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. |
Prove that the functionf(x)-x" is continuous at x = n, where n is a positiveinteger |
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| 2. |
UJU(a) 42. The factors of expression r? + (a + b)x + ab are-( h |
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| 3. |
( x + i y ) ^ { 3 } = u + i v , \text { then show that } \frac { u } { x } + \frac { v } { y } = 4 ( x ^ { 2 } - y ^ { 2 } ) |
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| 4. |
( x + i y ) ^ { 3 } = u + i v \text { then show that } \frac { u } { x } + \frac { v } { y } = 4 \left( x ^ { 2 } - y ^ { 2 } \right) |
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| 5. |
Show dhat ane and onlu one uandis |
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Answer» x is an integer. So,it is of the form 3k,3k+1 or 3k+2 where k is an integer. If x=3k,then x+1=3k+1,not divisible by 3 x+2=3k+2,not divisible by 3 If x=3k+1(not divisible by 3),then x+1=3k+2,not divisible by 3 x+2=3k+3=3(k+1), divisible by 3 If x=3k+2(not divisible by 3),then x+1=3k+3=3(k+1),divisible by 3 x+2=3k+4=3(k+1)+1,not divisible by 3 Hence by seeing all the above cases,we can safely say that:out of x,x+1 and x+2,only one is divisible by 3. Like if you find it useful |
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| 6. |
)What number is 748 more than 66 443 |
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Answer» We are looking for a new number which is 748 more than 66443.We will get the new number by adding 748 to 66443.We write it down as:66443+748=67191 66443 more then numbers |
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| 7. |
In a two digit number, digit at the ten's place is twiceplace. If the number obtained by interchanging the digits is added to theoriginal number, the sum is 66. Find the number. |
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Answer» I want equation in one variable😅 |
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| 8. |
मैदान का परिमाप 200 मीटर है। और इसकी चौड़ाई 40 मीटर है तो इर मैदान को 1.25 रं/मी* की दर से समतल कराने की लागत ₹ 900 हैं यदिसकी चौड़ाई कितनी है?SOy i) e s e |
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| 9. |
In a two digit number, digit at the ten's place is twice the digitplace. If the number obtained by interchanging the digits is addedoriginal number, the sum is 66. Find the number |
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Answer» Let the tens digit be x and the units digit be y. So the number=10x+y A.q.=>x=2y(equation 1) After interchanging the digits we get10y+x Also,=>(10x+y)+(10y+x)=66 =>10x+y+10y+x=66 =>11y+11x=66 =>11(y+x)=66 =>y+x=66/11 =>y+x=6 From equation 1 x=2y So, y+2y=6 =>3y=6 =>y=6/3 =>y=2 And x=2(2)=4 Hence the number is 42. Like my answer if you find it useful! |
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| 10. |
Question No. 89The difference between Compound Interest and Simple Interest on a certain sum for 2 years at 12.5% rate isRs.45. What is the sum?A)Rs.2880B)Rs.2440C)Rs.3000D)Rs.2000 |
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Answer» A. us right answer A is the correct answer 1st si is 360 and second principal+ si then 405 difference is 45 B) is correct answer option C ) is the correct answer |
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| 11. |
(b) Find the greatest number that will divide 33, 44 and 66 exactly. |
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Answer» By using prime factorisation 33 = 3*11 44= 2*2*1166= 2*3*11 so, in all these only 11 is common.. so the answer is 11. |
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| 12. |
latOne of the digits of a two-digit number is five times the other. If we interchange the digits ofthis number and add the resulting number to the original number, we get 66. What is the originalnumber? |
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Answer» Let the two digit number be (10a+b)According to the question(10a+b)+(10b+a)=66; 11a+11b=66;a+b=6;And also it is given that a=5b or b=5aIf a=5b then put in the above equation 6b=6; then b=1 then a=5...then the number is 51 and if a=1 then b=5 then the number is 15 |
