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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 2551. |
RS20 / 1500 family with 2 children were selected randomly and the following data was recorded.Number of girls infamily10Number of family 475 814 211Compute probability of a family chosen at random havingat most 1 girlii)at least 2 girls2 boys |
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Answer» (1) 2) 475/1500=19/60 |
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| 2552. |
Suppose four balls labelled 1, 2, 3, 4 arerandomly placed in boxes B1, B2, B3, B4.The probability that exactly one box isempty is[19 Nov, 2017] |
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| 2553. |
9. Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability[CBSE Sample Paper 2011, CBSE 2012]that the card has a square number |
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Answer» Total number of cards in the box = 100 Let A be the event of getting a number which is a perfect square. Elementary events favourable to the event A are 4, 9, 16, 25, 36, 49, 64, 81 and 100. ∴ Number of cases in favour of the event A = 9 We know that, Probability will be 9/100 |
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| 2554. |
1Atot qr20 bulbs contain 4 defective oues. One bulb is drawn at random from the lot.What is the probability that this bulb is defective?Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulbis drawn at random from the rest. What is the probability that this bulb js notdefective2 |
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| 2555. |
There is a circular path around a sports feld. Sonia takes 13 minutes to drive one roundof the field, while Ravi takes 12 minutes for the same. Suppose they both start at thesame point and at the same time, and go in the same direction. After how many minuteswill they meet again at the starting point? |
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| 2556. |
7. There is a circalar path around a sports field. Sonia takes 18 minutes to drive one roundof the field, while Ravi takes 12 minutes for the same. Suppose they both start at thesame point and at the same time, and go in the same direction. After how many minuteswill they meet again at the starting point? |
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| 2557. |
sin(-theta)/sin(180^circ %2B theta) %2B cos(theta)/sin(90^circ %2B theta) - tan(90^circ %2B theta)/cot(theta) |
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Answer» cos theta/ + sin(-theta)/sin(90+theta) sin(180 + theta)- tan(90+theta)/ cot theta = cos theta/ - sin(theta)/ cos (theta) - sin(theta)- cot theta/ cot theta = 1 + 1 - 1 = 2 - 1 = 1 |
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| 2558. |
cos(theta)^2/(-tan(theta) %2B 1) %2B sin(theta)^3/(sin(theta) - cos(theta))=sin(theta) %2B 1 |
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| 2559. |
cos(theta)/(sin(theta) %2B 1) %2B cos(theta)/(-sin(theta) %2B 1)=4 |
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Answer» cosx/ 1- sinx + cosx/1+sinx= cosx(1+sinx+1-sinx)/ (1-sinx)(1+sinx)=2. cosx/ cosx^2= 2/ cosx=2/(cos(π/3)=2/(1/2)=2×2=4 |
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| 2560. |
(-sin(theta) %2B 1)/cos(theta) %2B cos(theta)/(-sin(theta) %2B 1)=2*sec(theta) |
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Answer» 1- sinx/ cos x + cosx/ 1- Sinx= (1-sinxa^2)+ cosx^2/ cosx(1- sina)= cosx^2+ cosx^2/cosx-cosxsinx= 2 secx 1- sinx/ cos x + cosx/1- sinx=:(1-sinx^2)+ cosx^2/cosx(1+sinx)= 1+ sinx^2-2 sinx + cosx^2/ cosx(1+ sinx)=2+2sinx^2/cosx(1+ sinx)=2(1+sinx^2)/cosx(1+ sinx)=2/ cosx=2 secx |
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| 2561. |
\operatorname { sin } 3 x = 3 \operatorname { sin } x - 4 \operatorname { sin } ^ { 3 } x |
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| 2562. |
