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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. |
71. Ifa and b are unit vectors and θ is anglebetween them, then1s :(1) sine(2)sin20(3) sin 2(4) sin20 |
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| 2. |
. -326. Prove that SinAd—2sin” 4 _ 042cos” A—cos Aol o i दि न e s o I e Sl e o R |
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Answer» hit like if you find it useful |
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| 3. |
1. If 9 is added to a certain number, the result is 36. Find the number |
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| 4. |
Lt[x (x +1)] |
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Answer» please like my answer if you find it useful |
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| 5. |
Lt [x (x+ 1)] |
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| 6. |
Lt [l+ x + x.+ 10 |
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Answer» It will be 1as after putting limitsall will be cancelled out [1-1+1-1+1-1+1-1+1-1+1]0+1 = 1Answer= 1HIT THE LIKE BUTTON IF YOU ARE SATISFIED thnkuu |
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| 7. |
(ii)sin-i x + sin-ly + sin-iz =砢TAng R,2y2 + 2727222,2 2 |
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| 8. |
(ii) Lt x |
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Answer» please like my answer if you find it useful |
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| 9. |
(d) 4x2 +9y2+162 + 12xy-24yz_ 16xz |
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Answer» 4x*x + 9y*y + 16z*z + 12xy - 24yz - 16xz = (2x)(2x) + (3y)(3y) + (-4z)(-4z) + 2(2x)(3y) + 2(3y)(-4z) + 2(-4z)(2x) = (2x+3y-4z)(2x+3y-4z) 4 x square + 9 y square + 16 + 12 - 2 Y Z - 16 ZX |
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| 10. |
nettle katios28. In the figure, ABCD is a rectangle. Its diagonal AC -15 mand ZACD 0. If tan 0-2:3, find the perimeter of therectangle.15 mA. |
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Answer» part 1 part in |
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| 11. |
6. If sin x + sin' χ1,1hen write the value of cos12 x + 3 cos!"r-3 cos" + cose, |
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| 12. |
The value of sin A -sin B cos B - cos Acos A +cos B sin A + sin B11S |
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| 13. |
(x +1) dx-11.sin 2x dx4. |
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Answer» (x^2/2+x)=1/2(1-1)+(1+1)=2-cos2x/2=1/2(cospie/2-cos0)=-1/2 |
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| 14. |
x³+y³-12xy+64 where x+y=-4 |
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| 15. |
The H.C.F. of 6x4 y and 12xy- |
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| 16. |
11. Factorise (Tunes dollstu) : 4x2 +9y2 - 25z2 + 12xy |
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Answer» We have been given:4x² + 9y² - 25z² + 12xyArranging them: (4x² + 9y² + 12xy) - 25z² Using (a + b)² = a² + b² + 2ab, we have (2x)² + (3y)² + 2 × 2x × 3y - (5z)²= (2x + 3y)² - (5z)² Using (a + b)(a - b) = a² - b² = (2x + 3y + 5z)(2x + 3y - 5z) Hope this helps... |
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| 17. |
6. In the given figure, ZABD 54° andBCD 43 calculate(0)ZACD, (ii) ZBAD, (iii) 4BDA.54°43° |
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| 18. |
(d) 50ल। यदि 349 नारियलों का मूल्य १218125 हो तो, 26 दर्जन नारियलो को(a) 1500(e) 1200(b) 2000 |
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Answer» 11 2000 2000 is the right answer |
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| 19. |
1.In figure 3.8, ZACD is an exterior angle of A ABC.ZB = 40°, ZA = 70°. Find the measure of ZACD. |
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Answer» here the triangle ABC Where <B=40°<A=70° and <C=180°-(70°+40°)=180°-110°=70° hope this will help you like my answer and MARK IT AS BEST ANSWER. |
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| 20. |
(ii) 2x2 + 7x +3 |
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Answer» 2x² + 7x + 3 2x² + x + 6x + 3 x ( 2x + 1) + 3 ( 2x + 1) (x + 3) ( 2x + 1) Please hit like if you find my solution useful thnks |
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| 21. |
(ii) 2x2 +x-4 |
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| 22. |
(ii) 2x2 x- 4 0 |
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| 23. |
7. Evaluate (any one) :মান নির্ণয় কৰা (যি কোনাে এটা) :| x2 +2x(a)_lim -x-2 x + x2 -2x |
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| 24. |
Evaluate :(x+2)/√(x²+2x+3)dx |
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Answer» 1 2 |
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| 25. |
(ii) 2x2+x- 60 |