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| 13. |
Define a real function. Find the domain andrange of the real functionf(x) 12-1 1 |
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Answer» In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain. Many important function spaces are defined to consist of real-valued functions Domain (1/2 to infinity) and range (0 to infinity) |
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| 14. |
कै: + (4) + 3(100)(4)(100 न 4)0000 + 64 + 1248004864 |
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| 15. |
DEEP RIVEBecause weblend!Hever- OILSUNFLOWERexclusively inCookedGive a Chip3. If in a class of 40 students, 70% studentsare girls then what is the number of boys inthe class. |
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Answer» 12 boys are there in the classthis is the correct answer for this question Thank you sir this is the crispy snacks deep river is a snacks. 12 boys are there in the class ogdfubfeinhhgfxxf6fddbivfd deep river is the snacks... 12 boys are there in class Total students =40no. of girls= 70% of 40 =70/100*40 =28therefore number of boys= 40-28=12 12 is the correct answer for this question |
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| 16. |
Fill in the blank with proper alternative. 0000.......think then act.1) Secondly 2) First 3) Don't 4) Neverविषय - इंग्रजीप्रज्ञाशोध परीक्षा मार्गदर्शक इ. 6 वी (303) |
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Answer» first think then act is the right answer |
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| 17. |
Find the median of the values: 25, 31, 27, 29, 32.25 28.25The weight in kg) of 15 students of a class are |
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Answer» 25+31+27+29+32+28+25=190/15=12.667 25+31+27+32+28+25=190/15=12.667 12.667 is the correct answer 12.667 is the. correct. answer |
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| 18. |
UJU0) 29%23.0707. What per cent of(a) 60 is 600?(b) * 50 is * 250?(c) 8 hrs is 2 days?(d) 125 g is 2.5 kg |
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Answer» (a) Let the per cent be a. 600 x a /100 = 60 600a = 60 x100 a = 60 x 100/600 a = 10 % similarly you can do every question. But, for their unit should be sameLike in (c) convert 8hrs to day by dividing by 24 and in |
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| 19. |
ला 15९ 40.8. 210000/0000 -ढ 1 \ |
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Answer» 3+√2/4√2*4√2/4√2=12√2+8/32=3/8√2+1/4 |
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| 20. |
26] Poces 4 cnd 6 awe 0k obart on o highwous.0ne ey stkIdrom A ond_angthe Bt dhe same Giwe वी ity e braelI Aoume okirecfiof 0 cM_m_fiM&' 2८१1 sheeds ,m 05कलम अदा मर | 400५ नी! (०७००0 ch दि मच 10 000. (छा areफल -भु# 4७ 100 0000 है |
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Answer» Let, speed of faster car = x km/hSpeed ofslowercar = y km/h Relative speed when both cartravelsinsame direction= x - yIf the cars travel in thesame directionat different speeds, they meet in 5 hoursSpeed = distance/ timeTotal distance= 100 kmSpeed, x – y = 100/5x – y = 20x = 20 + y................…(1) Relative speed when both cartravelsin opposite direction = x + yIf they travel towards each other, they meet in 1 hour.Speed = distance/ timeTotal distance= 100 kmSpeed, x+ y = 100/1 Put the value of x from eq(1)We get, 20 + y + y = 1002y = 80y = 40 Put the value of y in eq(1)we get,x= 20 + 40x = 60 Hence speeds are 40 km/h and 60 km/h |
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| 21. |
If five times the 5th term of an A.P. is equal to eight times its 8th term, then show thatits 13th term is zero |
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| 22. |
36. If five times the ffth term of an AP is equalto eight times its eighth term, show that[CBSE 2012]its 13th term is zero. |
