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.
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4. If 4x + i(3x-y)-3+i(-6), where x.y eR then find x and y. |
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Answer» 4x + i (3x - y) = 3 + i(-6) Comparing real and imaginary parts 4x = 3 x = 3/4 Now, 3x - y = -6 3 × (3/4) - y = -6 9/4 - y = -6 y = 9/4 + 6 y = 33/4 |
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| 2. |
i) I#x2 + y2-25 then radius of circle isa) 2 b) 5 c) 0 d)-5 |
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Answer» Equation of Circle is x² + y² = r², with radius r and center (0,0) So, in x² + y² = 25 r² = 25 r = 5 ( taking postive value) b) 5 is correct answer |
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| 3. |
\text { find the slope of the tangent }\y = 3 x ^ { 4 } - 4 x \text { at } x = 4 |
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| 4. |
Find the slope of the tangent to the curve y=x-2, x#2atx.= 10. |
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| 5. |
Write the equation of tangent to x^2 + y^2 = 25which are parallel to x-axis. |
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| 6. |
Find the equations of the tangent and normal to the curve8-7y =at the point where it cuts the x-axis.(x-2)(x - 3) |
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| 7. |
EXERCISE 3.3VERY SHORT ANSWER TYPE QUESTIONSFind the perpendicular distance(length of the perpendicular) from the pointi) (-2,-3) to the line 5x-2y + 4-0 İİ) (-3,4) to the straight line 5x-12-Transform the equation x/a v/h-Linto normal form where a > 0 and b>0 |
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| 8. |
17.Find the perpendicular distance from the point (-3, 4) to the straight line 5x-12y-2 |
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Answer» ig u did some other question |
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| 9. |
26. If ä and b are two unit vectors such thatà +5b and 5a - 45 are perpendicular to eachother, then the angle between a and b is :(b) 3(d) coIN |
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| 10. |
d the equation of the circle which has its centre at the point (3, 4) and touchesthe straight line 5x + 12y-1 0. |
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| 11. |
8.Findtheequationof the circle which has its centre at the point (3, 4) and touchesthe straight line 5x+ 12y-1-0. |
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| 12. |
16,18. Find the equation of the circle which has its centre at the point (3, 4) and touches.18, Cthe straight line 5x+ 12y-10 |
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| 13. |
b) Find the distance between two parallel lines 2x+ 3y +5and2x +3y +90. |
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Answer» Like if you find it useful |
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| 14. |
Find the equation of the straight line which passes through the point of interse7 the straight lines 5x - 6y 1 and 3x +2y +5 0 and is perpendicular to theline 3x - 5y 11 0. |
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| 15. |
172X - syFor what value of K are 3x + 2ky = 2 and 2x +5y = 1 graphs are parallel |
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Answer» 3x+2ky=2=>2ky=-3x+2=>y=(-3/2k)x+(1/k)slope(m1)=(-3/2k) also,2x+5y-1=0=>5y=-2x+1=>y=(-2/5)x-(1/5)slope(m2)=(-2/5) Since, graph of lines are parallel Therefore, m1= m2that is, (-3/2k) = (-2/5)Value of k = 15/4 |
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| 16. |
Are the graphs of -5y=2x+3 and y=2/5x+4 parallel, perpendicular,of nether?A. BothB. ParallelC. PerpendicularD. Neither |
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| 17. |
find the have of k if lines 4x+6y-1=0 and 2x-ky=7 are parallel |
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| 18. |
4. In the given figure, PQ and PR are tangents to the circle with centre O such that QPR-50°, then findZOQR. |
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Answer» thanx mera answer right hai |
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| 19. |
Find the joint equation of pair oflines(i)/through (2,-1) and parallel to2x + 3xy-9y2=0. |
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| 20. |
7. If the lines 3x + 2ky- 2 and 2x + 5y +1 0 are parallel, then the value of k is |
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| 21. |
Find the point on the curvef(X) = x2 + 2x-8 at whichx)=tangent is parallel to x axis. |
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| 22. |
In the given Fig.if PA and PB are tangents to the circle with centre O such that.APB 50, then ZOAB is |
