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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४ हक G) d=i-j+2kb=i+j+kand é=2i~j+k ZA F O W निर्मम S T4 G5 =167 =2and ¢F =5 9% «f Fra =) |
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| 2. |
21. Two equal circles intersect in P and Q. A straightline through P meets the circles in A and B. Provethat QA QB. |
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13. Two equal circles intersect in P andQ. A straight line through P meetsthe circles in A and B. Prove thatQA = QB. |
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| 4. |
Comhateim |
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| 5. |
( i j f ( x + 1 ) ( x + 2 ) ( x + 6 ) = x ^ { 3 } + 9 x ^ { 2 } + 4 ( 7 x - 1 ) |
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| 6. |
Page NoDate:Holiday Homew carte1. The length of a rectangle is 15 cm greaterthan its besteath. Its her perimeter is 156 cmFind its dimension of the rectangle? |
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Answer» breath is 30 cmand length is 45 cm |
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| 7. |
Page No.6uestion Bank C-1Linear Equation In Two Variablesvi)in the figure, the sides of a rectangle are given. The lengths arein cm. Find the length and breadth of the rectangle.4x4272844+23x-y +32x + 3y + 4 |
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Answer» length is 14 cm and b is 13 cm |
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| 8. |
DATEPAGE NO3completethe following2x tyto24 Rectangle Ixt 4 -42-yTwo equation inxandy!Tvaluesofysy |
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| 9. |
P2Q² + (Pa2 Hate |
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| 10. |
Two equal circles intersect in PQ. A straight line through P meetsthe circles in A and B. Prove thatQA QB.13.and |
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| 11. |
3. Two equal circles intersect in P andQ. A straight line through P meetsthe circles in A and B. Prove thatQA QB |
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13. Two equal circles intersect in P andQ. A straight line through P meetsthe circles in A and B. Prove thatQA QB. |
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| 13. |
ărtn a class of 40 pupils, 35% are girls. How many girls are there in the class? How many of thepupils are boys? |
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Answer» 35 percentage of 40= 40*35/100= 14 girls26 boys |
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| 14. |
002. In the given fig. I is parallel to m and pll q. Find the measure of each of the anglesa,b,c,d.Тр100! |
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Answer» 100°=angle D (vertically opposite)as angle D=angle B=100°(alternative interior angles) angle B=angle B=100°(alternative interior angles)angle besides to 100°=80°(straight line)as angle 80° =angle A=80°(alternative interior angles) angle A=80°angle B=100°angle C=100°angle D=100° aA=80°aB=100°aC=100°aD=100° aA=80 degree aB=100 degree aC=100 degreeaD=100 degree Angle A= 80° Angle B=100° Angle C=100° Angle D=100° aA=80° aB=100° aC=100° aD=100° <A = 80,<B = 100,<C= 100,<D = 100 is right answer |
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| 15. |
lfsin 3θcos (9-69) here. 3θ and (8-6) are acute angles, find the value ore. |
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Answer» Sin 3A = cos (A-6) sin 3A = sin (90-(A-6)) ( since sin(90- A) = cos A) therefore, 3A = 90-(A-6) 3A = 90-A+6 3A+A = 96 4A = 96 A = 96/4 A = 24 |
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| 16. |
6.Simplify.5 15 20 |
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Answer» (-4×12-3×4+7×3)/60=(-48-12+21)/60=-39/60=-13/20 Thank u |
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| 17. |
There are 38 boys and 27 girlsin a class. How many pupilsare there in the class? |
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Answer» In the class boys are=38 & girls are=27. so The total students in the class are=38+27. The total number of pupils are 65. * |
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| 18. |
B and CD are two parallel lines and a transversal I intersects AB at X andCD at Y. Prove that the bisectors of interior angles form a rectanglePage 1 of4 |
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In the given figure, AB I| CD and PQ, QRintersects AB and CD both at E, F and G, Hrespectively. Find the value of x.120°80°(A) 40° (B) 20° (C) 100° (D) 30° |
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Answer» 1 2 |
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| 20. |
In the given figure<122 and ΔNSQsANATR, then prove thatOr |
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Answer» the triangles PTS and PQR, let us assume that Q = angle 3 and R = angle 4. So, angle 1 = angle 3 (corresponding angles) and angle 2 = angle 4 (corresponding angles) Angle P is common angle. By AAA similarity triangle PTS is similar to PQR. Hence proved hit like if you find it useful |
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| 21. |
In Δ PQR. If PQ > PR and bisectors of <Q and <Rintersect at S. Show that SQ > SR.Fig. 3.58 |
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| 22. |
7Two equal circles of radius r, intersect such that each passes through the centreof the other. The length of their common chord isb. 2rd.2 |
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| 23. |
. Solve:4x2 + 4bx-(a2-b2)=0 |
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Answer» yes it is right |
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| 24. |
26/ The diagonals of a trapezium ABCD with AB | DC intersect each other at point O. IfAB 2CD, find the ratio of the areas of triangles AOB and COLD |
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is a trapezium in which ABIICD andCD. Its diagonals intersects each other at O6ABCDthen what is the ratio of the areas of the trianglesAOB and COD ?(A) 1 2(B) 2 1 |
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| 26. |
of the students are boys. If there are 240 girls, find the number of51520a schoolthe school.many nages are there in the booka |
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Answer» what is the difference between 40% of 60 and 60% of 40? |
