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 value of the expression given below?(3a?+2ax 5-4) + 5a-2, when a = 41. |
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Answer» Given expression (3a^2 + 2a*5 - 4)/4 +5a - 2 For a = 4Value of expression = (3*4*4 + 2*4*5 - 4)/4 + 5*4 - 2= (48 + 40 - 4)/4 + 20 - 2= 84/4 + 18= 21 + 18= 39 |
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| 2. |
i so lets stoot,1-ę¸ |
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Answer» pqr = 1 r = 1/pq 1/r = pq (1/1+p+q^-1) + (1/1+q+r^-1) + (1/1+r+p^-1) (1/(1+p+1/q) + (1/(1+q+pq) + (1/(1+1/pq+1/p) (1/(q+pq+1/q) + (1/(q+pq+1) + (1/(q+pq+1/pq) (q/q+pq+1) + (1/q+pq+1) + (pq/q+pq+1) (q+pq+1) / (q+pq+1) = 1 |
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| 3. |
Home treghemalt4. Find Hef of 25,40 and Ro by PaXachrization and division methods19.45, 90 and 120. |
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| 4. |
7. If S, denotes the sum of the first n terms of an A.P, prove that S3o3(S2-Sto).20 10) |
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| 5. |
centre be (6, 6). Fiid ule coordna16. The three vertices of a parallelogram taken in order are (1, o), (3, 1) and (2. 2respectively. Show that the coordinates of the fourth vertex are (-2, 1). |
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Answer» Let the vertices be as follows,A(-1,0) ; B(3,1) ; C(2,2); D(x, y) The line segments that make up our parallelogram is AD is parallel to BC, and CD is parallel to AB. Since the definition of a parallelogram is a quadrilateral with 2 pairs of parallel sides, we can use this fact to find the coordinate to the 4 vertex. A pair of parallel side also means that these 2 lines have the same slope. So if we do this on both pairs of parallel lines, we should have 2 equations with 2 variables, which should be simple to solve. Slope of CD =Slope Slope of AB(y - 2)/(x - 2) = (1 - 0)/(3 - - 1)(y - 2)/(x - 2) = 1/44(y - 2) = (x-2)4y - 8 = x-2equation #1: 4y - x = 6 A(-1,0) ; B(3,1) ; C(2,2); D(x, y)Slope of AD = Slope of BC(y - 0)/(x - -1) = (2 - 1)/(2 - 3)(y)/(x + 1) = 1/-1-1(y) = (x + 1)-y= x+1equation #2: y+x = - 1 We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix)to solve for the x and y coordinates. equation #1: 4y - x = 6equation #2: y + x = - 1 Add equation 1 to equation 2 equation 1: 4y - x = 6equation 2: y + x = -1eq 1 + eq 2: 5y = 5y = 1 Using the equation#2 to solve for x: y + x = -11 + x = - 1x=-2 So the 4th vertex will be (-2,1) |
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| 6. |
In parallelogram ABCD, two points P and Q areBQtaken on diagonal BD such that DP(see Fig. 8.20). Show that:(i) AP CQ(iii) Δ AQB 4CPD(iv) AQ CPy APco)s a parallelogramFig. 8.20 |
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| 7. |
Q2 lpe wvolue o0 o L L \Lfim’, of | cokTen>+sin B Tan"30 +£C540 ik e iR 45 1 g9n =30 + 0८ व |
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Answer» If you find this solution helpful, Please give it a 👍 |
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| 8. |
-194) and D(p, 3) are the vertices of aExample 10: If the points A(6, 1), B(8.2), C(9, 4) and D(p. 3) are theparallelogram, taken in order, find the value of p. |
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Answer» By using distance formula, take two points B(8,2) and D(p,3) distance formula is √(x₂-x₁)²+(y₂-y₁)² in point B 8 is x₁ and 2 is y₁ in point D p is x₂ and 3 is y₂Now, =√(p-3)²+(3-2)² =√(p-8)²+(1)² =p-8+1 =p-7 ⇒p=7 |
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| 9. |
If 25x-1-52x-1-100, find the value ว#x. |
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| 10. |
4.is the coefficient of x in expression 22-52x |
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Answer» The coefficient of x is -52. -52 is the co efficient of x |
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| 11. |
5th Grade Georgia Milestones Test PreWhich expression is equal to ?a. 3+5b. 5 + 3c. 3×5d. 5 X 3Which number shows the decimal form fa |
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Answer» a -3 is the right answer...... a"0.6b."1.6c"15d"15 3÷5 = 0.65÷3 = 1.6673×5 = 155×3 =15 -3 ,is the right answer... -3 is the right answer -3 is the right answer -3 is the right answer -3 is the right answer -3 is the right answer -3 is the right answer -3 is the right answer |
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| 12. |
3. Is 4x+3y+2x a trinomial expression? |
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Answer» No it is not trinomialbecause it can added and written as 6x+3y |
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| 13. |
Is 4x +3y +2x a trinomial expression ? Why not? |
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Answer» No, is is not trinomialbecause it can be written as 6x+3y This answer is right .thanks |
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| 14. |
38. If x2 is a factor of the expression (x1)+ (2x + k)3, what is the value of k? |
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Answer» tq but there is( k-4)cube |
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| 15. |
35. There are some expression given below. Which of these are equations?ii) 8+5=9iii) 9K5iv) 2x +1=15 |