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| 23. |
(i) x +x +x+1(ii) x +xxx+1(ii) x + 3x +3x+x+1(iv) x-x- (2 + -2) x + 12गुणनखड प्रमेय लागू करके बताइए कि निम्नलिखित स्थितियों में से प्रत्येक स्थितिp(x) का एक गुणनखंड है या नहीं:(i) p(x) = 2x +x2-2x-1, g(x) = x +1(ii) x) =x+3x+3x+ 1,g(x) =3x+2(iii) p(x) =x3-4x2 +x+6, g(x) =x-3..kका मान ज्ञात कीजिए जबकि निम्नलिखित स्थितियों में से प्रत्येक स्थिति में () =r+1) |
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Answer» 1) p(x)=2x^3+x^2-2x-1, g(x)= x+1, p(g(x))=2( x+1)^3+( x+1)^2- 2(x+1)-1 = 2( x^3+1+3(x)(1)(x+1))+x^2+1+2x-2x+2-1 = 2x^3+2+3x(x+1)+x^2+1+1= 2x^3+x^2+3x^2+3x+2+2= 2x^3 + 4x^2 +3x +4 |
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| 24. |
If the lines 3x + 2Ky = 3 and 2x + 5y + 1-0 are parallel then find the valueof 'K'.1. |
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| 25. |
(2+1) -1) el ) 3 ÂĽ |
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Answer» ( x + 1)² = 2 ( x - 3) x² + 2x + 1 = 2x - 6 x² + 7 = 0 As higehst degree is 2 so it is quadratic Equation |
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| 26. |
-sin 20° sin 70° 31 5 होगा2 EL A - g0 |
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| 27. |
5.) If a, b, c are non-zero real numbers, then\left| \begin{array}{lll}{b c} & {c a} & {a b} \\ {c a} & {a b} & {b c} \\ {a b} & {b c} & {c a}\end{array}\right|vanishes, when |
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| 28. |
21. If a, b, c are non-zero real numbers such that a?+b+ c2- ab + bc + ca, then show that a+b+ c3 3 abc. |
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| 29. |
If v and w are two mutually perpendicularunit vectors and uv +bw, where a and bare non zero real numbers, then the anglebetween u and w is |
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| 30. |
Define decision tree |
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Answer» A decision tree is a graphical representation of possible solutions to a decision based on certain conditions. It's called a decision tree because it starts with a single box (or root), which then branches off into a number of solutions, just like a tree. |
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| 31. |
SL - = ****+ Z€ - ()SYTRIA aunmy |
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Answer» 22 is the correct answer for this question i.e.-37+22=-15 the answer is 22 is correct -37+__ =-15=-37-15=22 answer -37+_=-15x=37-15x=22 |
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| 32. |
Q. 5. If a chord is drawn through the point ofcontact of the tangent to a circle then prove that theangles formed by this chord with the given tangentsare equal to the angles formed in the alternate |
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Answer» A chord AB of a circle and a line PAQ. Such thatangle BAQ=angle ACB where c is any point in the alternate segment ACB. To Prove:- PAQ is a tangent to the circle. Construction:- Let PAQ is not a tangent then let us draw P' AQ' another tangent at A. Proof: - AS P ’AQ’ is tangent at A and AB is any chord angle BAQ'=angle ACB Butangle BAQ=angle BAQ(given) hence angle BAQ=angle BAQ' Hence AQ' and AQ are the same line i.e. P' AQ' and PAQ are the same line. Hence PAQ is a tangent to the circle at A. |
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| 33. |
.Describe any five functions of a political parties.OR |
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Answer» Mainfunctions of a political party: (i) To contest elections: In most democracies, elections are fought mainly among the candidates put up by political parties. Parties select their candidates in different ways. In India, top party leaders choose candidates for contesting elections, (ii) Forming policies and programmes: Parties put forward different policies and programmes and the voters choose from them. Each of us may have different opinions and views on what policies are suitable for the society. (iii) Making laws: When parties come to power, they make laws for the country. Formally, laws are debated and passed in the legislature. Members of the ruling party follow the directions of party leaders, irrespective of their personal opinions. (iv) Parties form and run governments: Parties recruit leaders, train them and then make them ministers to run the government in the way they want. (v) Role of opposition: Parties that lose in elections, play the role of opposition to the parties in power by criticising the government for its failures or wrong policies NominationFunction. Nominate candidates for public office.Informer-StimulatorFunction. Helps to inform & stimulate their members interest & participation.BondingAgentFunction.Partyserves as a bonding agent to ensure the good performance of its candidate & office holders.Govt.function. ...WatchdogFunction. thnx |
