This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
5 90°Find the roots of quadratic equation 2x2 -7x+3=0by the method of completing the square. |
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Answer» 2x^2 - 7x + 3 = 02x^2 - 7x = -3X^2 - 7x/2 = -3/2X^2 - 2*1/2*7x/2 = -3/2X^2 - 2*1/2*7x/2 + (7/4)^2 = -3/2 + (7/4)^2(X - 7/4)^2 = -3/2 + 49/16(X - 7/4)^2 = 25/16X - 7/4 = + or -5/4 x = +5/4 + 7/4X = 12/4 =3Also X = -5/4 + 7/4 = 1/2Hence x = 3 and 1/2 |
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| 2. |
4x416=Three Numbers are in Arithmetic Progression and their sum is 18 and sum oftheir squares is 140. Find the Numbers. |
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| 3. |
18 The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sumand sum of itseight terms. |
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| 4. |
Find the roots of the following quadrcompleting the square:(i) 2x2-7x +3 0 |
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Answer» tnx for the help |
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| 5. |
y theFind the roots of the quadratic equation 2x2 -5x 3 0 bmethod of completing the square. |
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| 6. |
((i %2B 1)/(-i %2B 1))^3 - (-i %2B 1)^3/(i %2B 1)^3=a %2B b*i |
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Answer» (1+i/1-i)³-(1-i/1+i)³=x+iyor, x+iy=[(1³+3i+3i²+i³)/(1³-3i+3i²-i³)]-[(1³-3i+3i²-i³)/(1³+3i+3i²+i³)]or, x+iy={1+3i+3(-1)+(-1).i}/{1-3i+3(-1)-(-1).i}-{1-3i+3(-1)-(-1).i}/{1+3i+3(-1)+(-1).i}or, x+iy=(1+3i-3-i)/(1-3i-3+i)-(1-3i-3+i)/(1+3i-3-i)or, x+iy=(-2+2i)/(-2-2i)-(-2-2i)/(-2+2i)or, x+iy={(-2)(1-i)/(-2)(1+i)}-{(-2)(1+i)/(-2)(1-i)}or, x+iy=[(1-i/1+i)-(1+i/1-i)or, x+iy={(1-i)²-(1+i)²}/{(1)²-(i)²}or, x+iy=(1-2i+i²-1-2i-i²)/{1-(-1)}or, x+iy=(-4i)/(1+1)or, x+iy=-4i/2or, x+iy=-2ior, x+iy=0+i.(-2)where x=0 and y=-2 Let a and b be X and y option 3 is the correct answer of the given question |
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| 7. |
1. Find the roots of the following quadratic equations, if they exist, by the method ocompleting the square:(1) 2x2-7x+3-0(iii) 4x2 + 4V3x + 3-0(ii) 2x +x-40(iv) 2x+4-0in01 ahove hy applying the quad |
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| 8. |
\frac{4}{x-3}-\frac{3}{x-1}=\frac{5}{x-1}-\frac{4}{x-2} |
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Answer» (4x-4-3x+9)/((x-3)(x-1))=(5x-10-4x+4)/((x-1)(x-2))(x+5)/(x-3)=(x-6)/(x-2)x*x+3x-10=x*x-9x+1812x=28x=28/12=(7×4)/(3×4)=7/3 |
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| 9. |
[लता । बला नg6, If 5in 0+ 2080 = 1 prove that 2sin 8 - cos 0 = 2. INCERT EXEMPL? |
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Answer» Like my answer if you find it useful |
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| 10. |
(i) x -2r -8 |
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Answer» x² -2x - 8x² +2x -4x -8x(x+2) -4(x+2)(x+2)(x-4) thank u mam |
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| 11. |
Incert five numbers between 8 and 26 such that the resulting sequence is an A.P. |
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Answer» So here |
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| 12. |
Solve for x\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4} |
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| 13. |
axis of yShow that the curves 2r-y2 and 2xy - k cut at right angles if h-8 |
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Answer» complete ans.? |
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| 14. |
divided in four section ,BSection A(EQ1)-Represent 0.99999.... in the form of rompass |
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Answer» Letx= 0.99999There is only one repeating digit so multiply by 10 we get10x= 9.99999x= 0.99999subtract x now we get9x= 9Divide by 9 we getx= 9/9 = 1 |
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| 15. |
the lowest formaEXERCISE 4.3whether the following rational numbers are in the lowe24(i) 128(iv)Eseach of the following rational numbers to the lowest form-36132(i) -4281803.in the blanks |
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| 16. |
10) In the given figure find LBOC.SECTION: B |
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Answer» Angle BOC=2*Angle BACAngle BOC=2*70=140 |
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| 17. |