integrate sqrt of 1+2tanx(secx+tanx).dx |
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| 2563. |
TODUD JEI upel 2017(ü) Find A-1, where A =12-372 3 2 . Hence, solve the following system of linear equations:3 -3 -4 |x + 2y - 32 = -42x + 3y + 2z = 23x - 3y - 4z = 11.[CBSE Sample Paper 2013: AICBSE 2010) |
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| 2564. |
3.CBSE 2007, Outside Dein (0 )Find the zeroes of the quadratic polynomial x2 + 5x + 6 and verify the relationship between thezeroes and the coefficients.CBSE Sample Paper II 2008 |
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Answer» accept as best answer |
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| 2565. |
Ifa AB and BC are twoadjacent sides of a Teglar berag ABCDEF, find thaCD, DE, EF, FA, AE and CE in terms of a and bCBSE Sample Paper 20071 |
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Answer» thanks |
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| 2566. |
5. It being given that /3 1.732, 5 2.236, /6 2.449 and 10 3.162,find to three places of decimal, the value of each of the following.v/56V3(i)[2014](ii)12011] (iii)3-3.CBSE Sample Paper+v |
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| 2567. |
278-155+55 |
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Answer» 278-155+55333-155178 278-155+55278+55-155333-155178 278-155+55=278+55-155=333-155=178 178 is the correct answer 278-155+55=333-155=178 is correct answer. |
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| 2568. |
\left. \begin{array} { l } { ( 4 ) \text { Simplify the following using } p ^ { 2 } - q ^ { 2 } = ( p + q ) ( p - q ) } \\ { ( a ) 38 ^ { 2 } - 12 ^ { 2 } } & { 65 \times 55 } \end{array} \right. |
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Answer» (38+12)*(38-12)=50*26=1300 |
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| 2569. |
7.)In a certain examination, thenumber of those who passed was 4times the number of those whofailed. If there had been 35 fewercandidates and 9 more had failed,the ratio of passed and failedcandidates would have been 2 1,then the total number ofcandidates was(a) 135(c) 145(b) 155(d) 150 |
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| 2570. |
sin(x)/(cosec*x %2B cot(x))=2 %2B sin(x)/(-cosec*x %2B cot(x)) |
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| 2571. |
x*cos(theta*cot(pi/2 %2B theta)) %2B cosec(pi/2 %2B theta)=sin(pi/2 %2B theta) |
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Answer» cosec(90+$) cos#cot(90+$)=sec$+x cos$-tan$= ==sec$+x(-sin$)=sin(90+$), = sec$+×(sin$)= cos$; =1/cos$+×( sin$)= cos$;=1-xsin$ cos$= cos$^2=1- cos$^2=sin$ cos$=sin$=xsin$ cos$=x=tan$ |
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| 2572. |
— _tan45° sec6(° ज्प्व' Cosec30%.sind3e B OWF x G T et काना । |
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| 2573. |
(sin(x)^3 %2B cos(x)^3)/(sin(x) %2B cos(x)) %2B (-sin(x)^3 %2B cos(x)^3)/(-sin(x) %2B cos(x)) |
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Answer» answer will be zero of this question |
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| 2574. |
3.If y=x+et, find - |
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Answer» dy/dx= 1+e^xnow again differention0+e^xso final resultse^x |
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| 2575. |
प्रदत्त समीकरण को x, y, 2 qo / के लिए हल कीजिए यदिil eto |
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| 2576. |
(cos(3*x) %2B cos(4*x) %2B cos(2*x))/(sin(3*x) %2B sin(4*x) %2B sin(2*x))=cot(3*x) |
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Answer» L.H.S. = (cos4x + cos2x) + cos3x / (sin4x + sin2x) + sin3x = 2cos[(4x+2x)/2].cos[(4x-2x)/2] + cos3x / 2sin[(4x+2x)/2].cos[(4x-2x)/2] + sin3x = 2cos3x.cosx + cos3x / 2sin3x.cosx + sin3x = cos3x(2cosx + 1)/ sin3x(2cosx + 1) // Taking common = cos3x(2cosx + 1) / sin3x(2cosx + 1) = cos3x / sin3x = cot3x Hence, L.H.S = R.H.S. |
