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. |
Ifthe point (m, 3) lies on the line segment joining the points Ae lime segment joining the points .6 and B(2, 8), find the value of m |
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| 2. |
Find the midpoint of the line segment joining the points (3,0) and (-1,4) |
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| 3. |
thatthel in the mid-point of the line segment joining thepoints(2,0)and 0,,thenshowIf 1,2 is the mid-point of the line segment joining the points (2,0) and othe showthat the line 5x+3y+2-0 passes through the point (-1,3p). |
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Answer» let ( x1 , y1 ) = A( 2 , 0 ) , ( x2 , y2 ) = B ( 0 , 2/9 ) ; mid point of joining of A and B = ( x1+ x2 /2 , y1 + y2 /2 ) = ( 0 + 2 /2 , 0 + 2/9 / 2 ) = ( 1 , 1/9 ) p/3 = 1/9 [∵ If ( a , b ) = ( c , d ) then a = c and b = d ] p = 1/3 --- ( 1 ) according to the problem given , put ( -1 , 3p ) in the equation 5x + 3y + 2 =0 5 ( -1 ) + 3× ( 3p ) + 2 = 0 -5 + 3× 3 ( 1/3 ) + 2 =0 [ from ( 1 ) ] -5 + 3 + 2 =0 0 = 0 [ true ] Therefore , 5x + 3y + 2 =0 line passes through thepoint ( -1 , 3p ) . Like my answer if you find it useful! thanks |
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| 4. |
2,61 andIfthe points P (m, 3) lies on the line segment joining the points Ai,618.18. If the points P (m, 3) lies on the line segment joining the points and B(2, 8). Find the valuem. |
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| 5. |
Let us prove that the mid point of line segment joining two points(2, 1)and(6,5) lie on theline joining two points (-4,-5) and (9,8).and , 6). |
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| 6. |
Find the mid point ofthe line segment joining the points (3,0) and (-1,4) |
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Answer» ( 1, 2 ) is the right answer (1,2) is the correct answer of the given question (1,2) is the answer ....... (1,2)is the correct answer for the given question |
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| 7. |
The points which trisect the line segmentjoining the points (0, 0) and (9, 12) are |
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| 8. |
Line segment joining the centre to any point on the circle is a radius of the circle. |
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Answer» This statement is True |
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| 9. |
The coordinates of the midpoint of the line segment joining thepoints P/-4, 2) and Q8.6) ae |
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Answer» Mid point= (x1+x2/2;y1+2/2) X1= -4; x2= 2 Y1= 8; y2= 6 》[(-4+(-2))/2,(8+6)/2] =[-3,(7)]........ |
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| 10. |
Find the coordinates of the points of trisection of the line segment joining (4and (-2,-3). |
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| 11. |
In the adjacent figure ABCD is a square and AAPB is anequilateral triangle. Prove that AAPD: ABPC.(Hint: In AAPD and ABPC AD=BC, AP = BP andPAD = Z PBC = 90° -60° - 30) |
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Answer» Solution : part 1GivenΔ ABP is an equilateral triangle.Then, AP = BP (Same side of the triangle)and AD = BC (Same side of square)and,∠ DAP =∠ DAB -∠ PAB = 90° - 60° = 30°Similarly,∠ BPC =∠ ABC -∠ ABP = 90° - 60° = 30°∴∠ DAP =∠ BPC∴Δ APD is congruent toΔ BPC ( SAS proved)2nd partInΔ APDAP = AD II as AP = AB (equilateral triangle)We know that∠ DAP = 30°∴∠ APD = (180° - 30°)/2 (Δ APD is an isosceles triangle and∠ APD is on of the base angles.)= 150°/2 = 75°=∠ APD = 75°Similarly,∠ BPC = 75°Therefore,∠ DPC = 360° - (75°+75°+60°)=∠ DPC = 150°Now inΔ PDCPD = PC asΔ APD is congruent toΔ BPC∴Δ PDC is an isosceles triangleAnd∠ PDC =∠ PCD = (180° - 150°)/2or∠ PDC =∠ PCD = 15°∠ DPC = 150°;∠ PDC = 15° and∠ PCD = 15° Answer. |
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| 12. |
हल | कि रा 13 B PO, Numbver of Stadomts-2 o1 10 |