Find the numbers, if their sum 18.SECTION - B |
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| 18. |
nd the roots of the folimpleting the squarei) 2x2 -7x +3 0 |
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Answer» 1) 2x^2 - 7x +3 =0 2x^2 - 6x - x + 3 =0 2x(x-3) - 1(x-3) =0 (2x-1)(x-3) = 0 x = 1/2, 3 2) 4x^2 + 4sqroot(3)x + 3 = 0 4x^2 + 2sqroot(3)x + 2sqroot(3)x + 3=0 2x(2x+sqroot(3))+sqroot(3)(2x+ sqroot(3)) =0(2x + sqroot(3)) (2x + sqroot(3)) =0x = - sqroot(3)/2 |
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| 19. |
(2^x %2B 2^(x - 1))/(-2^x %2B 2^(x %2B 1))=3/2 |
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Answer» Taking 2^x comman from denominator and numeratorand will be cancelled2^-1+1/2^1-1 = 1/2+1= 3/2 |
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| 20. |
(x^2 %2B 2*x)*(x^2 %2B 2*x - 11) %2B 24=0 |
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Answer» let x^2+2x= pp(p-11)+24=0p^2-11p+24=0p^2-8p-3p+24=0p (p-8)-3(p-8)=0(p-8)(p-3)=0putting the value of p (x^2+2x-8)(x^2+2x-3)=0{x^2+4x-2x-8}{x^2+3x-x-3}=0{x(x+4)-2(x+4)}{x(x+3)-1(x+3)}(x+4)(x-2)(x+3)(x-1) x^2+2x=0, p^2-8p-3p+24; p(p-8)-3(p-a)=0( p-3)(p-3)=0; ( x^2+4x-2x-8)( x^2+3x-3)= (x(x+4)-2(x+4)-(x)(x+3)(x-1) (x+4)(x-2)(x+3)(x-1) |
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| 21. |
(x - 2)/(x %2B 2) %2B (x %2B 2)/(x - 2)=4 |
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Answer» THANK YOU FOR YOUR HELP. |
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| 22. |
2^x %2B 2^x %2B 2^x=192 |
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Answer» 3(2^x)=192 2^x=192/3 2^x=64 2^x=2^6 => x=6 |
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| 23. |
9. f the sum of squares of the zeroes of the polynomials 6x2+ + k isfind the valueof k?( CBSE 2014-15)yy-9 is negative of the other |
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| 24. |
1. Find the zeros of each of the following quadratic polynomials and verify therelationship between the zeros and their coefficients:( f(x) 2-2r 8 INCERT](i) g(s) 4s2 - 4s+ 1(ii) )15 INCERTI(v)f(x) 6x2 -3-72(v) p(x) - 2 +2/2x - 6INCERTNCERT(vi)g(x) = V3x2 + 10x + 7V3 |
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Answer» how did you complete this some in next to no time? |
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| 25. |
( \frac x %2B 1 x %2B 2 ) ^ 2 = \frac x %2B 2 x %2B 4 |
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Answer» (x + 1)^2 (x + 4) = (x + 2)^3 (x^2 + 2x + 1)(x + 4) = x^3 + 8 + 6x^2 + 12x x^3 + 2x^2 + x + 4x^2 + 8x + 4= x^3 + 8 + 6x^2 + 12x 9x + 4 = 12x + 812x - 9x = 4 - 83x = - 4x = - 4/3 |
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| 26. |
\frac 1 x %2B 1 %2B \frac 2 x %2B 2 = \frac 4 x %2B 4 |
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| 27. |
x+y= 14x-y=14 |
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| 28. |
428*(100/550) |
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Answer» first divide 100 by 550. then answer comes 50.5 now multiply the answer by 428 .The answer will come 21614.0 |
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| 29. |
13. Through what different angles should a rectangle be rotated to be in symmetricalposition with the original position? |
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| 30. |
eould 81s be análysed using symmetrical components.64 |
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Answer» what is the value of sin(π/6)? sin (π/6) = 1/2. and what is cos(π/3)? cos π/3 = 1/2. value of tan 45? tan 45° = 1. |
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| 31. |
Symmetrical line |
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Answer» Something is symmetrical when it is the same on both sides. A shape has symmetry if a central dividing line (a mirror line) can be drawn on it, to show that both sides of the shape are exactly the same. |
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| 32. |
Answer the following:(a) What is a symmetrical object? |
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Answer» symmetrymeans that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For twoobjectsto besymmetrical, they must be the same size and shape, with oneobjecthaving a different orientation from the first. There can also besymmetryin oneobject, such as a face. |
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| 33. |
