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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.
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12. A box contains 6 distinct dolls. From the box, 3 dollsare randomly selected one by one with replacementWhat is the probability of selecting 3 distinct dolls?\begin{array}{ll}{\text { (a) } \frac{5}{54}} & {\text { (b) } \frac{12}{25}} \\ {\text { (c) } \frac{1}{20}} & {\text { (d) } \frac{5}{9}}\end{array} |
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Answer» 6C3/(6*6*6)=20/216=(5×4)/(54×4)=5/54 answer in book is 5/9 |
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nd umlume, lateral surfaceasures: () 7 m (ii)5.6 cm (iii) 8 dm 5 cmarea and the total surface area of a cube each of wrea of a cube is 1 176 cm". Find its volume.a cube is 729 cm3. Find its surface area.meons ofa metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recansiof side 45 cm. How many cubes are formed?h of each edge of a cube is doubled, how many times does its volume by times does its surface area become?hical block of fine wood costs 256 at 500 per m2. Find its volumeach side.RIGHT CIRCULAR CYLINDERee around us many objects such as a road roller, a gas cylinder,circular pillar, a circular pipe, a circular pencil, a measuring jar, |
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Answer» the surface area of cube is 1350 cm2 . find the volume of the cube . the volume of a cube is 512 cubic centimetre find the side of a cube |
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| 3. |
बिक ey -14, निम्नलिखित व्यंजक को ८ +19 के रूप में व्यक्त कोलिए(3+5)( 5)(दिन (पिन 2) |
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| 4. |
. o 3 A ey & ?}Ifi\ o Sl गेंद तक न -थैले में 5 लाल और 5 काली गेंदे हैं। इस थैलें में से एक गेंद यादूच्छाया eहि इसकी प्रायिकता क्या है कि गेंद 0) लाल हो? (0) लाल नहीं हो? & |
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Answer» एक थैला में 3 लाल बॉल और 5 काली बॉल हैं।थैला में सरबयुक्त बॉल है=8∴लाल बॉल की प्रयिक्ता है=3/8प्रयोक्ता की लाल बॉल नहीं हो=5/8 |
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| 5. |
हिन्ली में स्वर वर्ण कितने हैं ?बिके e /DA ऑल (™ जेल |
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Answer» उच्चारण के समय की दृष्टि से स्वर के तीन भेद किए गए हैं: ह्रस्व स्वर - जिन स्वरों के उच्चारण में कम-से-कम समय लगता हैं उन्हें ह्रस्व स्वर कहते हैं। ये चार हैं- अ, इ, उ, ऋ। इन्हें मूल स्वर भी कहते हैं। दीर्घ स्वर - जिन स्वरों के उच्चारण में ह्रस्व स्वरों से दुगुना समय लगता है उन्हें दीर्घ स्वर कहते हैं। आ, ई, ऊ, ए, ऐ, ओ, औ दीर्घ स्वर के उदाहरण है। प्लुत स्वर - जिन स्वरों के उच्चारण में दीर्घ स्वरों से भी अधिक समय लगता है उन्हें प्लुत स्वर कहते हैं। प्रायः इनका प्रयोग दूर से बुलाने में किया जाता है। |
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| 6. |
1. Who use first word of geography ? |
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Answer» The first person to use the word "geography" wasEratosthenes(276–194 BC). |
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| 7. |
1) Evalueatedirectlythedibbricationof asepo 31. |
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| 8. |
ase arngis 83ulate the angles marke100(i) Rectangle |
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| 9. |
2. lim (x - ———22)XN 7 |
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| 10. |
दा गे नलहु र्क सर . २० था 9y XN |
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Answer» Given series is 3, 8, 13, ...... 253 here, first term , a = 3 common difference , d = 5 Let us find total number of terms at first.use Tn=a + (n-1)d=> 253 = 3 + (n - 1)5 => 250 = 5(n - 1) => n - 1 = 50 => n = 51 so, there are 51 terms in given series.now we know, mth term from last =last term - mth term + 1 so, 20th term from last =51 - 20 + 1 = 32 hence, 20th from last = 32th term from first use , T32=a +(32-1)d = 3 + 31 × 5 = 3 + 155 = 158 hence , 20th term from last = 158 |
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| 11. |
If y1 + x"-m + xp-m1+x=" + XP-n.1 + xm-p + xn-p?(A) xn-p-1(C) xml(B) 0(D) X-1 |
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Answer» option B is the right answer |
