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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. |
(1) Write each of the following in logarithmic form(a) 2^3 = 8 |
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| 2. |
ntiationLogarithmic Differentiation :31. If y=2?", thendr |
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Answer» ..................... hope it helps youwith answer |
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| 3. |
1.Express the following numbers in standard form.1) 0.0000000000085 |
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| 4. |
Devesh gave Manavt 1,250 on compound interest for 2 yearsless would Devesh have got had he given the money to Manav for 2 years on simple interest at the rateof 4% per annum?2at the rate of 12% per annum. How much |
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Answer» Given,For compound interestP=1250, R = 12%, n = 2 A1 = P(1 + R/100)^nA1 = 1250(1 + 12/100)^2A1 = 1250(29/25)^2A1 = 1250(1.3456)A1 = 1682 For simple interestP = 1250, R = 4%, T = 2 SI = P*R*T/100SI = 1250*4*2/100SI = 100 A2 = P + SI = 1250 + 100A2 = 1350 Therefore, Devesh would get (1682 - 1350) = Rs 332 less |
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| 5. |
\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} \frac{a}{b}\right)+\tan \left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} \frac{a}{b}\right)=\frac{2 b}{a} |
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| 6. |
\cos ^{-1} \frac{x}{a}+\cos ^{-1} \frac{1}{b}=\alpha\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{2 x y}{a b} |
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| 7. |
Simplily Express -16 in exponential811m |
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Answer» 16 = 4^281 = 9^2-16/81 = -4^2/9^2 (-2/3)^4 is the correct answer of the given question. |
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| 8. |
CAMPLE 4.Simplify and express the result in exponential form:(1) |
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Answer» (1) (3/4)^7 * (3/4)^5 = (3/4)^[7 + 5] = (3/4)^12 (2) (-2/5)^11 * (-2/5)^4 = (-2/5)^[11 + 4] = (-2/5)^15 |
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| 9. |
6-3-24|8-64-48|7-4-? |
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Answer» -19663 is the correct answer If 6 becomes 3 (6 divided by 2), then 3 becomes 24 (6 x 4 = 24).8 becomes 64 (8 x 8 = 64) then 64 becomes 48 (6 x 8 = 48)7 becomes 4 (7 - 3 = 4) then 4 becomes (6 x 12 = 72) |
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| 10. |
( 1 + \frac { 1 } { 2 ^ { 2 } } ) + ( \frac { 1 } { 2 } + \frac { 1 } { 2 ^ { 4 } } ) + ( \frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 2 ^ { 6 } } ) + \ldots . . \text { upto } \infty |
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| 11. |
6. Write the following in the logarithmic form1.82 = 64 2.323/5-8 |
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Answer» 8*8 = 64 2log8 = log64 32^(3/5) = 8 (3*log32)/5 = log8 If you find this answer helpful then like it. |
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| 12. |
1/2+1/2+1/2*1/2-1/2 |
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Answer» 1/2 + 1/2+ (1/2×1/2)- 1/2=0.5+0.5+(0.5×0.5)-0.5=1+0.25-0.5=1.25-0.5=0.75 is the answer |
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| 13. |
Q.11The parametric coordinates of a point on thecircle x2 + y2 - 2x + 2y - 2 = 0 are -(A) (1 - 2 cos a, 1-2 sin a)(B) (1+2 cos , 1 + 2 sin a)(C)(1+ 2 cos ,- 1 + 2 sina)(D) (-1 + 2 cos a., 1 + 2 sina)12The equation(x2 + y2) - X -Y+= |
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| 14. |
15: In how many ways can 4 boys and 5 girls be seated in a row so thatthey are alternate? |
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Answer» they need to alternateso BGBG.... or GBGB..so ways=2(5×4×4×3×3×2×2×1×1)=5760 |
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| 15. |
Express in exponential\frac{7}{9} \times \frac{7}{9} \times \frac{1}{8} \times \frac{1}{8} \times \frac{1}{8} |
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Answer» (7/5) power 5 as 7 is 5 times ans 8 is also 5 times |
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| 16. |
LuIt t8 factorise.Solved ExamplesPLE 1. Solve 4x2 -3x-1ution: Here, we have4x2-3x-1=0r2 32 3 13 (32 1 (34 8 4 823-30 1.032 1 9 25 (58 4 64 64 88orHence, the solution set of the given equation is |
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| 17. |
