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. |
\operatorname lim _ u \rightarrow 13 \frac \operatorname sin ^ 2 \alpha - \operatorname sin ^ 2 \beta \alpha ^ 2 - \beta ^ 2 |
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Answer» lim α→β (sin²α-sin²β/α²-β²)we are getting 0/0 form so using L hospital rulelim α→β(2sinα/2α)=sinβ/β |
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| 2. |
\operatorname lim _ u \rightarrow 1 ^ 1 \frac \operatorname sin ^ 2 \alpha - \operatorname sin ^ 2 \beta \alpha ^ 2 - \beta ^ 2 |
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Answer» lim α→β (sin²α-sin²β/α²-β²)we are getting 0/0 form so using L hospital rulelim α→β(2sinα/2α)=sinβ/β |
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| 3. |
area of the fesgAnswer the following.. Evaluate : (1+tan +Sect)(1+coto-cosecg).e out of a sol |
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Answer» please like my answer if you find it useful |
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| 4. |
Fig. 9.39, two circles touch each otherrnally at C. Prove that the common tangentbisects, the other two common tangents.(C.B.S.E. 2007) |
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Answer» Let PQ and RS are two direct common tangents and EF is the transverse common tangent. We know that tangent line segments are equal in length from an external point to circle. Therefore, EP = EC and EQ = EC ⇒ EP = EQ and FR = FC, FS = FC ⇒ FR = FS Hence, ECF bisects PQ and ECF bisects RS. ∴ The common tangent bisects the other two common tangents |
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| 5. |
d CD are common tangents to two circles of equal radii. Prove that AB CD. |
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Answer» u can see the theorem 10.2 in ncert |
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| 6. |
AB and CD are two common tangents to two circleswhich touch each other at C. If D lies on AB such thatCD 4 cm, then find AB. |
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| 7. |
AB and CD are common tangents to two circles of equal radii. Prove that AB = CD. |
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| 8. |
If m and nave two separations guantatiessuch that minsther any one of thetonowing reactions (conditions) were befenceTe eithen cimn.On mynCD m. <n.or men. |
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Answer» I think option 2 is the correct answer to this question. option (ii) is the correct answer the Second one is the correct answer |
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| 9. |
the patnr (vwnte thhe answet ConedThe area enclosed between the circumference of two concentric circles is 16 Ď cm" and their radii are inthe ratio 5 3. What is the area of the outer circle? (Use T 3.14)thlaest circle that can be drawn inside a square of side 28 cn? |
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| 10. |
Find two consecutive positive integers, sumof whose squares is 365.3.(HSLC 15] |
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| 11. |
The radii of internai and extstnal a hollow spherical shellare 3 em and 5 erespectire2el ed and recast into a solidvinder of diameter 1Finneled and recast into a solidzight of the cylinder |
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Answer» please like my answer if you find it useful |
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| 12. |
TSsiarrnoăŞă§d22 a/ ny 21- |
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Answer» let p(x) = x³-6x²+9x+3we will use remainder theorem so reaminder will be p(1) = 1³-6×1²+9×1+3 = 1-6+9+3 = 7 |
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| 13. |
\operatorname sol u e : \frac 2 x - 3 3 x - 1 = \frac 2 x %2B 5 3 x %2B 1 |
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| 14. |
20. SolIve the equation x2 -(v5+1) x+5 by the method of completing the square. |
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| 15. |
hm dhanwan hai kintu sukhi nhi change simple sentence |
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Answer» We are wealthy but not happy. nhi aa RHA hai |
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| 16. |
4. The solution set ofx +1+ 6 = 0 is :x +1)COINNICONICO |