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| 2577. |
If cosec x - sin x = a^3 and sec x - cos x = b^3 , than prove that , a^2 × b^2 (a^2 + b^2) = 1 |
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Answer» Thanks a lot sir. |
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| 2578. |
cos(x)/(cosec*x %2B 1) %2B cos(x)/(cosec*x - 1)=2 |
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| 2579. |
(sin(x) %2B sin(3*x))*sin(x) %2B (-cos(x) %2B cos(3*x))*cos(x)=0 |
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Answer» (sin3x + sinx) sinx + (cos3x - cosx) cosx= sin3x sinx + sin²x + cos3x cosx - cos²x= (cos3x cosx + sin3x sinx) - (cos²x - sin²x)= cos(3x - x) - cos2x= cos2x - cos2x= 0 ( sin3x+ sinx)sinx+ ( cos3x-cosx) cosx= sin3xsinx+ sinx^2+ cos3xcosx-cosx^2= ( cos3xcosx+ sin3xsinx)-( cosx^2-sinx^2)= cos(3x-x)- cos2x= cos3x- cosx- cos2x= cos3x- cos3x=0 (sin3x+sinx)sinx+( cos3x-cosx)cosx= sin3x sinx+sin^2x+ cos3xcosx- cos^2x= cos3xcosx +sin3xsinx-(cos^2x-sin^2x)= cos(3x-x)-cos2x= cos2x-cos2x=0 |
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| 2580. |
Let A -Z-(0) and let f:A A be defined by f(C) -What type offunction is f? |
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Answer» Given f(x) = |x|/x So, f(-x) = - |x|/xSo, f(x) is odd function |
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| 2581. |
tan(x)/(-cot(x) %2B 1) %2B cot(x)/(-tan(x) %2B 1)=sec(x*(cosec*x)) %2B 1 |
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| 2582. |
(cos(A) %2B 1 %2B sin(A))/(cos(A) %2B 1 - sin(A))=(sin(A) %2B 1)/cos(A) |
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Answer» divide numerator and denominator by cos and apply suitable identity |
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| 2583. |
cos(x)/(-sin(x) %2B 1)=(cos(x) %2B 1 %2B sin(x))/(cos(x) %2B 1 - sin(x)) |
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| 2584. |
(cos(theta) %2B 1 %2B sin(theta))/(cos(theta) %2B 1 - sin(theta))=(sin(theta) %2B 1)/cos(theta) |
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Answer» sorry I didn't know |
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| 2585. |
(sin(A) - cos(A) %2B 1)/(sin(A) %2B cos(A) - 1)=cos(A)/(-sin(A) %2B 1) |
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| 2586. |
((-sin(theta) %2B 1)*(sin(theta) %2B 1))/(((-cos(theta) %2B 1)*(cos(theta) %2B 1))) |
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| 2587. |
13. People of Sundergram village planted a total of 102 trees in the vi d en Someothe trees were tree The number of non-fruit trees were two more than three timethe number of the tree What was the number of fruit tres planted |
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Answer» non fruit tree is 34 and fruit tree is 68 fruit tree = 68and non fruit tree = 34 fruit tree = 68and non fruit tree = 34 fruit trees is 25non fruit trees is 77 hey I don't know the answer but don't be upset any will give you the answer don't think me bad I am a good person 🙉 let the number of fruit trees be X and number of non-fruit trees be y, Given, x+y=20.......eqn. 1According to question, y=3x+2putting value y in eqn. 1,x+y=102or x+3x+2=102or 4x+2=102or 4x=100or x=25......eqn. 2putting X in 1,x+y=102or y=77 : fruit trees =x=25non-fruit trees=y=77 non fruit tree is 34 and fruit trees is 68 |
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| 2588. |
1/(sin(theta) %2B 1) %2B 1/(-sin(theta) %2B 1)=2*sec(theta)^2 |
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Answer» 1/ 1+ sinA + 1/ 1-sinA= 1-sinA+1+SinA/(1+sinA)(1-sinA)=2/1-sinA^2=2/cosA^2=2secx^2 |
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| 2589. |