A certain number is 4 times the sum of thedigits.If 18 is added to the number, the digitget interchanged. Then the number is(A) 42(C) 36(B) 24(D) of these |
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Answer» suppose number is 10x+yso 10x+y=4x+4y6x=3yso y=2x10x+y+18=10y+x10x+2x+18=20x+xso x=2 and y=4so number is 20+4=24 |
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| 18. |
write herons formula |
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Answer» Area of a Triangle with sides a, b, c using Heron’s Formula is- A= √s (s-a) (s-b) (s-c) where,Semi-perimeter of a triangle (s) = (a+b+c)/2 |
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| 19. |
explain the term herons formula |
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Answer» Heron's formulais named after Hero of Alexendria, a Greek Engineer and Mathematician in 10 - 70 AD. You can use thisformulato find the area of a triangle using the 3 side lengths Heron's formula is named after Hero of Alexendria, a Greek Engineer and Mathematician in 10 - 70 AD. You can use this formula to find the area of a triangle using the 3 side lengths. |
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| 20. |
5. In a classroom, 4 friends areseated at the points A, B, C andD as shown in Fig. 7.8.Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,"Don't you think ABCD is asquare?" Chameli disagrees.Using distance formula, find |
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| 21. |
5. In a classroom, 4 friends arseated at the points A, B, C andD as shown in Fig. 7.8. Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,"Don't you think ABCD is a Rosquare?" Chameli disagrees.Using distance formula, find |
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| 22. |
4.In a classroom, 4 friendseated at the points A, B, CaD as shown in Fig. 7.8. Champaand Chameli walk into the classand after observing for a feminutes Champa asks Chameli"Don't you think ABCD is asquareUsing distance formula, findwhich of them is correct.?" Chameli disagrees |
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Answer» thank u |
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| 23. |
5. In a classroom, 4 friends areseated at the points A, B, C andD as shown in Fig. 7.8. Champaand Chameli walk into the classand after observing for a fewminutes Champa asks Chameli,Don't you think ABCD is asquare?" Chameli disagrees.Using distance formula, findwhich of them is correct. |
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| 24. |
How much is 10 times 5 less than 6 times 9? |
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Answer» This will be solved in reverse order. 6 times 9 = 6 * 9 = 545 less that the above number = 54 - 5 = 4910 times above number = 49 * 10 = 490 Therefore, answer is490 |
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| 25. |
5) Give the full form of ATM. |
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Answer» ATM is Automatic Teller Machine |
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| 26. |
33. Mansils / yculumuch is 10 times 5 less than 6 times 9?LO |
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Answer» As per given condition 10*5 - (6*9) = 50 - 54 = - 4 Given (10 *5) -(6*9) =50-54= -4 |
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| 27. |
If 10 be is added to 4 timesca certain number, the result is 5 less than 5 times the number . Find the number. |
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| 28. |
Arectangular box has height h cm. Its lengths 5 times the height and breadth is 10 cm lessthan the length. Express the length and thebreadth of the box in terms of the height. |
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| 29. |
years) would have been I more dll( -5) = 5xtil.INCERI EXLIIPresent Asha's age (in years) is 2 more than the square of her daughter Nisha's age.When Nisha grows to her mother's present age, Asha's age would be one year less than10 times the present age of Nisha. Find the present ages of both Asha and Nisha.[NCERT EXEMPLAR]TA |
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Answer» ( x +5)^2= x^2 + 25 + 2 (x) (5) |
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| 30. |
At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age.When Nisha grows to her mother's present age. Asha's age would be one year less than10 times the present age of Nisha, Find the present ages of both Asha and Nisha. |
