)\times R\) ?
\(2(x^2+y^2)\)
\((P\div Q)\times R\) \(={x^3+y^3\over (x-y)^2+3xy}\div {(x+y)^2-3xy\over x^3-y^3}\times {(x+y)^2+(x-y)^2\over x^2-y^2}\)
\(={(x+y)(x^2+y^2-xy)\over x^2+y^2-2xy+3xy}\times {(x-y)(x^2+y^2+xy)\over x^2+y^2+2xy-3xy}\times {x^2+y^2+2xy+x^2+y^2-2xy\over (x+y)(x-y)}\)
= \(2(x^2+y^2)\)
SSC CGL 2020224)If \(16a^4 + 36a^2b^2 \)\(+ 81b^4 = 91\) and \(4a^2 + 9b^2\)\( - 6ab = 13\), then what is the value of 3ab ?
\(-{3\over2}\)
\(4a^2 + 9b^2 - 6ab = 13\) ;
⇒ \((4a^2 + 9b^2 - 6ab)^2 = (13)^2\);
\((\because(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ac))\)
⇒\( (4a^2)^2 + (9b^2)^2 + (6ab)^2 +2(4a^2.9b^2 - 9b^2.6ab - 6ab.4a^2) = 169\) ;
⇒ \(16a^4 + 36a^2b^2 + 81b^4 + 2(36a^2b^2 - 54ab^3 - 24a^3b) = 169\) ;
⇒ \(36a^2b^2 - 54ab^3 - 24a^3b = \frac{169 - 91}{2}\) ;
⇒ \(6ab(6ab - 9b^2 - 4a^2) = 39\) ;
⇒ 6ab = -3 ; ⇒ 3ab = -3/2
SSC CGL 2020225)If \(x^2-2\sqrt5x +1=0\) , then what is the value of \((x^5+{1\over x^5})\) ?
\(610\sqrt5\)
\(x^2-2\sqrt5x +1=0\) ; ⇒ \(x^2+1=2\sqrt5x\) ;
⇒ \({x^2+1\over x}={2\sqrt5x\over x}\) ; ⇒ \(x+{1\over x}=2\sqrt5\) ___(i) ; \(x^2+{1\over x^2}= 18\) ____(ii) ;
Again, \((x+{1\over x})^3= (2\sqrt5)^3\); ⇒ \(x^3+{1\over x^3}=34\sqrt5\) ___(iii) ;
Multiplying equation (ii) by (iii), we have \((x^2+{1\over x^2})(x^3+{1\over x^3}) = 18\times 34\sqrt5\) ;
⇒ \(x^5+{1\over x^5}+x+{1\over x}=612\sqrt5\) ; \(x^5+{1\over x^5} = 610\sqrt5\)
SSC CGL 2020226)If \(20x^{2} — 30x + 1 = 0\), then what is the value of \(25x^{2}+\frac{1}{16x^{2}}\) :
\(53\frac{3}{4}\)
\(20x^2-30x+1=0;\)
Dividing by x
\(20x-30+1/x=0;\)
\(20x+1/x=30;\)
\(5x+1/4x=15/2;\)
\(25x^{2}+\frac{1}{16x^{2}}=
(5x+{1\over4x})^2-2\times5x\times{1\over4x}\)\(=({20x^2+1\over4x})^2-{5\over2}\)
\(=({30x\over4x})^2-{5\over2}= (\frac{15}{2})^2 - \frac{5}{2}
= \frac{225}{4} - \frac{5}{2}
= \frac{215}{4} = 53\frac{3}{4}\)
SSC CGL 2020227)If \(x^{4} + x^{2} y^{2} + y^{4} = 273\space and \space x^{2} - xy + y^{2} = 13\), then the value of xy is :
4
\(x^{4} + x^{2} y^{2} + y^{4} =( x^{2} +xy + y^{2}) ( x^{2} - xy + y^{2}) \); ⇒ \(273=13( x^{2} +xy + y^{2}) \) ; ⇒
\(( x^{2} + xy + y^{2}) =21\);
\(\therefore ( x^{2} + xy + y^{2}) -( x^{2} - xy + y^{2}) =21-13\); ⇒ 2xy = 8 ; ⇒ xy = 4
SSC CGL 2020228)What is the value of \({x^2(x-4)^2\over(x+4)^2-4x}\div {(x^2-4x)^3\over(x+4)^2}\times {64-x^3\over16-x^2}\) ?