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Answer» Explanation : 5*5th term = 8*8th term 5(a + 4d) = 8(a + 7d) 5a + 20d = 8a + 56d 3a = -36d a = -12d a + 12d = 0 13th term = a + 12d = 0 13th term is 0. If you find this answer helpful then like it. |
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| 23. |
(4) If five times the 5th term of an A.P. is equal to eight times its 8th term, then show thatits 13th term is zero. |
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Answer» let first term be a and common difference be daccording to given question5 × a(5) = 8 × a(8)5(a + 4d) = = 8(a + 7d)5a + 20d = 8a + 56d3a + 36d = 0a + 12d = 0a = -12dso,a(13) = a + 12d = -12d + 12d = 0 |
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| 24. |
(1 + 0000 - 005600) (1 + рео8119 + 8600) > 2 |
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Answer» (1+cot A -cosec A)(1+ tan A + sec A) Lhs =(1 +cos A/sin A - 1/sin A)(1 + sin A/cos A +1/cos A) =(sin A+cos A -1/sin A)(cos A +sin A+1/cos A) =(sin A+cos A-1)(sin A+cos A+1)/sin Acos A =[(sin A+cos A)^2-(1)^2]/sin Acos A =[sin^2A+cos^2A +2sin Acos A- 1]/sin Acos A =[1-1+2sin Acos A]/sin Acos A =2sin Acos A/sin Acos A =2 =Rhs |
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| 25. |
if rs 2500 becomes rs 3000 in 5 years ,then what will be the rate of interest? |
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Answer» Interest = 3000- 2500= 500.INTEREST = PRT/100=> R = (500*100)/(2500*5)=> R = 4 % PLEASE HIT THE LIKE BUTTON |
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| 26. |
am - aAnTo foto ye, —t given)(given)am n = 1 |
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Answer» am=1/na+(m-1)d=1/n--------(1) an=1/ma+(n-1)d=1/m---------(2) (1)-(2)(m-n)d=1/n - 1/md=1/mn put in eq(1)a+(m-1)/mn=1/na=1/n - (m-1)/mna=1/mn amn=a+(mn-1)damn=1/mn+(mn-1)/mnamn=1 |
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| 27. |
Find the domain and the range of the real functionf defined byf(x) =\sqrt{(x-1)} |
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Answer» Therangeof an even indexed radical starts at its startingpoint(1,0)(1,0)and extends toinfinity. [0,∞)[0,∞) {y|y≥0} Domain:[1,∞),{x|x≥1} |
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| 28. |
EXAMPLE 1 Find the mean deviation about the mean for the following data15, 17, 10, 13,7, 18, 9, 6, 14, 11 |
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| 29. |
2 , then what is x equal to?80. If x+1+2+(A) 1013(B) 10(C) 1017(D) 10 |
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| 30. |
Calculate the speed of sound in air at N.T.P.if thedensity of air at N.T.P. is 1.29 kg/m and y for air is1.4 |
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| 31. |
I 4. A certain sum of money at compound interest becomes?7396 in two years andRs7,950.70 in three years. Find the rate of interest. |
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| 32. |
le 32. A manufacturer's catalogued price of a scooty is 45000, but he allows the retailer 30%discount. What does the retailer pay for the scooty? |
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| 33. |
If cos (40% xo ).ur sin-30°itherA) 2024.B) 40C) 60° |
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| 34. |
8. A sum of money doubles itself at compoundinterest in 15 years. In how many years it willbecome eight times ? |
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Answer» If the sum doubles (x2) in 15 years. Then it to become 2*2*2 = 8 times as large it should double three times. so three 15 years time period are needed, which is 3*15 = 45 years. So the answer is 45 |
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| 35. |
At what rate percent will a principal amount of Rs.1000becomes Rs.1102.50 in 2 years at compound interest? |
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| 36. |
IF8809 6 , 7111: 02172 0 ,6666-40000 4,33330THEN,2581 ? |
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| 37. |
III6666666666666I + 66666I + 6666| + 666| + 66"+ 6 |
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Answer» 10100100010000100000100000010000000sab ke sab live wise answer hai isliye Ab Mujhe like karo, jawab mat khao a b c d e f g h s s i number likhe Hain |