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| 34. |
aun _Jo =N = 2el 89089 |
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| 35. |
RahimMPpurchased abut soldwatch at 20%it at MP finddiscount athis aun |
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| 36. |
315.cos θaun4and θ is acuteangle, then1tan θ-sin θcosec θ + cot θvalue ol |
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| 37. |
Thu Aunvio la calutat u est and S tav abuu |
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Answer» First term =a second term =blast term =ccommon difference=(b-a)tn =a+(n-1) d c=a+(n-1) d (c-a)=(n-1)(b-a) (c-a)/(b-a)+1=n ( c+b-2a)/(b-a)=n--------------------(1)now ,we know sum of n terms=n/2 (first term+last term)put equation (1)value = (b+c-2a)/(b-a)(a+c)hence Sn=[(b+c-2a)(c+a)/(b-a)] |
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| 38. |
o | न कि रा है न cente ही वो If lADcstवा... o e okt B the megoure heAC7e था LAt ( S e% |
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| 39. |
Ihat is,Example 5 : If acorresponding angles are parallel, then prove that the two lines are parallel.transversal intersects two lines such that the bisectors of a pair ofltrnvrral AR intersects two lines PQ and RS at points B |
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| 40. |
19Rahul drew two lines and a transversalcutting across the two lines. How can heknow if the two lines drawn by him areparallel or non-parallel? |
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Answer» if the two lines have same corresponding angle then the lines are parallel |
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| 41. |
1 A square has(a) one line of symmetry(b) two lines of symmetry(c) three lines of symmetry(d four lines of symmetry |
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| 42. |
Theorem 3ersal intersects two lines such that a pair of alternate interior angles are equal,then the two lines are parallel. |
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Answer» A transversal AB intersects two lines PQ and RS such that∠PLM = ∠SML To Prove: PQ ||RSUse same figure as in Theorem 2.Proof: ∠PLM = ∠SML ……………equation (i) (Given)∠SML = ∠RMB …………equation (ii) (vertically opposite angles)From equations (i) and (ii);∠PLM = ∠RMB But these are corresponding angles.We know that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines ate parallel to each other.Hence, PQ║RS Proved. |
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| 43. |
Theorem : If a pair of alternate angles formed by atransversal of two lines is congruent then the two linesare parallel. |
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| 44. |
Find the magnitude of angle A, if:2 \sin A \cos A-\cos A-2 \sin A+1=0 |
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Answer» 2sinAcosA-cosA-2sinA+1=02sinA(cosA-1)-cosA+1=02sinA(cosA-1)=cosA-12sinA=cosA-1/cosA-12sinA=1sinA=1/2sinA=sin30A=30therefore magnitude of angle A is 30 |
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| 45. |
find:\begin{array} { l } { \text { Find the magnitude of angle A, if : } } \\ { \text { (i) } 2 \sin A \cos A - \cos A - 2 \sin A + 1 = 0 } \end{array} |
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| 46. |
If θ is an acute angle and sin θ = cos θ, find thevalue of 2 \tan ^{2} \theta+\sin ^{2} \theta-1 |
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| 47. |
| परीक्षा-04.07.1999 द्वितीय पाली)11. एक व्यक्ति अपने धन का 50% भाग अपने पुत्रको और 30% भाग अपनी पुत्री को देता है। शेषराशि का 80% भाग किसी ट्रस्ट को दे दिया | 1जाता है। अब यदि उस व्यक्ति के पास 16,OOOरुपए बचे हों, तो उसके पास प्रारंभ में क्याधनराशि थी?(1) 40,000 रुपए (2) 8,00,000 रुपए(3) 80,000 रुपए (4) 4,00,000 रुपए।Com PAISA |
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Answer» 3) is correct answer |
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| 48. |
ooo micaometne can also be usitten as |
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Answer» It can also be written as 1 mm. |
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| 49. |
A solid sphere of radius 10.5 cm is melted and recast into smaller solidcones, each of radius 3-5 cm and height 3 cm. Find the number of conesso formed. (Use π-)22 |
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| 50. |
A solid metallic sphere of diameter 21 em is melted and recast into a number of smaller conesof diameter 7 cm and height 3 cm. Find the number of cones so formed.each |
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