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Answer» Equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. Variables are also called unknowns and the values of the unknowns that satisfy the equality are called solutions of the equation Thus (iv) 2x +1 = 15 is only equation |
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| 16. |
the algebraic expressions for the followinga) 2 more than 3 times of a |
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Answer» 3 times a=3a2 more than 3 times a = 3a +2 3a+2 is the answer for your question 3 times a = 3a2 more than 3 times a=3a+2 |
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| 17. |
यXि = 10 औरका मान ज्ञात करो-d9 लो 12+y2 |
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Answer» 181 is the right answer |
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| 18. |
Representsto onnumberline |
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Answer» do like this sun in photo |
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| 19. |
A school has a student population of560 The number ofgrls is 14% of the number ofbo s How manygirls are in the school? |
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| 20. |
x-2and2x+Fegpeuioery,lllremainder wereIr (1.2). (4. y ) and (3, 5) are the vertices of a parallelogram taken in order , find the value ofx and y ? |
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Answer» Like my answer if you find it useful! |
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| 21. |
2Verity ax (b + c) = (a x b) + (ax c) and writethe result for = 45,5-4 and c = 423Simplify:15 5 4 682 25 11XXX5subtract 1 from the sum of 2 and 3.f of the total number of students in aschool are boys, what fraction of the totalnumber of students are girls? If there are165 girls in the school, find the numberof boys. |
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| 22. |
Ir tan au, find the value of see .12 |
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Answer» tana=5/12=opposite/adjacentnowhypotenuse^2=opposite^2+adjacent^2hypotenuse^2=12^2+25^=144+25=169hypotenuse=13hencesecA=hypotenuse/adjacent=13/12 |
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| 23. |
ILULLIURE13. Ir 52x+1 + 25 = 125. find the value of x |
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| 24. |
ir-2IF3.-3=3, then find the value of x.2x |
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| 25. |
9. Ir-r- 42 = x + k) (x + 6). then find the value of k.Solution : |
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| 26. |
3. Find the terms of the expression 2x+3 |
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Answer» terms are 2x² , 3x and 1 |
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| 27. |
The sum of two algebraic expressions is 6x3-2xy +4y, if one of the expressions is4xy- 2y then find the other expression. |
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Answer» other expression= 6x^3 -2xy +4y^2 -4xy +2y^2= 6x^3 -6xy +6y^2 |
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| 28. |
2) For a field trip 4 students rode in cars andthe rest filled nine buses. How manystudents were in each bus if 472 studentswere on the trip? |
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Answer» Total number of students = 472Let number of students in each bus is n Then,9n + 4 = 4729n = 472 - 49n = 468n = 468/9 = 52 Number of students in each bus is 52 |
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| 29. |
2 ( 28 - 6 ) |
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Answer» 2(28-6)=2(22)=44is the value 2(28-6)=2×22=44 =2×28-2×6=56-12=44 |
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| 30. |
12 students participated in a quiz. There were 4 students in each team. Howmany teams were there? |
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| 31. |
5. The average age of 5 students is 10 years. A student aged 14 drops out, find the new averageof the remaining 4 students. |
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Answer» Average of 5 students is 10 years so total 10×5 = 50 years A student of 14 years drops out so remaining weight = 50 - 14 = 36 So average of 4 students = 36/4 = 9 years If you find this answer helpful then like it. Thanks thanks |
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| 32. |
Is P (0, 7) and Q (7, 0) represent the same point? |
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Answer» No, (0,7) and (7,0 ) are two different points. P is on y axis and Q is on x axis |
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| 33. |
Q.7. Factorize : (x-y)2-7(x2-y2)+12(x+y)2 |
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Answer» aree. yaar question Kya hai answer kya de rahe ho |
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| 34. |
find the LCM of the followingexpressions - 2228 and 22-5x46 |
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Answer» 2x^2-8=( x+4)( 2x-2); x^2-5x+6; x^2-3x+2x+6; x( x-3)+2( x-3); ( x+2)( x-3); x=-2, 3 1st term 2x^2-8=2(x^2-4)= 2(x-2)(x+2)2nd term= x^2-5x+6=x^2-3x-2x+6=x(x-3)-2(x-3)(x-3)(x-2)LCM= 2(x-2)(x+2)(x-3)= 2(x^2-4)(x-3) X=-2, 3 is correct answer |