\begin{aligned} \text { Ex. } 3 : \text { If } f(x) \text { is continuous at } x=0, \text { where } \\ f(x)=\frac{1-\cos k x}{x^{2}}, & \text { for } x \neq 0 \\=\frac{1}{2}, & \text { for } x=0 \end{aligned} |
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| 2590. |
((-sin(theta) %2B 1)*(sin(theta) %2B 1))*(tan(theta)^2 %2B 1)=1 |
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| 2591. |
\begin{aligned} \text { If } f(x) \text { is continuous at } x=0, \text { where } \\ f(x)=\frac{8^{x}-2^{x}}{k^{x}-1}, & \text { for } x \neq 0 \\=2, & \text { for } x=0 \end{aligned} |
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Answer» page 2 |
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| 2592. |
\begin{array}{l}{\text { If } f(x)=x \sin x, \text { then } f^{\prime}\left(\frac{\pi}{2}\right) \text { is equal to }} \\ {\text { (a) } 0} \\ {\text { (c) } 1}\end{array} |
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| 2593. |
f ( 0 ) = - 2 , f ^ { \prime } ( 0 ) = 3 , \text { find } h ^ { \prime } ( o ) \cdot \text { where } h ( x ) = x f ( x ) |
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| 2594. |
F ( x ) = \left[ \begin{array} { c c c } { \operatorname { cos } x } & { - \operatorname { sin } x } & { 0 } \\ { \operatorname { sin } x } & { \operatorname { cos } x } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right] , \text { show that } F ( x ) F ( y ) = F ( x + y ) |
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| 2595. |
f(x)=\left\{\begin{array}{ll}{0} & {\text { if }} & {x \text { is irrational }} \\ {1} & {\text { if }} & {x \text { is rational }}\end{array}\right.show that Lt f(x) does not exist for any c ER |
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| 2596. |
f(x)=\frac{e^{1 x}-e^{2 x}}{\sin 3 x} \left.\begin{array}{l}{\text { for } x \neq 0} \\ {\text { for } x=0}\end{array}\right\} \text { at } x=0 |
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| 2597. |
Example 11: There are chaits in the room. If 2 guests share a chair, one chair remains vacantand if each guest sits on a chair one guest remains standing. What is the number of guests?ple 12: There are birds on two trees. If a bird flew from first to second tree then there areExamequal number of birds in each tree. However if a bird flew from second to first tree then the birdson first tree are double then the birds on second tree. How many birds are on each tron? |
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Answer» The answer to this question is that there are '3' chairs and '4' guests in a room. Explanation:If two guests share one chair then only 2 chairs are needed for 4 guests and in this way one chair is vacant. But when each guest sits on separate chairs, only 3 guests get chairs while the 4th guest remains standing. |
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| 2598. |
Example 12: There are birds on two trees. If a bird flew from first to second tree then there areequal number of birds in each tree. However if a bird flew from second to first tree then the birdson first tree are double then the birds on second tree. How many birds are on each tree? |
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Answer» Let birds on first tree=xBirds on second tree=yx-1=y+1x-y=2 x=y+2x+1=2(y-1)x+1=2y-2x-2y=-3y+2-2y=-3-y=-5y=5x=7First tree had 7 birdsSecond tree had 5 birds hit like if you find it useful |
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| 2599. |
write e Luillates UI U PUL ULUM .Find the value of ((16)7]In the given figure(i) If ZDAB 50° and LABD=50°, then find ZACB |
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Answer» 70° use triangle properties in triangle ADB to find Angle ADB,Use circle properties. |
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| 2600. |
=\frac{4 \cdot 6 \times 10^{-4}}{1 \cdot 1 \times 10^{-2}} |
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