\(x+4\over x(x-4)\)
\({x^2(x-4)^2\over(x+4)^2-4x}\div {(x^2-4x)^3\over(x+4)^2}\times {64-x^3\over16-x^2}={x^2(x-4)^2\over x^2+16+4x}\times {(x+4)^2\over x^3(x-4)^3}\times {(4-x)(x^2+16+4x)\over(4-x)(4+x)}\) = \(x+4\over x(x-4)\)
SSC CGL 2016229)If a - b = 3 and \(a^2 \)+ \(b^2\) = 25, then the value of ab is
8
SSC CGL 2016230)if \(({x + {1 \over x}})^2 = 3 \ then \ the \ value \ of \ x^3 + {1 \over x^3} \ is\)
0
SSC CGL 2016231)If \({2p \over p^2-2p+1} = {1\over 4}\), then the value of \(p+ {1 \over p}\) will be
10
SSC CGL 2020232)If \(x-{1\over x}=11\), then the value of \((x^3-{1\over x^3})\) is :
1364
\(x-{1\over x}=11\);
Cubing both sides,
\((x-{1\over x})^3= 11^3\) ; ⇒ \(x^3-{1\over x^3}-3\times x\times{1\over x}(x-{1\over x})=1331\) ;
⇒ \(x^3-{1\over x^3}=1331+33\); ⇒ \(x^3-{1\over x^3}=1364\)
SSC CGL 2020233)\((a+b+c-d)^2-(a-b-c+d)^2=?\)
4a (b + c - d)
Put a=b= c=d=1 in \((a+b+c-d)^2-(a-b-c+d)^2\)= 4..
Now check all the given options value 4 will come in option C only i.e.
= 4a(b + c - d)
SSC CGL 2020234)The coefficient of \(x^2\) in \((2x+y)^3\) is:
12y
\((2x+y)^3= (2x)^3+y^3+3(2x)y(2x+y)=8x^3+y^3+12x^2y+6xy^2\); Co-efficient of \(x^2\) = 12y
SSC CGL 2020235)If \(a+b+c=9\) and \(ab+bc+ca=-22\), then the value of \(a^3+b^3+c^3-3abc\) is:
1323
a + b + c = 9; ⇒ \((a+b+c)^2=9^2\); ⇒ \(a^2+b^2+c^2+2(ab+bc+ca)=81\); ⇒ \(a^2+b^2+c^2+2\times (-22)=81\); ⇒ \(a^2+b^2+c^2=125\) ; \(a^3+b^3+c^3-3abc= (a+b+c)[a^2+b^2+c^2-(ab+bc+ca)]=9[125-(-22)]=1323\)
SSC CGL 2020236)If \(3^a=27^b=81^c\) and abc = 144 then the value of \(12({1\over a}+{1\over2b}+{1\over5c})\) is :
\(33\over10\)
\(3^a=27^b=81^c\); ⇒ \(3^a=3^{3b}=3^{4c}\); ⇒ a = 3b = 4c = k (let); (a = k, b = \(k\over3\), c = \(k\over4\)) and abc = 144; ⇒ \(\therefore k\times {k\over3}\times {k\over4}=144\) ; ⇒ k = 12; \(12({1\over a}+{1\over2b}+{1\over5c})= 12({1\over12}+{1\over2\times4}+{1\over5\times3})={33\over10}\)
SSC CGL 2020237)If the value of \((a+b-2)^2+(b+c-5)^2+(c+a-5)^2=0\), then the value of \(\sqrt{(b+c)^a+(c+a)^b-1}\) is :
3
\((a+b-2)^2+(b+c-5)^2+(c+a-5)^2=0\) ; If \(x^2+y^2+z^2=0, then\space x =0=y=z\) ; \((a+b-2)^2=0\); ⇒ a + b = 2; Similarly, b + c = 5 and c + a = 5; therefore b + c = c + a ;⇒ b = a; so a + b = 2; ⇒ a + a = 2; a = 1; a = b =1; Again, c + a = 5; ⇒ c = 4; \(\therefore \sqrt{(b+c)^a+(c+a)^b-1}=\sqrt{(1+4)^1+(4+1)^1-1}=3\)
SSC CGL 2020238)If \(a+{1\over a}=5\) then \((a^3+{1\over a^3})\) is :
110
\(a+{1\over a}=5\) ; Cubing both sides, \((a+{1\over a})^3=5^3\); ⇒ \(a^3+{1\over a^3}+3a\times{1\over a}(a+{1\over a})=125\); ⇒ \(a^3+{1\over a^3} = 125-15 = 110\)
SSC CGL 2020239)The coefficient of x in \((x-3y)^3\) is :
\(27y^2\)