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| 13. |
3. Simplify.(G)(x2-5) (x +5) + 25 |
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| 14. |
5.Fig.5.19Line / is the bisector of an angle A and B is anypoint on 7. BP and BQ are perpendiculars from Bto the arms of Z A (see Fig. 5.20). Show that:(1) AAPB=AAQB(ii) BP = BQ or B is equidistant from the armsof ZA.Fig. 5.20 |
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Answer» In triangle APB & AQBThen,AB=AB (common)AQ=AP(side)QAB=PAB(angle)Then,We can say that,Triangle APB is congruent toAQB |
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| 15. |
1.e the following pair of linear equations by the substitution method(i) x+y 14(i) s-t 3st3 26 |
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| 16. |
pratisthapan Vidhi se 3x-y=3 , 9x3y=9 |
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Answer» 3x-y=3........19x-3y=9..(divided by 3)3x-y=3......2 3x=3-yX=3-y/3 sub X in 13x-y=33(3-y/3)-y=33-y-y=3-2y=3-3 y=0 sub y in 2 3x-y=33x-0=33x=3 X=1 (3x-y =3)3= 9x - 3y = 9; 9x+3y = 9:; 9x + 3y =9/6y =18; y = 18/6=3, ; 3x -3=3; 3x= 6:; x= 6/3=2 |
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| 17. |
In the given figure ABC is right angled triangle, right angled at C. DELAB. ProveThat Δ ABCΔ ADE and hence find the lengths of AE and DE |
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| 18. |
15. ABC is a right triangle, right angled at C and AC = V3.BC. Prove thatZ ABC = 60° |
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Answer» Draw a median CD to AB from C. Now, by Pythagoras theorem in ABC, AB=2*BC.Thus, BD= half of AB = BC. But, the point of bisection of the hypotenuse is equidistant from all sides. Thus, CD=BD=AD. That implifies, CD=BD=BC. Thus, CDB is an equilateral triangle. Therefore, angle DBC = angle ABC = 60 degrees. |
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| 19. |
() In figure (G) given below, ABCis a right triangle right angled at c teof BC, prove that AB2 4AD2-3AC2. |
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| 20. |
en figure, XOY is a straight line. OP and OQ stand onivn the gnd all the linear pairs of angles.les anline XY. Write all the pairs of ayen figure, OP and Ol are opposite rays and OR stands on PO.5%,. (23-16")(i) If y-73°, find the value of χ(ii) If x= 14°, find the value of y. |
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Answer» If y = 73°Then2y-16= 130And 130+x= 180°X= 50°Please like the solutionAnd when x= 14°70+2y-16= 1802y= 126Y= 63°Please like the solution 👍 ✔️ |
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| 21. |
iactors o botn the polynomialsynomial f(x) is divided by (-1), the remainder is 5 and when it is dividedWhen a polby (x -2), the remainder is 7. Find the remainder when it is divided by (r-1) (a - 2) |
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| 22. |
ynomial each with the given numbers a1I31-4' 4 |
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| 23. |
6.P is a point in the interior of a parallelogramABCD. Show that(i) ar(AAPB)+ ar(APCD)ar(ABCD)(ii) ar(AAPD) + ar(APBC) - ar(AAPB)+ ar(APCD)Hint: Through P, draw a line parallel to AB) D |
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| 24. |
6. P is a point in the interior of a parallelogramABCD. Show that(i) ar(AAPB) +ar(APCD) -ar(ABCD)(ii) ar((Hint: Through P, draw a line parale toAB) DAAPD)+ ar(APBC)-ar(APB) arAPCDllal eides multinlied by |
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| 25. |
2xx283.75 = ?[UBI PO 2005] |
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Answer» s = 6/5 × 15/26 ×283.75s = 3 × 3/13 × 283.75s = 196.4423 s= 196.4423 is the correct answer of the given question is |
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| 26. |
Po10. Divide the polynomial x + 3x + 3x + 1 by X+1 and findy ofthe remainder. |
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| 27. |
Therefore, the solution is (0,I. Draw the graph of each of the following linear e2y = - x + 1 ii) - x + y = 6 iii) 3 x +Duuuthohofeach ofthe following linear e |