The mode of a moderatly symmetricalseries is 18 and mean is 24. The median is |
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Answer» median is 22,M-M°=3(M-Me) An empirical relationship exists between mean, median and mode. Mode = 3(Mean - Median)18 = 3(24 - Median)Median = 24 - 18/3Median = 24 - 6 = 18 |
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| 34. |
8.550<A =<B = |
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Answer» As AB= AC both will have equal angles soangle b= angle c= 55°now angle A= 180-(55+55)= 80°as sum of all the angles is 180° |
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| 35. |
4. The first and last terins of an A.P. are 1 and 11. If the sum of its terms is 36, then thenumber of terms will beyo |
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Answer» 6 |
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| 36. |
If the sum of squares of the zeroes of the polynomials 6x2 x kis 26 find the valueof k?( CBSE 2014-15) |
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| 37. |
ldots %2B 2 %2B 2*3 %2B 3*4 %2B 4*5 |
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Answer» 1×2+2×4+3×4+4×5+.....=2+8+12+20+..=infinity infinity answer hoga ashant 5*6+6*7. infinite 2+8+12+.......infini |
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| 38. |
2/(x %2B 2) %2B 1/(x %2B 1)=4/(x %2B 4) |
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| 39. |
atan((x %2B 2)/(x %2B 4)) %2B ((x - 2)/(x - 4))/n=pi/4 |
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Answer» this questions of answer is [√2]... the answer is +- √2...... |
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| 40. |
15-8 \frac{5}{8}-3 \frac{3}{4}+6 \frac{1}{2} |
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Answer» by basic calculation 15 - 69/8 - 15/4 + 13/2 = (120-69-30+52)/8 = 73/8 = 9 1/8 |
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| 41. |
है Ly 1o आए |
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| 42. |
36 %2B 94 %2B 607 %2B 753 |
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Answer» 753+607+0+94+36 = 1490 When we add 753+607+0+94+36 we'll get 1490 as the answer correct answer is 1490 exactly 1490 is the correct and perfect |
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| 43. |
cover te box aH22 A well is dug 20m deep and it has a dameter 7m. Theearth which is so dug out is spread evenly on a rectangular plot 22m long and 14m broad What is the height of theplatform formed ? |
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| 44. |
The angle of elevation of the top of a 36 m tall tower from the initial position of a personon the ground was 60°. She walked away in a manner that the foot of the tower, her initialposition and the final position were all in the same straight line. The angle of elevation ofthe top of the tower from her final position was 30. How much did she walk from herinitial position? |
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Answer» sorry ma'am try again please |
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| 45. |
The rain water from a roof of 44 m x 20 m drains into a cylindrical tankhaving diameter of base 4 m and height 3.5 m. If the tank is just full, findthe rainfall in cm.CBSE 2014] |
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| 46. |
Through what different angles should a rectangle be rotated to be in symmetricalposition with the original position?3. |
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Answer» no no |
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| 47. |
21. The rain water from a roof of 44 m x 20 m drains into a cylindrical tankhaving diameter of base 4 m and height 3.5 m. If the tank is just full findCBSE 2014the rainfall in cm. |
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| 48. |
21. The rain water from a roof of 44 m x 20 m drains into a cylindrical tankhaving diameter of base 4 m and height 3.5 m. If the tank is just full, findCBSE 2014]the rainfall in cm. |
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| 49. |
21. The rain water from a roof of 44 m x 20 m drains into a cylindrical tankhaving diameter of base 4 m and height 3.5 m. If the tank is just full, findCBSE 2014]ins into a cylindrical vessethe rainfall in cm. |
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| 50. |
-8/15 %2B 2*(4/6) |
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