\((x-3y)^3= x^3-(3y)^3-3x\times 3y(x-3y)=x^3-27y^3-9x^2y+27xy^2\); Co-efficient of x = \(27y^2\)
SSC CGL 2020240)If \(x^2-4x+4=0\), then the value of \(16({x^4}-{1\over x^4})\) is :
255
\(x^2-4x+4=0\); ⇒ \((x-2)^2=0\); ⇒ x = 2; \(\therefore 16({x^4}-{1\over x^4}) =16({2^4}-{1\over 2^4})= 255\)
SSC CGL 2020241)If \(a^3+{1\over a^3}=52\) then the value of \(2(a+{1\over a})\) is :
8
\(a^3+{1\over a^3}=a^3+{1\over a^3}+3(a+{1\over a})\) ; ⇒\((a+{1\over a})^3-3(a+{1\over a}) =52\); From options, If, \(a+{1\over a}=4\), then \((4)^3-3\times4 = 52\); \(2(a+{1\over a}) = 2\times4 = 8\)
SSC CGL 2020242)If b + c = ax, c + a = by, a + b = cz then the value of \({1\over9}[{1\over x+1}+{1\over y+1}+{1\over z+1}]\) is:
\(1\over9\)
Put, a = b = c 1 . then x = 2 ; y = 2 ; z = 2. \({1\over9}[{1\over x+1}+{1\over y+1}+{1\over z+1}]= {1\over9}[{1\over3}+{1\over3}+{1\over3}]={1\over9}\)
SSC CGL 2020243)If \(1-64x^3-12x+px^2=(1-4x)^3\), then the value of p is:
48
\(1-64x^3-12x+px^2=(1-4x)^3\) ⇒ \(1-64x^3-12x+px^2=(1)^3-(4x)^3-3\times1\times4x(1-4x)\) ⇒ \(1-64x^3-12x+px^2=1-64x^3-12x+48x^2\); Therefore, p = 48
SSC CGL 2020244)The coefficient of y in the expansion of \((2y-5)^3\), is:
150
\((2y-5)^3=(2y)^3-(5)^3-3(2y)\times5(2y-5)=8y^3-125-60y^2+150y\) ; Co-efficient of y = 150
SSC CGL 2020245)Expand \(({x\over3}+{y\over5})^3\) .
\({x^3\over27}+{x^2y\over15}+{xy^2\over25}+{y^3\over125}\)
\(({x\over3}+{y\over5})^3=({x\over3})^3+3({x\over3})^2({y\over5})+3({x\over3})({y\over5})^2+({y\over5})^3\)= \({x^3\over27}+{x^2y\over15}+{xy^2\over25}+{y^3\over125}\) \([\because(a+b)^3=a^3+3a^2b+3ab^2+b^3]\)
SSC CGL 2020246)If \(a^2+b^2+c^2=300\) and ab + bc + ca = 50 then what is the value of (a + b + c)? (Given that a, b and c are all positive.)
20
Here, \(a^2+b^2+c^2=300\); ab + bc + ca = 50; \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\) = 300 + 2 x 50 = 400; ⇒ So \(a+b+c=\sqrt{400} = 20\)
SSC CGL 2020247)If x + y + z = 10 and xy + yz + zx = 15, then find the value of \(x^3+y^3+z^3-3xyz\).
550
Given, x + y + z = 10 and xy + yz + zx = 15; \((x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)\); ⇒\(100=x^2+y^2+z^2+2\times15\); ⇒\(x^2+y^2+z^2=70\);
\(x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)\) = 10(70-15) = 550
SSC CGL 2020248)Find the product of \((a+b+2c)(a^2+b^2+4c^2-ab-2bc-2ca)\)
\(a^3+b^3+8c^3-6abc\)
\((a+b+2c)(a^2+b^2+4c^2-ab-2bc-2ca) =(a+b+2c)(a^2+b^2+(2c)^2-a\times b-b\times (2c)-(2c)\times a)\); ⇒\(a^3+b^3+(2c)^3-3ab(2c)=a^3 +b^3+8c^3-6abc\)
SSC CGL 2020249)\(25a^2-9\) is factored as:
(5a + 3)(5a - 3)
\(25a^2-9 =(5a)^2-(3)^2=(5a+3)(5a-3)\)
SSC CGL 2020250)If \(a^4+\frac{1}{a^4}=50\), a > 0, then find the value of \((a^3+\frac{1}{a^3})\).