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| 12. |
5ey (xn)G |
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| 13. |
q+xp+o+ XN1 |
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Answer» Please hit the like button if this helped you. |
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| 14. |
length of a rectangle is 5m more than twice its breadth, find out the dimensions of the rec(Given: Perimeter106m)Iftange |
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2144. Prove that the tangents drawn at the ends of a diameter of a circleProve that the perpendicular at the point of contact to the tangeer of a circle arentto |
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| 16. |
coteet /ertf the answers,) 4888Ase verite the ans |
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Answer» 488÷8=61is the value |
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| 17. |
: A box contains 5 different red and 6 different white balls. In how many ways can 6balls be selected so that there are atleast two balls of each colour ? |
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Answer» For selecting6 balls so that atleasttwo balls of each colours = 5c2*6c4 + 5c3*6c3 + 5c4*6c2 = 10*15 + 10*20 + 5*15 =150 + 200 + 75 = 425 |
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| 18. |
Activity-2: Play with balls(Description) - Students are supposed to take different coloured sketch pens, same number of identicalballs are to be drawn for one integers as indicate. Perform activity according to given example.(We know -ve symbol means opposite or change of colours).Example- Let black for the and Red for -veinteger.*-2 X (-3) ={-2 times (-3)} = {6}Tost.] --Dahle :::) |
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Answer» 6jdndlsmab78283+63jdkdgsmaksjsgj 6 hdyshsuisisusyegegehueueyuee hzja HCl usnahzksjdsjkahxne ed dmsljdbdjs |
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| 19. |
7- (the domain of real function f(x) = V9 - x? is equal to-) |
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| 20. |
Find six rational numbers between1 and O. |
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Answer» Rational numbers between 2 numbers a and b is ( a + b) / 2. Rational numbers between 2 numbers -1 and 0 is = ( -1 + 0) / 2 = -1/ 2 Rational numbers between 2 numbers -1 and -1/ 2 is = (-1 + (-1/ 2)) / 2 = -3 / 4 Rational numbers between 2 numbers -1/ 2 and 0 is = (-1/ 2 + -3 / 4) / 2 = -5 / 8. Rational numbers between 2 numbers -1 and -3 / 4 = ( - 1 + ( -3 / 4) ) / 2 = -7 / 8 Rational numbers between 2 numbers -3 / 4 and -7/8. = ( -3/ 4 + ( -7 / 8) ) / 2 = -13 / 16 Rational numbers between 2 numbers -1 and -13/16 = ( -1 + ( -13/16) ) / 2 = -29/32 Therefore, Six rational numbers between -1 and 0 are -1/2 , -3/4 , -1/4, -5 /8 , -7/8 , -13/16, - 29/32 |
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| 21. |
Find six rational numbers between 1/2 and 3/2 |
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| 22. |
1A =2270. ARk a+btet+dte + 2 (atb+ctdtef +—_ एप: के मान निकातियेatbtctdte (a+tbtcidie)®01 1/2(|2 (दि) 0 |
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| 23. |
write8 rational nos bekoFands |
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Answer» 64/9, 65/9, 66/9, 67/9, 68/9, 69/0, 70/9, 71/9 By multipication of 9/9 now 63/9 and72/9 now 64/9, 65/9, 66/9, 67/9, 68/9, 69/0, 70/9, 71/9 |
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Nos. 26 to 30 carry 6 m |
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| 25. |
、 Find the range of the real function f(x)1-1-21, |
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| 26. |
0 203x+2)+L-e 34 Isa52-23saтLese multiples;-The sunи - с 2. СиатораLulehiples of t1 is 363. finelthThe design byw two coholenos ais 66. The matice oftwo nos IS 2:5 what are thetwo no.)et Yt5.) -3 (1-1) -02 (58+4)-[6x = 1 *x]+* ++2 |
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| 27. |
| Date:a sind 3 vrational nos between Land |
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Answer» -1.2/5,-1.5/5,-1.75/5 |
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| 28. |