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Answer» 1. ii -x+y=6 if x=0 0+y=6 y=6if x=1 -1+y=6 y=7 |
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| 28. |
2,50,000 . It depreciates at the rate of 4% per annumThe cost of a machine isFind the cost of the machine after three years.4. |
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| 29. |
Let A-15,6t;howmanybinaryopera |
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Answer» Please post complete question |
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| 30. |
Exercise 12ASolve the following equations1, x+ 2x = 9seoperalethe equati |
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Answer» x + 2x = 9 We know same variable can be equated So, 3x = 9 x = 3 |
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| 31. |
“हा कप्य (05-0८) न6-+ ४) ( ंL) E1 5 L41५1८४ -)०)] |
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Answer» thank you so much |
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| 32. |
) = 879me= 979e1= G teG= hth |
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Answer» The answer of 5+8 = 13 The answer is 9in to 5=45 34 is the best answer The answer is 34 because1+4=52+5=7 then add before answer 7+5=123+6=9 9+12 =21 1×4 = 4 +1 =42×5 =10 +2 =123×6 =18 +3 = 215×8 = 40+5 = 45 ✔ there are two ways1)1+4=5 2+5=7+5=12 3+6=9+12=21 5+8=13+21=342) 1*4=4+1=5 2*5=10+2=12 3*6=18+3=21 5*8=40+5=45the answer may be 34 or45 34 os the correct answer exactly 34 is the right answer |
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| 33. |
hc. draw a line parallelo ARDraw a line, say AB, take a point outside it. Through C, draw a literusing ruler and compasses only. |
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Answer» Answer:The steps of construction are as follows.(i)Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P.(ii)Taking P as centre and with a convenient radius, draw an arc intersecting line AB atpoint D and PC at point E.(iii) Taking C as centre and with the same radius as before, draw an arc FG intersectingPC at H.(iv) Adjust the compasses up to the length of DE. Without changing the opening ofcompasses and taking H as the centre, draw an arc to intersect the previously drawn arcFG at point I. |
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| 34. |
Q.10 If from a point P outside a circle, exactly n tangents can be drawn to the circle, then nis equal toa) 1b) 2c) 3d) none of these |
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| 35. |
ht triangle, right-angled at C. If p is the length of the perpendBC is a right triangle, rightand a, b, c havee the usual meaning, then prove that:meile of radius 3.5 cm. Take a point T outside the circle at a dit |
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| 36. |
In the given figure, if LPOR +LQOR+ <QOS = 312°, find all the four angles. |
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| 37. |
Draw a line 1. Take a point A outside the line. Through point A draw a lineparallel to line /. |
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| 38. |
m wide. What is the area of the rellaliing p0. By splitting the following figures into rectangles, find their areas(The measures are given in centimetres). |
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| 39. |
The(4x -30)° and (2x-20)° respectively; then find the measure of the smallesexterior angle of it.measures of four angles of a quadrilateral are (2x + 10) , (3x + 15)。(2) 120°(3) 100°(4) 80° |
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Answer» Sum of all angles of a quadrilateral=360°2x+10+3x+15+4x-30+2x-20=36011x-25=36011x=385x=35Smallest exterior angle will of biggest angleAngles will be2x+10=2*35+10=80°3x+15=3*35+15=120°4x-30=4*35-30=110°2x-20=2*35-20=50°Hence biggest angle is 120°Hence ,exterior angle will be 180-120=60°option a |
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| 40. |
