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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. |
The Supplement of 105° is ............... |
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Answer» the supplement of 105° is 75° thanks 180-105=75 is the answer can you please try my sum given |
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| 2. |
The supplement of 35° is |
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Answer» Ans :- Subtract 35 from 180 = 180 - 35 = 145 |
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| 3. |
Hint: Let the measure of the requifed angic oThe supplement of an angle is one-third of itself. Determine the angle and its supplement. |
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Answer» x = 135 |
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| 4. |
THE somoE the digits ap2original oumtea Fad thenunbez |
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| 5. |
\overline{c}=\frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \dot{j}-\frac{1}{\sqrt{3}} \hat{k} |
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| 6. |
\begin{array} { l } { \text { Prove that } | \overline { a } \times \hat { i } | ^ { 2 } + | \overline { a } \times \hat { j } | ^ { 2 } + \left| \frac { 1 } { a } \times \hat { k } \right| ^ { 2 } = 2 | \overline { a } | ^ { 2 } } \\ { \text { Prove that } \overline { a } \times ( \overline { b } + \overline { c } ) + \overline { h } \times ( \overline { c } + \overline { a } ) + \overline { c } \times ( \overline { a } + \overline { b } ) = 0 } \end{array} |
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| 7. |
38.Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 1 6 is divisible by5, where n is any positive integer, |
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| 8. |
38. Show that one and only one out of n,+4,n+8, n+12 and n+ 16 is divisible by5, where n is any positive integer, |
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Answer» Let n be any positive integer and b = 3n = 3q+rwhere q is the quotient and r is the remainder0<r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1, 3q+2 CASE-1If n=3qn+4=3q+4n+2=3q+2here n is only divisible by 3 CASE 2If n=3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3 CASE 3If n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3 Hence it is justified that one and only one among n, n+2, n+4 is divisible by 3 in each case. |
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| 9. |
66 \frac { ( 7.1 ) ^ { 3 } + .001 } { ( 7.1 ) ^ { 2 } - 7.1 \times 1 \times ( .1 ) ^ { 2 } } \overline { c h } |
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| 10. |
2 \log _ { 3 } 5 - _ { 5 } \log _ { 3 } 2 |
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| 11. |
Prove that us Ps irrational |
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| 12. |
13. Mr. Khanna spent 83% of his salary and saved1870. Calculate his mon |
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| 13. |
in the given fure, prove atPO-RSPS-OR |
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Answer» as we know that parralelogram has both lengths same and breadth are also same so they are equal i am not sure about answer |
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| 14. |
INCERTI2.Find five rational numbers between 1 and 2.INCERTI |
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| 15. |
(-1 %2B sqrt(3))/(1 %2B sqrt(3)) %2B (1 %2B sqrt(3))/(-1 %2B sqrt(3))=a %2B sqrt(3)*b |
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Answer» +1√3−1+√3−1√3+1=a+√3b Solving for a. Want tosolve for binstead? 1 Simplify3-13−1to22. \frac{\sqrt{2}}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}=a+\sqrt{3}b√3+1√2+√3−1√3+1=a+√3b 2 Subtract\sqrt{3}b√3bfrom both sides. \frac{\sqrt{2}}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}-\sqrt{3}b=a√3+1√2+√3−1√3+1−√3b=a 3 Switch sides. a=\frac{\sqrt{2}}{\sqrt{3}+1}+\frac{\sqrt{3}+1}{\sqrt{3}-1}-\sqrt{3}ba=√3+1√2+√3−1√3+1−√3b Done  |
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| 16. |
1/(-sqrt(5) %2B 2) %2B 1/(sqrt(3) %2B 2) %2B 2/(-sqrt(3) %2B sqrt(5)) |
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| 17. |
Cef |
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| 18. |
Prove h cef |
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Answer» Given cosec theta - sin theta = m, sec theta - cos theta = nGiven that cosec theta - sin theta = m→ !/sin theta - sin theta = m⇒(1-sin² theta)/sin theta = m→ cos² theta/sin theta = mand sec theta - cos theta = n⇒1/costheta - cos theta =n→ (1-cos² theta)/cos theta = nsin² theta/cos theta = nNow (m²n)²/³ + (mn²)²/³⇒(cos⁴ theta/sin² theta × sin² theta/cos theta)²/³ + (cos² theta/sin theta× sin⁴ theta/cos² theta)²/³⇒ (cos³ theta)²/³ + (sin³ theta)²/³⇒cos² theta + sin² theta= 1 Hence proved |
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| 19. |
10 \text { th term of the AP } 2,7,12 |
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| 20. |
刎Prove the quotient rule using-= a |
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Answer» a^m/a^n = a^m × 1/a^n = a^m × a^-n = a^(m-n) |
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| 21. |
T N N l\fl8$in 40° — cos 70° = /3 .cos80° |
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Answer» LHS =sin40-cos70 =sin40-cos(90-20) =sin40-sin20 now use formulasinA-sinB=2cos(A+B)/2.sin(A-B)/2 hence.sin40-sin20=2cos30.sin10 =2 x √3/2 x cos80 =√3cos80° =RHS Like my answer if you find it useful! |
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| 22. |
Howmany terms of an A.P 9, 17,25,... must be taken to give a sum of 636?38. In the given figure, ABAC. E is a point on CB produced. If AD is perpendicular to BC and EFperpendicular to AC. Prove that "ABD is similar to ÎCEF. |
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Answer» In ΔABD and ΔCEFAB = AC (Given) ∠ABC = ∠ACB (Equal sides have equal opposite angles) ⇒ ∠ABD = ∠ECF∠ADB = ∠EFC (Each 90°)So, ΔABD ~ ΔECF (AA - Similarity) |
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| 23. |