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Answer» (x / x+ 1)^2-5(x/ x+1) + 6 =0; ( x^2 / x^2+2(x)( x+1))-5x / x+1+6 = = ( x^2/ x^2 + 2x^2+x)-5x/x +7 =(x^2/3x^2+x - 5x / x+7)= =( x^2/3x^2+x -5x/ x+7)+6=0 = x^2( x+7)-5x(3x^2+x)+6= x^3 +7x^2 - 15x^3+5x^2 +6= -14x^3+12x^2+6=2(-7x^3+6x^2+3) = (-2, 3/2) Let x/(x+1) be y.Therefore,y^2-5y+6=0y^2-2y-3y+6=0y(y-2)-3(y-2)=0(y-2)(y-3)=0Therefore,y=2 or y =3.Putting the value of y,x/(x+1)=2x=2x+2x=-2.x/(x+1)=3x=3x+3.-2x=3.x=-3/2. |
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| 17. |
= AoeoCanee.Co\/-â.c 2o oze |
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| 18. |
* (12) If a 1200 W electric iron is used daily for30 minutes, how much total electricity isconsumed in the month of April? |
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| 19. |
TERCISE 10.4, cireles is 4 cm. Find the length of the common chord.of radii 5 cnradii 5 em and 3 cm intersect at two points and the distance betweent theual chords of a cirele interna |
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| 20. |
HWSloveD22-3 =2+2 |
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Answer» 2x-x=3+2x=5is the correct answer 2x - 3 = x + 22x - x = 2 + 3x = 5 =2x-3=x+2=2x-x=2+3=x=5 x=5 is the answer ok |
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| 21. |
.8. In the given figure, find the value of xSol. |
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| 22. |
8. In the given figure, find the value of x200Sol. |
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Answer» According to angle sum property, the sum of all the angles should be 180°.So here, the sum of 90°, 20° and x should be 180°90° + 20° + x = 180°110° + x = 180°x = 180 -110 x = 70°Therefore, x is equal to 70° |
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| 23. |
3A number is as much greater than 21 as is less than 71. Find the number. |
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Answer» thankyou so much |
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| 24. |
A number is such that it is as much greater than 84 asit is less than 108. Find it. |
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Answer» The number is 84+108/2 = 192/2 = 96 |
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| 25. |
a number is as much greater than 21 US it is less than 71 find the number |
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| 26. |
15.NICO~, which is greater and by how much? |
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Answer» First read the question then answer idiot 2/3 is greater than 5/9 and by 1/9 factor. |
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| 27. |
which is greater 2115x41 or 2015x27 and by how much? |
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Answer» 2115×41=86,7152015×27=54,405 86,715 is greater |
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| 28. |
G CITIES21. Of cas (40+2). In 80", Find the value of asol |
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Answer» sin30=sin(90-30)=cos60; cos(40+x)=sin30; cos(40+x)=cos60; 40+x=60; x=60-40=20; x=20 cos(40+x)=sin30cos(40+x)= cos (90-30)40+x= 60x= 60-40=20 cos(40+x)= sin30; cos(40+x)= cos(90-30); 40+x=60; x=60-40=20 |
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| 29. |
रण P AR Akt T o the CenmagcudiwHW . % AP find ¥ 3~ |
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Answer» When a, b, c are in AP 2b = a + c So, here we have 2(2k - 1) = k + 9 + 2k + 7 4k - 2 = 3k + 16 4k - 3k = 16 + 2 k = 18 |
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| 30. |
quare of 32 with the help of a formula.Find the square of 32 with thSol. |
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Answer» ✓32=5.65 is the correct answer applying formula (a+b)²=a²+2ab+b² we get32²=(30+2)²=(30)²+2(30)(2)+2²=900+120+4=1024 1024 is the correct answer |
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| 31. |
HWp(x)=x+2 is*-*+X-2 is a later |
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Answer» x+2=x=-2 p(x) =(-2)^3-(-2)^2+(-2)-2 =8-4-2-2 =8-8 =0 And |
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| 32. |
Verify cos60 1-2sin60 |
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Answer» Rong answer please specify your questions |
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| 33. |
L.Theradiioftwocirclesare19cmand9cmrespectively.Findtheradius of the circle which has circumference equal to the sum of |
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| 34. |
