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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. |
Find the area of a parallelogram with base 32 cm and height 16.5 cm. |
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| 2. |
18. The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. Find its area. |
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Answer» thank you for your time and consideration and I will be in the future of our games are based on the question of whether you are not the intended recipient you are not the intended recipient you are not the intended recipient |
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| 3. |
JEUsing determinant, find the area of thetriangle whose vertices are (-3, 5), (3, – 6)and (7, 2). |
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| 4. |
of the triangle.18. The base of an isosceles triangle is 12 cm, and its perimeter is 32 cm. Find its area. |
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| 5. |
Using appropriate properties find2 3 5 3 1 |
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| 6. |
Workshe1. Using appropriate properties find :3 3 3 52 5 4 |
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Answer» = - 3/10 + 3/2 - 3/4= (-6+30-15)/20= 9/20=4.5/10= 0.45 |
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| 7. |
DatePagefor ab bShaw |
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Answer» your writing is not clealry visible. |
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| 8. |
noure some triangles have been gveDATE:3(a+b) + 4 ( 2a - 3b ) - ( 2a - b) |
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| 9. |
1Date:Page No.:20 cota: 3 and cot B=5 then proneQ+B= 451 |
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Answer» happy environment day |
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| 10. |
3. The solution set of | x-| | + | x + 5 |= 6 is :IS: |
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| 11. |
23. The price of2 tables and 3 chairs is 340, but a table costs20 more than the chairFind the cost of each. |
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| 12. |
है। यदि। उदाहरणः-16. एक त्रिभुज ABC में ZA , B 37° और C =359:" - 30° हो तब सिद्ध कीजिए कि यह एक समकोण त्रिभुज है। |
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| 13. |
1PZ0 m of cloth costs 180, how much would 75 m cost? |
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Answer» If 20m cost 180then 1 m will cost =180/20=9rupeesHence for 75 m of cloth it will be 75*9=675rupees. |
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| 14. |
Example 1 In a triangle ABC, it is given that <B = 105° and <C-50ăFind ZA. |
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Answer» Given: B=105 degreeC=50 degreeFormula used: Sum of angles of triangle = 180 degreeSolutionA+B+C= 180 degreeA+105 degree+50 degree=180 degreeA=180 degree-105 degree-50 degreeA=25 degree |
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| 15. |
IF2D m of cloth costs 180, how much would 75 m cost |
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Answer» 20 m cloth costs= 180 ruppes1 m will cost= 180/20= 9then 75 m will cost= 75*9= 675 ruppesplease like the solution 👍 ✔️ |
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| 16. |
10 km on foot. Find the length of his total journey.. A table costs 200 more than a chair. The price of two tables and three chairs is 1400.Find the cost of each.nrs nnn. Anu was three times Sunil's age. |
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| 17. |
.Flnd the area of a parallelogram with base 32 cm and height 16.5 cm. |
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| 18. |
is 3.5 cm." Flnd the altitude of a parallelogram inhose area is 82.28the hese s 128m |
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Answer» If you like the solution, Please give it a 👍 |
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| 19. |
sing appropriate properties f2 35 3 1 |
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| 20. |
hhtk_’9 1§ Pk 1€ |
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Answer» Let√n−1+√n+1be a rational number which can be expressed as p/q, p and q are integers and coprime. q is not equal to 0squaring on both sides we get n-1+n+1+2√n2−12n+2√n2−1=p2q2 2(n+√n2−1)=p2q2 2(n+√n2−1)q2=p2 this mean 2 dividesp2and also divides p.then let p=2k for any integer k then 2(n+√n2−1)=(2k)2q2 2(n+√n2−1)=4k2q2 q2=2k2/(n+√n2−1) so 2 dividesq2and also q p and q have common factors 2 which contradicts the fact that p and q are co-primes which is due to our wrong assumption. so√n−1+√n+1is irrational. |