17. Fill in the missing nos. in each case |
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Answer» 8×3 + 5×4 = 24 +20 = 44 So 3×7 + 8×5 = 21 +40 = 61 Its 61⭐ 61 is the answer of this question 8×3+4×5=24+20=44 3×7+5×8=21+40=61 The answer is 61 61 is the correct answer of the given question |
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0como two nos 23 & 2x3 in 2 30 2x3W) 2°x3 |
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Answer» First number = 2^3 * 3^2Second number = 2^3 * 3^3 Therefore,LCM = 2^3 * 3^3 (c) is correct option |
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| 30. |
e -recived dividend at 40 .., ad her nos gain |
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Answer» please post some clear image |
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| 31. |
Question Nos 1Find six rational numbers between 3rs bet |
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Answer» Somultiply by 7so 3*7/7= 21/7and 4*7/7= 28/7nowrational number21/7,22/7,23/7,24/7,25/7,26/7,28/7 |
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1) 5605 0- था 01, णि 0= 0°,30°, 45°, 60° . follousyjii) cosec2 9 cot29= 1, for g= 30, 45%, 60:90 |
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Answer» ii) sec0*sec0-tan0*tan0 = 1-0 = 1 sec30*sec30-tan30*tan30 = 4/3-1/3 = 1 sec45*sec45-tan45*tan45 = 2-1 = 1 sec60*sec60-tan60*tan60 = 4-3 = 1iii)cosec30*cosec30-cot30*cot30 = 4-3 = 1 cosec45*cosec45-cot45*cot45 = 2-1 = 1 cosec60*cosec60-cot60*cot60 = 4/3-1/3 = 1 cosec90*cosec90-cot90*cot90 = 1-0 = 1 |
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| 33. |
A function f(x) has x-intercepts of -3 and -5. What is the constant term in the function?f(x) = x2 + 8x + |
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Answer» Constant term in the function is 15 correct answer isf(x) = x² + 8x + 15 please like and accept as best answer 15 is the correct answer x^2+8x+15 = x^2+3x+5x+15=x(x+3)+5( x+3)=( x+3)(x+5)=0; x=-3,-5 15 is the correct answer |
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| 34. |
, then show that4. If the function f : R R defined by f (x) =f (x + y) + f (x - y)=2f (x) f (y). |
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| 35. |
1) 6The function f R R is defitied1) an odd function 2) neither an odd function nor an even function3) an even functionby f(x) x+x2 is4) both odd function and even functiond e the roots of x2 +dx + b 0, then t |
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Answer» f(x) = x + x² f(-x) = - x + (-x)² = - x + x² So, it is neither even nor odd 2) option is correct what is the mari gold color |
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| 36. |
Q. 1,A function f : Râ R is defined as f(x) = x2 + 2, then evaluate f-1 (-6) |
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Answer» f(x) = y = x*x + 2 so x*x = y - 2 so x=root(y-2) so inverse(f(x)) = root(x-2) inverse (f(-6)) = root(-6-2) = root(-8) |
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| 37. |
4. Find the domain and the range of the real function f defineFind the domain and the range of the real function f detineby fC) - )n / defined by /) - |
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Answer» Pls give the answer of 5 q's also |
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| 38. |
1. Find12. Find the antiderivative F(x) of the function f(x) = cos4x if Fmph passes thr |
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Answer» Anantiderivativeis a function that reverses what the derivative does. One function has manyantiderivatives, but they all take the form of a function plus an arbitrary constant.Antiderivativesare a key part of indefinite integrals. |
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| 39. |
(F5)+H(+T)= |
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Answer» (+5)+(+7)=+ x + = ++5+7=12,, |
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| 40. |
f5 times the jfifth term of an AP is equal to 8 times its eishone that its 13th term is zero. |
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Answer» Let of the APfirst term= acommon difference=dATQ5[a+(5-1)d]=8[a+(8-1)d]5(a+4d)=8(a+7d)5a + 20d = 8a + 56d3a = 36da= -12dNow 13th terma+(13-1)d=-12d+12d=0(proved) Like my answer if you find it useful! |