The radii of two circles are 19 cm and 9 cm respectivelyFind the radius of the circle which has circumference equalto the sum of the circumferences of the two circles. |
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Answer» Radius (r1) of 1stcircle = 19 cm Radius (r2) or 2ndcircle = 9 cm Let the radius of 3rdcircle ber. Circumference of 1stcircle = 2πr1= 2π (19) = 38π Circumference of 2ndcircle = 2πr2= 2π (9) = 18π Circumference of 3rdcircle = 2πr Given that, Circumference of 3rdcircle = Circumference of 1stcircle + Circumference of 2ndcircle 2πr= 38π + 18π = 56π → r = 28 CM ________answer |
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| 35. |
\frac{13^{3} \times 7^{0}}{\left\{(65 \times 49)^{2}\right\}^{1}} |
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| 36. |
1-० ५» ०33.- Lo 1z ofapl |
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Answer» Ans :- विद्युत धारा का मात्रक एम्पीयर (ampere)होता है. |
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| 37. |
O=oz-Z-x 24Âť * |
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Answer» x²+5x-4x-20=0x(x+5)-4(x+5)=0(x-4)(x+5)=0x=4,-5 |
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| 38. |
of a number and its one-third is 36. Find the numbernumber is as much greater than 1z s is |
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| 39. |
LUrl2blltippcey #ph소迎쒸 0L ·OZ |
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Answer» 100 paise =1 rupees70 paise= (1/100)*70= 0.7 rupees |
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| 40. |
APETINTMENT / VEETINGSol Find your different solutions of the equation 2x=5y =10. |
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| 41. |
.(a) In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and heightis 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of 8per metre square. |
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Answer» Radius of cylinderical pillars = r = 28cm =0.28mheight ,h=4mcurved surface area of a cylinder =2πrhcurved surface area of a pillar= 2×22\6×0.28×4=7.04metresq.Curved surface area of 24 such pillars = 7.04×24=168.96metresq.cost of cementing an area of 1metresq. =Rs8so,cost of painting 1689.6metresq.=168.96×8=Rs1,351.68 THANKS |
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| 42. |
In two circles, the arcs of same lengths subtendangles 65° and 110° at the centre. The ratio oftheir radii are :(A) 22 : 13(B) 13:22Ver 1:1(D) of these |
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| 43. |
o sin30° + tan45° — cosec60”न निर्णय ८ 21125 न धरना...नस निर्श् करा) ¢c30° + cos60° + cot45?ST S SR i il ~ |
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| 44. |
[५०eo=2 $pbhibb 1988 1% |
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Answer» HCF of 3/5 ,5/7,1/8= hcf of 3,5,1/lcm of 5,7,8= 1/280 |
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| 45. |
4. One of the acute angles of a right triangle is 50°. Find the other acute angle...tand1 100 and the other tuo onolog areal What is the |
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Answer» Let the angle be xsum of all the angles of triangles = 18x + 50 + 90 = 180 x + 140 = 180 x = 180 - 140 x = 40 This question of answer is 30 |
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| 46. |
1. The radii of two circles are 19 cm and 9 cm respectively. Findthe radius of the circle which has circumference equal to thesum of the circumferences of the two circles. |
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| 47. |
Q10. Using factor theorem, factorize each of the following polynomials:(a) 3x3 – x2 – 3x + 1(b) y3 – 2y2 – 29y - 42 |
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Answer» a) = 3x^2(3×-1) -1(3×-1) = (3×^2-1) (3×-1)....ans.... |
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| 48. |
2.Theradii of two circles are 19 cm and 9 cmrespectively. Find the radius of the circle whichhas circumference equal to the sum ofcircumferences of the two circles.the |
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| 49. |
ercapacity and by how much?Find the cost of painting 15 cylindrical pillars of a building at 2.50 per square metre i tnediameter and height of each pillar are 48 cm and 7 metres respectively13. |
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| 50. |
1zEx oz (1)igmale (1 |
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Answer» 20 /21× 27/25=20×27/21×25=540/525=1.02 |
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