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Answer» Let Nisha's age is x years Aisha's age = (x² + 2) years Now, A/C to question , when Nisha grows to her mother present age .means Nisha's growth = Aisha's present age - Nisha's present age = x² + 2 - x Then, this time Aisha's age = Aisha's present age + growing time = x² + 2 + x² + 2 - x = 2x² - x + 4 Now, question said , Aisha's age = 10× times of Nisha's age -1 2x² - x + 4 = 10x -1 2x² - 11x + 5 = 0 2x² -10x - x + 5 = 0x = 5 and 1/2 x ≠ 1/2 because age doesn't in moths Hence , Nisha's present age = 5 years Aisha's present age = (5)² + 2 = 27 years |
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| 31. |
Q.1. If the interest on 1700 rupees is 340 rupees for 2 yearsthe rate ofinterest must be |
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Answer» Interest = Principle × Rate of Interest × Time/100 340 = 1700×2×Rate of Interest / 100 10% = Rate of Interest If you find this answer helpful then like it. |
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| 32. |
Practice Set 41If the interest on 1700 rupees is 340 rupees for 2 years the rate of interest must b(i) 12%(ii) 15 %(iii) 4 %(iv) 10%nt a certain rate for a certain numbe |
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Answer» Si = PTR/200 R = 340*100/1700*2 R = 10% Like my answer if you find it useful! |
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| 33. |
5. Give full form of MGNREGA? 1m |
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Answer» National Rural Employment Guarantee Act 2005 (or,NREGANo 42, later renamed as the "Mahatma Gandhi National Rural Employment Guarantee Act",MGNREGA), is an Indian labour law and social security measure that aims to guarantee the 'right to work'. mahatma Gandhi national rural employment guarantee act |
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| 34. |
ats the angles of aGiven below are the triads. Which of the following triads represents the anal100°, 30°, 40° (ii) 30°, 590, 91° (iii) 45°, 45°, 90° |
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Answer» from Triangle law sum of all angles must be equal to 180 and this is found in the third option |
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| 35. |
In Figure L,OA4 0B ore sppesise rayserr15 Vof Y |
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Answer» 180- 42 = 12y y = 11.5 but answer is 69 21°value of y= 21°. no 69 |
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| 36. |
Ashow5+3that sum and product of two locatimal numbersand 5-13 ore rational numberu.13) (5 ) |
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Answer» 1)(5+√3)(5 - √3)=(5²-√3²).....(a+b)(a-b)=(a²-b²)(25-3)=222) (5+√3)+(5 - √3)= 25 |
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| 37. |
७54 4 सके रू बटन e2 श्रऔर& के किन मानों के लिए, निम्न रैखिक समीकरणों जेg ol के अंपर्रिमित्त रूपe I के" अपरिभित रूप से2x+3y=7(a-byx+(+b)y=3a+b-2 |
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Answer» यदि सॉल्व करने पर दो equation प्राप्त हुईa-9b=-4तथा2a-4b=6 तथा a =5 Itna nahi hoga okk app Aur samjhai aga ka thik ha ajya to batiya Soory right answer |
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| 38. |
An equilateral triangular park with each side 12m needs to be exactly covered bya tarpaulin cover. Which of the following covers will exactly cover the park?o. |
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Answer» Side of equilateral triangle = 12 m Area of equilateral triangle =√3/4(side)²=√3/4(12)m²=√3/4(12×12)=√3/4×144m²=62.35m² ans. |
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| 39. |
The sides of a triangular park are 25 m, 18 m, and 17 m. Find the total distance travelled by a man aftercompleting three rounds of the park |
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Answer» total length covered is : 3x perimeterperimeter is= 25+18+17=60cmtotal length= 3x60= 180cm |
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| 40. |
Find the semi-perimeter of a triangular park whose sides are 40 m, 24 m and 32 m. |
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Answer» Perimeter of triangle = sum of length of three sides of triangle Then,Perimeter of triangle = 40 + 24 + 32= 96 m Semi Perimeter = 96/2 = 48 m |
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| 41. |
23, At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. WhenNisha grows to her mother's present age, Asha's age would be one year less than 10 timesthe present age of Nisha. Find the present ages of both Asha and Nisha. |