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| 41. |
Q. 18. If cote = - prove that:yupower as soon as posiblePleasesece-cosecesec 0 + cosecomwer as soon1e - cosece |
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Answer» V secx- cosecx/ V secx + cosecx=V(3/4)-(V7/3) / 3/4+ V7/3=(V9-4V7/12× 12/4V7+9=1/V7 |
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1. In Fig. 9. 15,ABCD is a parallelogram, AE丄DCand CF丄AD. If AB = 16 cm, AE-8 cm andCF = 1 0 cm, find AD |
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| 43. |
outcomes are thereGiven 5 flags of different colours, how manyeach signal requires the use of 2 flags, one belowmany differentheg in |
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| 44. |
sove that loeia(N hea e allo and C are all Pos/uvenoscre al po |
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EXERC1. Which of the following are quadratic equations?(i) x2 + 6x - 4 = 0(ii) 13x? - 2x + 1 = 0(ii) x + = 5(v) 2x2 - 3x + 9 = 0(vii) 3x? - 5x + 9 = x? - 7x + 3(vi) x2 - 2x - VX-5=0(vii) x++ = 1(ix) x2 - 3x = 0(xi) (2x + 1) (3x + 2) = 6(x - 1)(x - 2)(xii) x + 1 = x,x+0(xiv) (x + 2) = x3 - 4(xiii) 16x? - 3 = (2x + 5) (5x - 3)(xv) x(x + 1) + 8 = (x + 2)(x - 2) |
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Answer» any equation having highest power of x is 2 then that equation is called quadratic equation. and power must be positive.let's take an example:- (i) x2 + 6x - 4 = 0above equation has highest degree of the polynomial is 2 so it is a quadratic equation. https://youtu.be/wSMHWy_IQyAmore details study (2x+1)(3x+2)=6( x-1)(x-2); (6x^2+4x+3x+2)=6(x^2-2x-x+2); (6x^2+7x+2)=6(x^2-x+2); 6x^2+7x+2=6x^2-6x+12; 7x+6x=12-2; ; 13x=10; x=10/13; ; (xiii)16x^2-3=(2x+5)(5x-3); 16x^2-3=(10x^2-6x+25x-15); 16x^2-3=10x^2+19x-15); 16x^2-10x^2-3+15=19x; 6x^2+12-19x x^2+1/x^2=3; . ( x+1/x)(x-1/x)=3; ; ( x^2+1/x)( x^2-1/ x^2)=3; ( x^2+1/x^2)=3; ( x+1/x)(x-1/x)= ( x^2+1/x)(x^2-1/x)=3,; ( x^2+1)( x^2-1)=3; x^4-x^2+x^2-1=3; x^4=3+1=4, x^4=(1)^4; x=1 viii)x+1/x=1; squares on both; (x+1/x)^2=1^2; x^2+(1/x^2)+2.x.1/x=1; x^2+1/x^2=1; iv)x-3/x=x^2; (x-3/x)^2=( x^2)^2; ) ( x^2+3/x^2-2.( x)(1/x)= x^4; x^2+3/x^2-2= x^4 (xiv)( x+2)^3=x^3-4; ( x+2)^3=x^3+8+3(x)2(x+2)= x^3+8+6x( x+2)=x^3-4; 8+6x^2+12x=-4; 6x^2+12x+4=0; (xv)x(x+1)+8=( x+2)( x-2); x( x+1)+8=x^2+x+8; ( x+2)( x-2)=( x^2-2x+2x-4)=( x^2-4); x^2-4=x^2+x+8, x+8+4=x+12; x=-12 x= 3 is the correct answer x= 3 is the correct answer any equation have power 2 is called quadratic equation general quadratic equationax^2+bx+C=0x^2+2x+1=0x^2-6x-4=0 |
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TRY THESEFind the area of the following trapeziums (Fig 11.8)0)-7 cm-6 cm10 cm5 cm3 cmFig 11.8 |
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Answer» Area of trapezium = 1/2*(sum of parallel sides)*height(i) area = 1/2*(7+9)*3 = 1/2*(16)*3 = 24cm^2(ii) area = 1/2*(5+10)*6 = 1/2*(15)*6 = 45cm^2 |
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| 47. |
of a rectande 2 x (lengh + breadithpom- 1 om 100 cm-1Find the pertmeter of each of the following cl13 cm7 cm8 cm6 cm10 cm5 cm |
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Answer» perimeter is the sum of all the sidessides are a=7cm,b=13cm,c=8cmso perimeter is a+b+c=7+13+8=28cm |
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| 48. |
find the lcm of each pair of number1. 25 and 502. 6 and 103. 14 and 214. 5 and 11 |
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| 49. |
find the lcm of each pair of number1. 25 and 502. 6 and 103. 14 and 214. 5 and 11 |
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| 50. |
\left. \begin{array} { l } { x ^ { 2 } - 3 x + 2 = 0 } \\ { x ^ { 2 } - x - 6 = 0 } \\ { x ^ { 2 } - 6 x + 8 = 0 } \\ { x ^ { 2 } - 5 x + 4 = 0 } \end{array} \right. |
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Answer» 1) x^2-3x+2=0 so (x-2)(x-1)=0so x=1,22) x^2-x-6=0so (x-3)(x+2)=0so x=-2,33) x^2-6x+8=0(x-4)(x-2)=0so x=2,44) x^2-5x+4=0(x-4)(x-1)=0x=1,4 |
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