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| 21. |
( 37 ^ { 2 } - 35 ^ { 2 } ) ^ { 3 / 2 } |
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| 22. |
Page NoDateDeterminant2232 35 |
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Answer» please like my answer if you find it useful |
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| 23. |
जे Pk A0 ले?f = OPE +8 —o i |
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| 24. |
प्रश्नावला 12.3AT 5= — का प्रयोग कौीजिए।) 4 में, छायांकित भाग का क्षेत्रफल ज्ञातf PQ =24 cm, PK था एज |
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| 25. |
Do ana,. b 2 o JWW‘A_Q_A_ eResemn L Pk old I e हैके stl) Maoea ke |
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| 26. |
6. In the adjoining igure. it is given that CE BA. BAC-0and (ECD = 35°.Flnd (I)LACE. ()LACB. )LABC |
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| 27. |
. Flnd the angles in each of the following(a) The angles are complery and the smaller is 40° less than the larger |
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Answer» complementary angles add up to 90°so if the smaller is x, then the other angle is 90-xAccording to questionx = 90-x - 402x = 50x = 25so smaller is 25° and the larger is 90-25 = 64° |
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| 28. |
Let: RRbe defined by f(x) = 3x - 4. Then f(x) is given by |
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Answer» if u satisfied.give me a like |
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| 29. |
Let R be a relation on N defined by R-((a, b):a is a factor of b). Then show that R isreflexive and transitive but not symmetric |
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| 30. |
an its Sppiementalry aingle tnenABC ZA B: C 6:8: 10 then flnd all angles and which type thattriangle is? |
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Answer» suppose A=6k B=8k C=10kA+B+C=1806k+8k+10k=18024k=180so k=7.5A=6k=6×7.5=45B=8k=8×7.5=60C=10k=10×7.5=75 |
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| 31. |
25. The total cost of 3 tables and 2 chairs is 1850. If a table costs 75 more than a chair, flndthe price of each. |
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| 32. |
\tan ^ - 1 ( \sqrt \frac 1 - \cos x 1 %2B \cos x ) , 0 < x < \pi |
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Answer» Like if you find it useful |
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| 33. |
\frac { 2 \operatorname { cos } x - 3 \operatorname { sin } x } { 6 \operatorname { cos } x + 4 \operatorname { sin } x } |
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Answer» thank u |
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| 34. |
\lim _{x \rightarrow 0} \frac{1-\cos 4 x}{1-\cos 6 x} |
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| 35. |
\int \frac { 2 \operatorname { cos } x - 3 \operatorname { sin } x } { 6 \operatorname { cos } x + 4 \operatorname { sin } x } |
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Answer» thanku thanku |
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| 36. |
(ii)[ę¸],[1.5-4-(5)3y-1(iv)IV |
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Answer» (iv) (iii) (ii) |
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| 37. |
\operatorname { cos } ^ { 2 } 2 x - \operatorname { cos } ^ { 2 } 6 x = \operatorname { sin } 4 x \operatorname { sin } 8 x |
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| 38. |
The highest value of sin θ + cos θ will be : |
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| 39. |
n9cosnB+Prove by using principle of mathematical induction that (cos θ+1 sini sin no, where i-1 and n E N |