\(\sqrt{2(1+\sqrt{13})}(-1+2\sqrt{13})\)
\(a^4+\frac{1}{a^4}={(a^2+\frac{1}{a^2})}^2-2\times a^2\times\frac{1}{a^2}=50\); \(a^2+\frac{1}{a^2}=2\sqrt{13}\); Similarly \({(a+\frac{1}{a})^2}=2(\sqrt{13}+1)\); \(a+\frac{1}{a}=\sqrt{2(\sqrt{13}+1)}\); Calculate \(a^3+\frac{1}{a^3}=\sqrt{2(\sqrt{13}+1)}(2\sqrt{13}-1)\)
SSC CGL 2020251)If x + 3y + 2 = 0, then value of \(x^3 +27y^3+8-18xy\) is :
0
x + 3y + 2 = 0; ⇒ x + 3y = -2; cubing both sides, \((x+3y)^3=(-2)^3\); ⇒ \(x^3+(3y)^3+3x(3y)(x+3y)=-8\); ⇒ \(x^3+27y^3+9xy(-2)=-8\); ⇒ \(x^3+27y^3+8-18xy=0\)
SSC CGL 2020252)If p + q = 7 and pq = 5, then the value of \((p^3+q^3)\) is :
238
p + q = 7; cubing both sides \((p^3+q^3)=7^3\); ⇒ \(p^3+q^3+3pq(p+q) =343\); ⇒ \(p^3+q^3=238\)
SSC CGL 2020253)If \(a^2+b^2-c^2=0\), then the value of \(2(a^6+b^6-c^6)\over3a^2b^2c^2\) is :
2
\(a^2+b^2-c^2=0\); \(a^2+b^2=c^2\); {cubing both sides}, \((a^2+b^2)^3=(c^2)^3\); ⇒ \(a^6+b^6+3a^2b^2(a^2+b^2)=c^6\); ⇒ \(a^6+b^6-c^6=-3a^2b^2c^2\);
\({2(a^6+b^6-c^6)\over3a^2b^2c^2}={2\times(-3a^2b^2c^2)\over3a^2b^2c^2}= -2\)
SSC CGL 2020254)If x,y,z are three numbers such that x + y = 13, y + z = 15 and z + x = 16, the value of \(xy +xz\over xyz\) is :
\(5\over18\)
x+y=13 ---(1);
y+z=15 ---(2);
z+x=16$$ ---(3);
By (1) + (2) + (3),
2(x + y + z) = 13 + 15 + 16;
x + y + z = 44/2 = 22;
put the value from eq(1),
13 + z = 22;
z = 9;
From eq(3),
9 + x =16;
x = 7;
From eq(3),
7 + y = 13;
y = 6;
Now,\({xy +xz\over xyz}={(7)(6)+(7)(9)\over(7)(6)(9)} ={5\over18}\)
SSC CGL 2020255)If a = 2b = 8c and a + b + c = 13, then the value of \(\sqrt{a^2+b^2+c^2}\over2c\) is :
\(9\over2\)
a = 2b = 8c; \({a\over8}={2b\over8}={8c\over8}\); \({a\over8}={b\over4}={c\over1}\); a : b : c = 8 : 4 : 1; and a+b+c=13; \(a={8\over13}\times13=8\), b = 4, c = 1; \(\sqrt{a^2+b^2+c^2}\over2c\) = \(\sqrt{8^2+4^2+1^2}\over2\times1\) = \(\sqrt{81}\over2\) = \(9\over2\)
SSC CGL 2019256)If \(x={\sqrt5-\sqrt3\over\sqrt5+\sqrt3}\) and y is the reciprocal of x, then what is the value of \((x^3+y^3)\)?