27. The lengths of tangents drawn from an external point (point outside the circle)fo a circle are equal. Prove it. |
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| 41. |
-28. In figure the sides QR ofAKOR is produced to a point S. If the bisectors ofLPOR andPRS meet at point T. Then prove that: LOTR =1/2LOPR243 |
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Answer» answer kya h |
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| 42. |
(4)150%निर्देश : नीचे दिये गये पाइ-चार्ट किसी एक स्थान का वार्षिक कृषि उत्पादन दर्शाताहै। चार्ट का अध्ययन करके निम्न प्रश्न का उत्तर दें :शक्कर809।चावल100X409 -अन्य५4- १०140940 x108{०१ -16ळ ४५०7 उत्पादन चावल से कितना अधिक है ?(1) 50%(2) 75%(3) 100%(4) 150%L |
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Answer» answer no 1 .50 % |
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| 43. |
3000 36 100 41080abba had invested 3000 after 4 months in the bonneLet us serbis calculatingmy friend Mala together have started a business with cuptas eft200 respectively. If we make a profitoft 16,800 in a year, let us seshall se cach get?m. Supriya and Bulu have opened a small shop of grocery shop wil0.710000 and 25000 respectively. But after a year there was a losite by calculating what each must pay to make up the losse |
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Answer» what is your question The profit share has to be proportional to the income u both earned. 15000: 25000 = 3:5 So the share of profit for 3x + 5x = 16800 x = 16800 / 8 = 2100 So, your share = 3x =$ 6300& her share = 5x =$ 10500 15000:250003:5(3x16800)/8=6300(5x16800)/8=10500 2100 is the correct answer of the given question |
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| 44. |
ee htth of sixty percent of a number is 36, the number is5100(b) 80(c) 75(d) 90 |
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Answer» Let the number be xThen,3/5 * (60/100) * x = 363/5 * 3/5 * x = 369/25 * x = 36x = 36*25/9x = 4*25x = 100 Therefore, Number is 100 (a) is correct option |
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| 45. |
SAMPLE PAPER-ecrtos-A |
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| 46. |
8. Find the value of x in each of the following figures:AN50045°a) Given PQIISR.(b) AB||DE |
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Answer» angle r is 52 alternate angle52+40+x=18092+x=180x=180-92x=88 8) a) =<QPT=52°=<TSR=40°given PQ||SRtherefore, we know that exterior angle is equal to the sum of two interior angle=QPT=STR+RST=52°=40°+xor, x=52°-40°=x=92° (a) . X = 88 , (b). X = 130 |
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| 47. |
MCQ (2 marks)1. Out of the following given figures which are on the same base but notbetween the same parallels? |
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| 48. |
In thefollowing figure findLPOR ond QosRS170(2x-25)Р P |
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Answer» sum of straight line 180 angles are 45 ,90,70 answer is 28•33° degree hoga the straight line forming is forming an angle of 180 so the all the angle forming are supplementary x degree +70 degree + (2x-25) degree equal to 180that is x+70+2x-25 equal to 1803x+45 equal to 180 3x equal to 180-45 3x equal to 135 x equal to 45 28.33333333 is ryt answer poq=45°and qos=65° hai |
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| 49. |
b) name the angles2. Find the degree measure of the angles in the given figure:+ + 20+ 409++30°РRven below: |
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Answer» z+40+z+20+z+30=180angles in linear pairso,3z+90=1803z=180-90so,3z=90so,z=90/3=30so,z+40=30+40=70z+20=30+20=50z+30=30+30=60 |
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| 50. |
Exercise 10.1Id withhave the sameL-60 mA square and a rectangular fieas given in the figure have the same(a)perimeter. Which field has a larger areae Jammu and Kashmir State Board of Educa |
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Answer» thnkew |
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