\left. \begin{array} { l } { \text { If } 11 m - 8 n = 6 m + 5 n , \text { find the value of } \frac { 2 m + 5 n } { 2 m - 5 n } } \\ { \text { ution: } } \end{array} \right. |
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Answer» 11m-6m = 8n+5n 5m = 13n 2m = 26n/5 2m+5n/2m-5n =( 26n/5 + 5n)/( 26n/5 - 5n) = 26n+25n/26n-25n = 51n/n = 51 |
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| 24. |
-3/(sqrt(2) %2B sqrt(5)) %2B 1/(sqrt(2) %2B sqrt(3)) %2B 2/(sqrt(3) %2B sqrt(5)) |
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Answer» 0 is answer of this question |
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| 25. |
\frac { 1 } { 1 + \operatorname { log } _ { b } a + \operatorname { log } _ { b } c } + \frac { 1 } { 1 + \operatorname { log } _ { c } a + \operatorname { log } _ { c } b } + \frac { 1 } { 1 + \operatorname { log } _ { a } b + \operatorname { log } _ { a } c } |
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Answer» using the identity loga to the base b = loga/logb we get = 1/(1+loga/logb +logc/logb) + 1/(1+loga/logc+logb/logc) +1/(1+logb/loga +logc/loga) = logb/(loga+logb+logc) + logc/(loga+logb+logc) +loga/(loga+logb+logc) = (loga+logb+logc)/(loga+logb+logc) = 1. |
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| 26. |
Solve: log(x+1) + log(x-1) = log 1 1 + 2 log 3 |
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| 27. |
2. The ratio of the sums of n terms of two A.P.s is (in +1) : (4their 5th terms.+ 27). Find the ratio of |
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Answer» 5:1 is right answer of this question. |
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| 28. |
2. If twice the son's age in years is added to the father's age, the sum is 70.But if twice the father's age is added toThe sum is 95.Find the ages of father and son. |
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| 29. |
18. 5th 8th and 11th terms of a G.P. are p, q and srespectively, Prove tINCERTIps INCERTI |
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| 30. |
11/The sum of first 10 terms of an arithmetic sequence is 305. Its 10th term is 53.a) What is the sum of its 5th and 6th terms?b) What is its first term?c) Write the sequence. |
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| 31. |
AT Find the supplement angle of 42Âş. |
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Answer» angle= 180 —42 = 138 |
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| 32. |
i) The sum of 5th and 7th terms of an A.P. is 4 and the 10 th term is 46. Find theA.P |
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| 33. |
find the difference between the number 738 and that obtained on reversing it s digits |
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| 34. |
LIL VOL.74 On dividing 55390 by 299, the remainder is 75. Find the quotient using the divisionalgorithm. |
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| 35. |
teakencPclcefclAuse |
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| 36. |
S 0ÂŤ2XGT WIS o .XC Uls() |
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| 37. |
A skirt costs 7650. If it is sold at a profit of7200, find the selling price.2) |
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| 38. |
Finc/ the simple interest on Rs.7200 at 5% p.a. for 8 l n onths. Also find the amount. |
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| 39. |
ne:Page:and brodect. C-33X C-62 XC-2) XC-1AI find prodest |
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Answer» 36 is the correct answer of the given question (-3) ×(-6) × (-2) ×(-1) = 36 is correct answer 36 is the right answer 36 is the right answer |
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| 40. |
> 1(1-â)dr7. |स (1-2 |
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Answer» hit like if you find it useful |
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| 41. |
Factorize:1. 64a3 + 125W + 240a2b + 300ap? |
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Answer» PLEASE LIKE THE SOLUTION |
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| 42. |
10, 7, 4 का 30वाँ पद निकालें ।व o e PR, A DR |
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Answer» a = 10 , d=-3 a30=a+29d =10-87 =-77 |
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| 43. |
32-2x+7)dr का मान ज्ञातपान 14324124te का मान जातकीजिए।(2017) |
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Answer» 6.772727272727728373727737372737737373733u3u3 |
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| 44. |
If Dr = 5, D = 7 and D = -95 find the value |
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| 45. |
UL. The difference of two numbers is 5 and the difference of theirreciprocal is - Find the numbers. (Ans. 5, 10 or -10,-5) |
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| 46. |
For the following A.P, write the first term and the common difference ,53'3'3' 3 |
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Answer» Lets the first term be a and common difference be da=1/3 d= 5/3-1/3 =4/3 |
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| 47. |
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of termsand the common difference.5. |
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Answer» Given for an APFirst term a = 5, Last term an = 45, Sum = 400 Let common difference is d and number of terms is n Sum of n terms400 = n/2(a + l)400 = n/2(5 + 45)n = 800/50 = 16 an = a + (n-1)d45 = 5 + 15dd = 40/15 = 8/3 |
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| 48. |
The difference of two numbers is 5 and difference of their reciprocals isFind the numbers.10 |
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| 49. |
The difference of two numbers is 5 and the difference of their reciprocals is. Find the numbers. |
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| 50. |
The difference of two numbers is 5 and difference of their reciprocal is 1/10. Find the numbers |
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