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Answer» 2x²+x-6=0 2x²+4x-3x-6=0 2x(x+2)-3(x+2)=0 (x+2)(2x-3)=0 x=-2,3/2 |
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| 26. |
1+cos Ď1-cos r -cosec x + cot x |
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Answer» thank u |
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| 27. |
6. If x = r cos A cos B, y = r cos A sin B andz = r sin A, show that : |
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| 28. |
Evaluate:3x +12dx2x +x+1 |
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Answer» hello |
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| 29. |
\begin{array} { l } { \text { If } x = r \sin A \cos C , y = r \sin A \sin C \text { and } z = r \cos A } \\ { \text { then prove that } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = r ^ { 2 } } \end{array} |
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Answer» Given, x=rsinAcosC ..equation..1 y=rsinAsinC .....equation 2 z=rcosA .....equation 3 squaring and adding all three equations we get the following x²+y²+z²=r²(sin2Acos2C + sin2Asin2C + cos2A) =r²{sin2A(cos2C + sin2C) + cos2A} =r²{sin2A+ cos2A} ∴x²+y²+z²=r² |
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| 30. |
MISCELLANEOUS EXAMPLESIf sín.1 x + sin-1 y + sin-1 z = π, prove that |
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Answer» Let sin-1x =A then x= sinA Let sin-1y=B then y =sinB Let sin-1z=C then z=sinC Then A+B+C =p Xv(1-X^2) +Yv(1-Y^2) +Zv(1-Z^2)=sinA v(1-sin^2A)+sinBv(1-sin^2B) +sinCv(1-sin^2C) =sinA.cosA+sinB.cosB+sinC.cosC =1/2[sin2A+sin2B+sin2C] =1/2 [4sinA.sinB.sinC] =2sinAsinBsinC =2xyz |
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| 31. |
(ii) 2x2+x-4-0 |
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Answer» 2x2+ x -4=02x2+ x = 4x2+ x/2 + 1/4 = 2+1/4(x + 1/2)2= 9/4 (x + 1/2) = ± 3/2 x = 3/2 - 1/2 = 1 orx = 3/2 + 1/2 = 2 Hence, x = 1 or 2. Like my answer if you find it useful! |
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| 32. |
Find the value of x, ys_ 12xy + 64 when x + y--4. |
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| 33. |
some Miscellaneous ProtamsEXAMPLE 1 Use Euclid's division algorithm to find HCF of 504 and 980 |
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Answer» Using Wuclid Division Lemma 980 = 1 × 504 + 476 504 = 1× 476 + 28 476 = 17× 28 + 0 So HCF(504,980) = 28. |
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| 34. |
Let y varies direct as x. If y 14, when x 7, then write a linear equation. What is thy when x2? |
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Answer» y varies direct as xso y=mxwhen y=14 and x=714 =m×7m=2eq. is y=2xwhen x=-2y=-4 |
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| 35. |
1200Miscellaneous26. Find the solution of the equationsa) Sm=60b) 2.7will the follos |
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| 36. |
Let us write the value of the other root if one root of the equation x2 (2+b)x+6-0 is 2. |
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| 37. |
(3)From the figure find the measure of ZACD.70°40° |
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| 38. |
(ii) 2x2+1-6-0 |
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| 39. |
(ii)/+](2x2 + 3)./x + 2 dx |
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| 40. |
3. In the given figure, find the measure of ZACD. |
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Answer» thanks |
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| 41. |
Lt (x + 3) |
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| 42. |
lt 3-x +9Evaluate x 2x +4x+7 |
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| 43. |
r cos x-log(1 + x). Evaluate: Lt.t |
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| 44. |
14. If α and βare the zeroes of the quadratic polynomial fix)-x x-4,find the-value of 1+1-αβ |
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| 45. |
1. If 9 is added to a certain number, the result is 36. Find the number. |
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| 46. |
ys_ defines a function on R, then72.If fix) =funx -4what is its domain? |
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| 47. |
61. Find whether 55 is a term of the AP 7,10, 13.,.. or not. if yes, find which term it is. |
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| 48. |
If tan (3A + 15)0 -1-0, then find the value of A that satisfy this condition. |
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| 49. |
CISE 4.2atic equations by factorisation:(ii), 2x2 +x -60 |
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| 50. |
28. In the figure, ABCD is a rectangle. Its diagonal AC -15 mand ZACD 0. If tan 0-2:3, find the perimeter of therectangle.15 m |
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