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| 35. |
Simplify the expressions and find the value ir=-4.a) x4 (2x -7)2. |
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| 36. |
ite two expressions yire. Find the area.6 in.3 in.5 in.2 in. |
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Answer» correct answer is área. 👉22 area of rectangle = L × B = 6 × 3 = 18area of square =( a)2 = ( 2 )2 = 4 Total of area = area of rectangle + area of square = 18 + 4 = 22 (6×3)+(2×2)18+422 sq. inches. ans. |
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| 37. |
2: Parts of an ExpressionFind the terms of the expressions.A. xy + 29.K8i |
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Answer» A. terms are x²y and +2 B. terms are 3xy² and -7x²y |
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| 38. |
(A) 3cosec x +5cosec x cot x(B) 3cot2x+5cosec2x(C) -3cosec x- 5cosec x cot xThe derivative of 3cotx +5 cosec x w.r.t. x is:(A) 3cosec2x + 5cosec x cotx(B) 3cot x+5cosec x(C) -3cosec2 x-5cosec x cot x(D) of these |
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Answer» answer will be C....y=3cotx+5cosecx... |
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| 39. |
29/0/6 / y, /âg JC- a7 /7/_.7 oc - l + X |
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| 40. |
tan x + cot x = sec x . cosec x |
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| 41. |
How many silver coins, 1.75 cm in diameter and of thicklessa cuboid of dimensions 5.5 cm Ă 10 cm x 3.5 cm?illllb |
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| 42. |
ght a bag of rice for t 1120 and sold it for 2 28 tess, What was theof the bag of rice? |
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Answer» Original cost = ₹1120 Loss price = ₹ 28 Selling price = CP - Loss Selling price = ₹1120 - ₹28 = ₹1092 Please hit like if you find my solution useful thanks |
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| 43. |
6, In a classroom there are r rows. If each row has benches and each bench can accomn4 students, find the seating capacity of the classroom |
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Answer» Number of rows=xNumber of benches in each row=x/3Total benches=x*x/3=x²/3 Number of of students accommodate in 1 bench=4Number of of students accommodate in x²/3 benches=4*x²/3=4x²/3 |
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| 44. |
1. Where in the classroom does Wanda sit and why? |
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Answer» Wanda sits in the seat next to the last seat in the last row in Room Thirteen. She sits there because her feet are normally caked with dry mud and that corner of the classroom is usually dirty with mud. Plz mention which class and which chapter as all might not have the same syllabus... |
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| 45. |
Find the area of the shaded region in the givenfigure, where a circular arc of radius 6 cm hasbeen drawn with vertex of an equilateraltriangle of side 12 cm as centre and a sectorof circle of radius 6 cm with centre B ismade. (Use/3 1.73 and 3.14.]A,ICRSE 20141 |
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Answer» thanks |
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| 46. |
CBSE2043. Find the area of the shaded region in the givenfigure, where a circular arc of radius 6 cm hasbeen drawn with vertex of an equilateraltriangle of side 12 cm as centre and a sectorof circle of radius 6 cm with centre B is0made. [Use V3 1.73 and T 3.14.]CBSE 2014) |
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Answer» thank u bro |
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| 47. |
29.Prove that( cosec x+cot x)sin χsin x(cosec x-cotx) |
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| 48. |
SIONS OF BINOMIAL ANDTupel DETERMINING THE NUMBER OF TERMS IN THE EXPANSIONS OF AMEXPRESSIONSEXAMPURT Find the number of terms in the expansions of the following:(i) (2x - 3y)(ii) (1 +5.2 x) + (1 -52x)=1 |
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Answer» (i) ans=Answer: See a solution process below: Explanation: First, find the y-intercept:Setx=0and solve fory: (2⋅0)−3y=9 0−3y=9 −3y=9 −3y−3=9−3 y=−3or(0,−3) Next, find the x-intercept:Sety=0and solve forx: 2x−(3⋅0)=9 2x−0=9 2x=9 2x2=92 x=92or(92,0) We can next plot the two points on the coordinate plane: graph{(x^2+(y+3)^2-0.075)((x-(9/2))^2+y^2-0.075)=0 [-20, 20, -10, 10]} Now, we can draw a straight line through the two points to graph the line: graph{(2x - 3y - 9)(x^2+(y+3)^2-0.075)((x-(9/2))^2+y^2-0.075)=0 [-20, 20, -10, 10]} ( 2x - 3y )^9 = (9C 4)(2x)^6(3y)^3= (216) (64x^6)(27 y^3)= 373, 243( x^6)( y^3) |
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| 49. |
cosec x (cosec x +cot x) dx |
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| 50. |
cosec x cot x dxcosec x+ Cvil |
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Answer» cosec(x) = 1/sin(x), and cot(x) = cos(x)/sin(x) . So, cosec(x)cot(x) = cos(x)/sin^2(x). ∫cos(x)/sin^2(x) dx : substitute sin(x) = u, du/cos(x) = dx. Substituting in, we have ∫u^(-2)du = -u^(-1) + C. Since u = sin(x), we have that ∫ = -1/sin(x) + C, or ∫ = -cosec(x) + C. |
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