488
\(x={\sqrt5-\sqrt3\over\sqrt5+\sqrt3}\); \(y={\sqrt5+\sqrt3\over\sqrt5-\sqrt3}\) Rationalize the equation we get
\(x = {4-\sqrt{15}}; y=4+\sqrt{15}\)
using identity \({a^3 + b^3} = ( a+ b )(a^2 +b^2 - ab)\)
\((x^3+y^3) = 488\)
SSC CGL 2019257)If \(8x^3-27y^3\)\(=(Ax+By)\)\((Cx^2-Dy^2\)\(+6xy)\), then \((A+B+C-D)\) is equal to :
12
SSC CGL 2019258)If \((5x+1)^3+\)\((x-3)^3+\)\(8(3x-4)^3=\)\(6(5x+1)(x-3)\)\((3x-4)\), then x is equal to :
\(5\over6\)
SSC CGL 2019259)If \(x^4-83x^2+1=0\), then a value of \((x^3-x^{-3})\) can be :
756
SSC CGL 2019260)If \(x+y+z=2, \) \(xy+yz+zx=-11\) and \(xyz=-12\), then what is the value of \(\sqrt{x^3+y^3+z^3-2} \)?
6
SSC CGL 2019261)If \(x+{1\over16x}=3\), then the value of \((16x^3+{1\over256x^3})\) is :
423
SSC CGL 2019262)If \(x+y+z=6\), \(xyz=-10\) and \(x^2+y^2+z^2=30\), then what is the value of \((x^3+y^3+z^3)\)?
132
SSC CGL 2019263)If (5x + 2y) : (10x + 3y) = 5 : 9, then \((2x^2+3y^2):\) \((4x^2+9y^2) = \space ?\)
31 : 87
⇒ (5x + 2y)/(10x + 3y) = 5/9
⇒ 45x + 18y = 50x + 15y
⇒ x : y = 3 : 5
Let x = 3 and y = 5
Now, (2x2 + 3y2) : (4x2 + 9y2)
⇒ (2 × 9 + 3 × 25) : (4 × 9 + 9 × 25)
⇒ 93 : 261
⇒ 31 : 87
SSC CGL 2019264)Let \(x=\sqrt [6]{27}-\sqrt{6\frac{3}{4}}\) and \(y={\sqrt {45}+\sqrt{605}+\sqrt{245}\over\sqrt {80} +\sqrt{125}}\), then the value of \((x^2+y^2)\) is :
\(223\over36\)
SSC CGL 2019265)a, b and c are three fractions such that a < b < c. If c is divided by a, the result is \(9\over2\), which exceeds b by \(23\over6\). The sum of a, b and c is \(19\over12\). What is the value of (2a + b - c)?
\(1\over4\)
SSC CGL 2019266)If \({3(x^2+1)-7x\over3x}=6\), \(x\neq0\), then the value of \(\sqrt x+{1\over\sqrt x}\) is :
\(\sqrt{31\over3}\)
SSC CGL 2019267)The value of \({2\sqrt{10}\over\sqrt{5}+\sqrt{2}-\sqrt{7} }\)\(-{\sqrt{\sqrt{5}-2\over\sqrt{5}+2}}\)\(-{3\over\sqrt{7}-2}\) is :
\(\sqrt2\)
Rationalize and solve the equation
SSC CGL 2019268)If \(5\sqrt5x^3+2\sqrt2y^3=\)\((Ax+\sqrt2y)\)\( (Bx^2+2y^2+Cxy)\), then the value of \((A^2+B^2-C^2)\) is :
20
SSC CGL 2019269)Given that \((5x-3)^3+(2x+5)^3\)\(+27(4-3x)^3=\)\(9(3-5x)\)\((2x+5)\)\((3x-4)\), then the value of (2x + 1) is:
15
SSC CGL 2019270)ab(a - b) + bc(b - c) + ca(c - a) is equal to :
(b - a)(b - c)(c - a)
ab(a - b) + bc(b - c) + ca(c - a) = -2; From option D, (b - a) (b - c) (c - a) = (1) (-1) (2) = -2
SSC CGL 2019271)If \(2\sqrt{2}x^3-3\sqrt{3}y^3=\)\(\left(\sqrt{2}x-\sqrt{3}y\right)\)\(\left(Ax^2+By^2+Cxy\right)\), then the value of \(( A^2 + B^2 - C^2 )\) is:
7
\(2\sqrt{2}x^3-3\sqrt{3}y^3=\left(\sqrt{2}x-\sqrt{3}y\right)\left(Ax^2+By^2+Cxy\right);\)
(because\( a^3 - b^3 = (a - b)(a^2 + ab + b^2)\));
On compression,
A =\( (\sqrt{2})^2 \)= 2;
A = \((-\sqrt{3})^2\) = 3;
C = \(\sqrt{2}\sqrt{3}\) =\( \sqrt{6}\);
Now,
\(A^2 + B^2 - C^2 \)= \(2^2 + 3^2 - (\sqrt{6})^2\)
= 4 + 9 - 6
= 7
SSC CGL 2019272)If \( a^3 + b^3 = 218 \) and a + b = 2, then the value of ab is:
-35
\((a + b)^3 = a^3 + b^3 + 3ab(a + b)\);