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Answer» De Moivre's theorem states that(cosø + isinø)n= cos(nø) + isin(nø). Assumingn = 1 (cosø + isinø)1= cos(1ø) + isin(1ø)which is true so correct forn = 1 Assumen = k is true so(cosø + isinø)k= cos(kø) + isin(kø). Lettingn = k + 1we know that(cosø + isinø)k+1= cos((k + 1)ø) + isin((k + 1)ø). But trying to derive the answer fromn = kwe get: (cosø + isinø)k+1= (cosø + isinø)kx (cosø + isinø) //Using law of indecies = (cos(kø) + isin(kø)) x (cosø + isinø) //We've assumed this to be true from n = k = cos(kø)cos(ø) + icos(kø)sin(ø) + isin(kø)cos(ø) - sin(kø)sin(ø)//ExpansionNow using the trigenomitery rules ofsin(a + b) = sin(a)cos(b) + sin(b)cos(a)andcos(a + b) = cos(a)cos(b) - sin(a)sin(b)and collectingterms to match these formulas we get =cos(kø + ø) + isin(kø + ø) = cos((k + 1)ø) + isin((k + 1)ø) //Taking out ø as a common factor inside the trig functions Which equals our expression gained from De Moivre's theorem for n = k + 1,and as theorem is true for n = 1 and n = k + 1,statement is true for all values of n >= 1. |
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| 40. |
A. Differentiate following1. x³ +4x2 +5x +7 |
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| 41. |
age wl be WU TIlQ.15 If an AP consists of n terms with first term a and nh term i. Show that the sum of the mterm form the beginning and mth term from the end is (a +),in ordet are ( A(35 3.-2) and |
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Answer» First term of A.P is anth term =lLet d be the common differencenth term=a+(n-1)dl=a+(n-1)dd=l-a/n-1 ------------1 Mth term from the beginning=a+(m-1)d=a+(m-1)(l-a/n-1 ) ----------------2 Mth term from the end we get:where we consider first term as l and the common difference=-d=l+(m-1)(-d)=l+(m-1)x(-(l-a)/n-1)=I-(m-1)(l-a)/n-1 --------------3 thus sum of mth term from beginning to end is=a+(m-1)(l-a/n-1 ) +I-(m-1)(l-a)/n-1=a+lHence proved |
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| 42. |
7. Let R = , b): 4, be Z and (a + b) is evenShow that is an equivalence relation on Z |
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| 43. |
4. Let R=(a, b): a, b e Z and (a - b) is divisible by 5).Show that is an equivalence relation on Z.labiondefined on the set-1123 |
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| 44. |
12. A right circular cylinder just encloses a sphere ofradius a cm, then the curved surface area of thecylinder is:(a) 4Ďa2cm(c) 3macmIT-II (2011)](b) 2na'cm2(d) 4Ďa2 cm2 |
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Answer» Curved surface area of the cylinder =2πah =2πa(2a)= 4πa^2Answer d. |
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| 45. |
stA right circular cylinder just encloses a sphere ofradius r (see Fig. 13.22). Find0) surface area of the sphere,(i) curved surface area of the cylinder,(ii) ratio of the areas obtained in (i) and (ii).9.atFig. 13.22 |
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| 46. |
5 cn. Find me outcr9.A right circular cylinder just encloses a sphere ofradius r (see Fig. 13.22). Find0 surface area of the sphere,(ii) curved surface area of the cylinder,(ii) ratio of the areas obtained in (i) and (ii).Fig. 13.22 |
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| 47. |
Find the surface area of a sphere of radius:0 10.5cnm1.(ii) 5.6 cm(ii) 14 cm |
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| 48. |
Let the vertex of an angle ABC be located outside a circle and let the sides of the angleIntersect equal chord AD and CE with the circle Prove that ABC is equal to half theDifference of the angles subtended by the cnords AC and DE at the centre |
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Answer» In triangle AOD and COE,OA=OCOD=OEAD=CEhence,they r congr.tnow,OAD=OCE (CPCT)ODA=OEC ( " )also,OAD=ODAi.e. OAD=OCEO=DA=OEClet them be 'x'now,in tri.OACOA=OC,so,it's an iso.tri.,let their equal ang's be 'a'lllylet the equal ang's of ODB be 'y'ADEC is a cyclic quad.now,AOC=180-2aDOE=180-2yDOE-AOC=180-2y-(180-2a)= -2y+a / 2a-2y2a-2y= 2a-(360-4x-2a) =2a-360+4x+2a 4a+4x-360ang.B=180-(180-x-a)-(180-x-a) =180-180+x+a-180+x+a=2x+2a-180i.e,measure of ang.B/difference = 2x+2a-180/4x+4a-360 =1/2 thanks👍👍👍👌👌👌👌 |
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| 49. |
rove that1cos01 + cos θtan-gsec0 +1Ora. Prove that2( |
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| 50. |
cos x 4 6} be j 3sis |
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Answer» Int. Of 5x sq. Will be 5 x cube divided by 3 and of - 6 it will be - 6x and 2cosx divided by 3 sinx sq. Take sinx = t and do derivative wrt x ex+ c is the correct answer |
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