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27. In a school, 8 of students are boys. If there are 240 girls, find the number of boys in the school,8 |
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| 28. |
IfAB|| CD, findx, y and z from the given figure:002B1300 |
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Answer» bcz AB ll DC z =180-130 =50x = 130y = 130 |
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14. The product of two fractions is 9 ore Un18. In a school of the students are boys. If there are 240 girls, find the number ofthe schoolnades are there in the booles |
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| 30. |
6.In a school the ratio of boys togirls is 3:5. If there are 240 boys,how many pupils are there in thatschool?A. 400 B. 640C. 144 D. 384 |
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Answer» Let the number of be 3x and number of girls be 5x Then,3x = 240x = 240/3 = 80 Therefore, total number of pupil in school = 3x + 5x = 8x= 8*8 = 640 (B) is correct option |
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| 31. |
-/a2+b2 , 0 < θ < 90 thenfind the values of secθ and tan8. |
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| 32. |
(ii) x2 2x-9 0Solution : Compare x2 + 2x-9 = 0 withax2 + bx + c = 0b= 2, c=1,b2-4ac- 22-4xD-4-□D= 40,'. b2-4ac > 0the roots of the equation are real andunequal. |
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Answer» a = 1, b = 2, c = - 9 b^2 - 4ac = 2^2 - 4*1*-9D = 4 - (-36)D = 40 |
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| 33. |
Diagonals AC and BD of a quadrilateralABCD intersect at O in such a way thatar (AOD) ar (BOC). Prove that ABCD is atrapezium.C |
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| 34. |
If ad(abe then prove that the equation2 + b2)x2 + 2(ac + bd)x + (c2 + d2)(,0 has no real roots. |
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21. Diagonals of a trapezium ABCD with AB II CD intersects at O. If AB = 2CD, find the ratio ofareas of triangles AOB and COD |
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| 36. |
i6. Diagonals of a trapezium ABCD with ABlIDC intersect each other at the point O. IA-2CD,find the ratio of the areas of triangles AOB and COD |
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Answer» Like if you find it useful |
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| 37. |
Diagonals of a trapezium ABCD with AB | DC intersect each other at the point O.IfAB 2CD, find the ratio of the areas of triangles AOB and COD. |
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In the given figure, AOB is a straight line and the rays OC and OD stand con it.If ZAOC 65°, BOD70° and CoD, find the value of x6570 |
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| 39. |
| DC intersect each other at the point O.IfAB 2 CD,findDiagonals of a trapezium ABCD with Aratio of the areas of triangles AOB and COD.21.B |
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18. Diagonals of a trapezium ABCD with AB I DCintersect each other at the point O. If AB 2CD,Find the ratio of the areas of triangles AOB and COD |
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15.4 cm, find BC.Diagonals of a trapezium ABCD with ABDC intersect each other at the point o.IfAB 2 CD, find the ratio of the areas of triangles AOB and COD. |
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Answer» thank u ... ☺☺ |
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| 42. |
2. In a school, of the students are boys. If there are240 girls, find the number of boys in the school? |
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| 43. |
If \mathrm{ad} \neq \mathrm{bc}, then prove that the equation(a2 + b) x+ 2 (ac + bd)x+ (e + d) 0 has no real roots. |
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Answer» (a²+b²)x²+2(ac+bd)x+(c²+d²)=0a=(a²+b²) b=2(ac+bd) c=(c²+d²)putting a,b,c in formula[-b +/-√(b²-4ac)]/2a{-2(ac+bd) +/-√[4(ac+bd)²-4(a²+b²)(c²+d²)]}/2(a²+b²)[-2(ac+bd) +/-√4a²c²+4b²d²+8abcd-4a²c²-4a²d²-4b²c²-4b²d²]/2(a²+b²)-2(ac+bd) +/-√ - (4a²d²-8abcd+4b²c²)Hence root cant be negative.So, it has no real roots. |
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Solve the following equation for X: 4x2 +4bx- (a2 -b2)=0 |
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Answer» 4x² +4bx -(a² -b²) = 0 4x² +4bx -a² + b² =0 (2x)² + 2.(2x).b + b² -a² =0 (2x + b)² -a² = 0 use formula, a²-b² = (a -b)(a + b) {2x + b -a}{2x + b +a} =0 Therefore, x = (a - b)/2 , - (a + b)/2 |
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| 45. |
== v& Sk, SISsec? (tan~" 5) + cosec? (cotโข} ยง) = |
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Answer» Please hit the like button if this helped you |
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| 46. |
Solve the following systems of linear equation:a(x+y) _ b (x-y)-a2 + ab + b2[HOTS |
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Answer» please like my answer if you find it useful |
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| 47. |
a का 2% = b, तो 10 का b%,बराबर होगा |(Aa का 200%Ba/100 का 20%Ca/10 का 20%(Da/10 का 200% |
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Answer» c answer a/10 ka 20% was the answer |
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| 48. |
डिक डी ~ ) TL हे... /5 |
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Answer» (5/3)^-(n-1)=( 5/3)^n-3n-3= -n+12n= 4n = 2 |
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| 49. |
()Tl).}S |
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Answer» {((x^(-5))^(2/3)}^(-3/10) {x^(-10/3)}^(-3/10) x^1 =x |
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In a trapezium ABCD if AB|ICD and diagonals intersect at O, prove that AO.OD BO.OC16. The angles of a triangle are x, y and 40°. The difference between the twoangles r and y is30°. Find r and y |
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Answer» x-y=30 →equation 1 x+y+40 = 180 (since sum of angles of a triangle = 180) x+y=140 →equation 2 (variables on one side,constants on one side) equation 1 → x-y=30 equation 2 → x+y=140 ⇒ 2x= 170 (∵ -y+y=0) ⇒x = 170/2 ⇒ x = 85 substitute x in equation 1 (or equation 2.its your choice. you'll get the same answer) equation 1 → x-y=30 85-30 = y (substituting x and bringing 30 on one side and y on one side) 55 = y ∴x=85 y=55 |
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