\((2)^3 = 218 + 3ab(2)\);
-6ab = 218 - 8 = 210;
ab = -210/6 = -35
SSC CGL 2019273)If x = \(\sqrt{1+\frac{\sqrt{3}}{2}-}\sqrt{1-\frac{\sqrt{3}}{2}}\), then the value of\( \frac{\sqrt{2}-x}{\sqrt{2}+x}\) will be closest to:
0.17
\(x=\sqrt{1+\frac{\sqrt{3}}{2}-}\sqrt{1-\frac{\sqrt{3}}{2}}; x^2 =(\sqrt{1+\frac{\sqrt{3}}{2}-}\sqrt{1-\frac{\sqrt{3}}{2}})^2; x^2 =1+\frac{\sqrt{3}}{2} + 1-\frac{\sqrt{3}}{2} - 2\sqrt{1+\frac{\sqrt{3}}{2}} \sqrt{1-\frac{\sqrt{3}}{2}};\)
\( x^2 =1+\frac{\sqrt{3}}{2} + 1-\frac{\sqrt{3}}{2} - 2\sqrt{1+\frac{\sqrt{3}}{2}} \sqrt{1-\frac{\sqrt{3}}{2}}; x^2 =1+\frac{\sqrt{3}}{2} + 1-\frac{\sqrt{3}}{2} - 2\sqrt{1- \frac{3}{4}} ; x^2 = 2 - 2\sqrt{ \frac{1}{4}} ; x^2 = 1;\)
x = 1 or x = -1;
Now,;\(\frac{\sqrt{2}-x}{\sqrt{2}+x} = \frac{\sqrt{2}-x}{\sqrt{2}+x} \times \frac{\sqrt{2}-x}{\sqrt{2}-x}; = \frac{2 - 2\sqrt{2}x + x^2}{2 - x^2}; \)Put the value of x = 1;\(= \frac{2 - 2\sqrt{2} + 1}{2 - 1}; = 3 - 2\sqrt{2} = 0.17 \)
SSC CGL 2019274)If \({(\sqrt2+\sqrt5-\sqrt3)\times k=-12}\), then what will be the value of k ?
\({(\sqrt2+\sqrt5+\sqrt3)(2-\sqrt10)}\)
\(\left(\sqrt{2} + \sqrt{5} - \sqrt{3}\right) \times k\) = -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
SSC CGL 2019275)The value of \({(253)^3+(247)^3}\over {25.3\times25.3-624.91+24.7\times24.7}\) is \({50\times10^k}\), then the value of k is :
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 2019276)If x + y + z =11, \({x^2 + y^2 + z^2 = 133}\) and \({x^3 + y^3 + z^3 = 881}\), then the value of \(\sqrt[3]{xyz}\) is :
-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 2019277)In a school, \({4 \over 9}\) of the number of students are girls and the rest are boys. \({3 \over 5}\) of the number of boys are below 12 years of age and \({5 \over 12}\) of the number of girls are 12 years or above 12 years of age.
If the number of students below 12 years of age is 480, then \({5 \over 18}\) of the total number of students in the school will be equal to :
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 2019278)If \({a^2+b^2+c^2+96}=8(a+b-2c)\), then \({\sqrt {ab-bc+ca}}\) is equal to :
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 2019279)If \({ \sqrt{86-60\sqrt2}}=a-b\sqrt2\), then what will be the value of \( {\sqrt{a^2+b^2} }\) , correct to one decimal place?
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 2019280)If \( {x^8-1442x^4+1}=0\), then a possible value of (x - \( {1\over x}\)) is :
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 2020281)\((3a - 4b)^3 \) is equal to:-
\(27a^3-64b^3-108a^2b+144ab^2\)
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 2020282)If A + B = 12 and AB = 17, what is the value of \({A^3 + B^3}\) ?
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 2020283)Expand: \({(4a + 3b +2 c)^2}\)
\({16a^2 + 9b^2 +4c^2+24ab +12bc + 16ca}\)
put a, b, c = 1 in the options
opton C will come out to be 81 as in the \({(4a + 3b +2 c)^2} = {(4 + 3 + 2)^2} = 81\)