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| 38. |
\left. \begin array l = 1 %2B 6666 \\ = \quad 1 %2B 666 \end array \right. |
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Answer» a. 10000b. 100000Yeh Hai Nabi Ka answer Ab Mujhe like karo please |
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| 39. |
1 1 the mapping fand g are given byf ((1,2)(3,5),(4, 1) andg (2, 3).(5, 1).(1.3))then write fog |
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| 40. |
he sum of two numbers is 80 and the greater number exceeds twiceFind the numbers. |
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Answer» Let smaller number be nThen greater number = 2n + 11 Given,n + 2n + 11 = 803n = 80 - 11 = 693n = 69n = 69/3 = 23 Smaller number = 23Greater number = 2*x + 11 = 2*23 + 11 = 46 +11 = 57 thankyou |
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| 41. |
12 The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers |
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Answer» plants whose stem we eat plants whose stem we eat Let the numbers be x and y where x>y so, x^2 - y^2 = 120.....(1) y^2 = 2 x.....(2) Putting (2) in (1), we get x^2 - 2x = 120 x^2 - 2x - 120 = 0 x^2 - 12x + 10x - 120 = 0 x(x -12) +10(x - 12) = 0 (x-12)(x+10) = 0 So x can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative, Thus x cant take value of -10 So x = 12, so y^2 = 2 (12) y^2 = 24 So y = √24 or - √24 y = 2√6 or -2√6 Hence the numbers are 12 and 2√6 or 12 and -2√6 |
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| 42. |
The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers.i) |
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Answer» Let the numbers be x and y where x>y so, x^2 - y^2 = 120.....(1) y^2 = 2 x.....(2) Putting (2) in (1), we get x^2 - 2x = 120 x^2 - 2x - 120 = 0 x^2 - 12x + 10x - 120 = 0 x(x -12) +10(x - 12) = 0 (x-12)(x+10) = 0 So x can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative, Thus x cant take value of -10 So x = 12, so y^2 = 2 (12) y^2 = 24 So y = √24 or - √24 y = 2√6 or -2√6 Hence the numbers are 12 and 2√6 or 12 and -2√6 |
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| 43. |
EXERCISE 1.1. Is gero a ational number? Can you write i in he fowhere p andg are integersis zero a rational number? Can you write it in the formand q #0? |
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| 44. |
-an.cach and three shirts marked atretailer wants toget aprofitof10% aftergiving a discount of 12.5 %on an article. What shbe the marked price of the article whose cost price is 1470?d8HOTS |
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| 45. |
tan A tan B+ tan A cot B7. For A B 90, prove that vsin A sec Bs= sec A.OR7. Prove the resultseco-tanosec θ + tan θ1-2sec θ , tan θ + 2 tan2 θ |
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| 46. |
2. For what value of p, x - b is a zero of the polynomial -(a+ bs ap-e |
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| 47. |
interest lof', Jul(3) Rs 1736 (4) Rs 1680(1) Rs 1765 (2) Rs 17473. A sum of money on compound interest becomes 8 times in 3 years. Findthe rate of interest(3) 40% (4) 60%(180%(2) 100%amounts to Bs 3840 in 2 years and |
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Answer» The answer to your question is 40% |
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| 48. |
4. of 50 is equal to45a) 30b) 40c) 50 |
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Answer» (4/5) of 50 is (4/5) x 50 =40 thx |
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| 49. |
1500 is divided between A, B and C in the ratio 1: 3:5. Bs share isl750 |
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Answer» Let the ratio be x so, A, B, C will get x, 3x, 5x parts According to questionx + 3x + 5x = 1500 9x = 1500 x = 1500/9 = 500/3 So, B will get 3x = 3 × 500/3 = ₹ 500 |
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| 50. |
5. 50% of 3 kg = |
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