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Answer» Let the age of Nisha be x. Then Age of Asha = y = 2+ x^2.Difference between age of Asha and Nisha = x^2 - x + 2 = y -x .When Nisha grows to Asha's present age, Nisha's age = x^2 + 2. 2*x^2 -x + 4 = 10x - 1=> 2x^2 - 11x + 5 = 0=> 2x^2 - 10x - x + 5 = 0=> 2x( x - 5) - 1(x -5) = 0=> (x - 5)(2x - 1) = 0=> x = 5. Nisha's age = 5 years. Asha's age = 27 years. PLEASE HIT THE LIKE BUTTON |
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| 42. |
2. At present Asha's age (in years) is 2 more than thesquare of her daughter Nisha's age. When Nishagrows to her mother's present age, Asha's age wouldbe one year less than 10 times the present age ofNisha. Find the present ages of both Asha and Nisha.INCERT Exemplar |
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| 43. |
13, Deepak is twice as old as his Ьґ0ther Vikas. If the difference of their ages be 11 years,their present ages.nnhos iuhtos Rolsho After 8 ers she will he twice as old a |
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| 44. |
9. At present Asha's age (in years) is 2 more than the square of her daughter Nisha's ageWhen Nisha grows to her mother's present age, Asha's age would be one year less than10 times the present age of Nisha. Find the present ages of both Asha and Nisha.[NCERT EXEMPLARÄ° |
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Answer» let Asha age=A and Nisha age= N A=2 + N2.......(1) present difference in age A-N years , so nisha will be of his mom's age after A-N years After A-N years his mother's age = A+A-N = 2A-N Now fron question 2A-N = 10N -1 2A=11N-1 Put value of A from equation 1 4+2N2= 11N-1 2N2-11N+5=0 (2N-1)(N-5)=0 N=5, A=2+25=27 |
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| 45. |
At present Asha's age (in years) is 2 morethan the square of her daughter Nisha'sage. When Nisha grows to her mother'spresent age, Asha's age would be one yearless than 10 times the present age of Nisha.Find the present ages of both Asha andNisha. INCERT Exemplar Problem) |
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| 46. |
At present Asha's age (in years) is 2 mthan the square of her daughter Nisha'sore 3L.31-When Nisha grows to her mother'sagepresent age, Asha's age would be oneear less than 10 times the present ageof Nisha. Find the present ages of bothAsha and Nisha. |
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Answer» let Asha age=A and Nisha age= N A=2 + N2.......(1) present difference in age A-N years , so nisha will be of his mom's age after A-N years After A-N years his mother's age = A+A-N = 2A-N Now fron question 2A-N = 10N -1 2A=11N-1 Put value of A from equation 1 4+2N2= 11N-1 2N2-11N+5=0 (2N-1)(N-5)=0 N=5, A=2+25=27 |
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| 47. |
(iv) 00560 31% -_ 86рео 59реж |
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Answer» cosec 31 - sec 59 cosec (90 - 59) - sec (59) sec(59) - sec (59) 0 |
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| 48. |
byILLUSTRATION 4 Divide the polynomial f(x) = 30x4 +11x°- 82x2 - 12x + 483x2 + 2x - 4. Also find the quotient and remainder. |
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| 49. |
places48 Divide the polynomail 3x42xStés2) by long division methodand remainder Verify the nemainder obtained byand write quotientremainder theoremke |
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| 50. |
At present Asha's age (inOper month, find their montnlg hh2 moreWhen Nisha grows to her mother'sears) is 2 more than the square of her daughter Nisha's age.O times the present age of Nisha. Find the present ages os present age. Asha's age would be one year less thanboth Asha and Nisha. |
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Answer» Let Nisha's age is x years Aisha's age = (x² + 2) years Now, A/C to question , when Nisha grows to her mother present age .means Nisha's grows = Aisha's present age - Nisha's present age = x² + 2 - x Then, this time Aisha's age = Aisha's present age + growing time = x² + 2 + x² + 2 - x = 2x² - x + 4 Now, question said , Aisha's age = 10× times of Nisha's age -1 2x² - x + 4 = 10x -1 2x² - 11x + 5 = 0 2x² -10x - x + 5 = 0x = 5 and 1/2 x ≠ 1/2 because age doesn't in moths Hence , Nisha's present age = 5 years Aisha's present age = (5)² + 2 = 27 years |
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