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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. |
EXERCISE 6.2In Fig. 6.28, find the values of x and y and thenshow that AB II CD1.5013 |
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Answer» Thank you for helping me |
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| 2. |
Sum of the reciprocals of a man's age (in years) 5 years ago and 4 years from now is29190Find his present age. |
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Answer» Let the man's age be AHis age 5 years ago will be A - 5His age 4 years from now will be A + 4 [ 1 / (A - 5) ] + [ 1 / (A + 4) ] = 29 / 190[ (A + 4) + (A - 5) ] / [ (A - 5)x(A + 4) ] = 29 / 190(2A - 1) / (A² + 4A - 5A - 20) = 29 / 190190 x (2A - 1) = 29 x (A² + 4A - 5A - 20)380A - 190 = 29 x (A² - A - 20)380A - 190 = 29A² - 29A - 580380A + 29A - 190 + 580 = 29A²409A + 390 = 29A²29A² - 409A - 390 = 0 By solving equation , A = 15 years |
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| 3. |
3. Find: () PTO(iii) ESUT(ii) ZOTU045iv) RU200Fig. Q. 13 |
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of5, How old is Ramesh, if 10 years ago he was 25 years old? |
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Answer» let present age be xthen 10 years ago his age=x-10sox-10=25x=25+10=35Ramesh is 35 years old |
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| 5. |
The population of a city increasedby 20% over a period of 5 years and stands at 18,00,000today. Find its population 5 years ago.e) i |
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| 6. |
4 The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5 yearsnow isFind his present age. |
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| 7. |
ent ages.(CBSE2008)Five years hence, a man's age will be three times theage of his son. Five years ago, the man was seventimes as old as his son. Find theirpresent ages |
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| 8. |
The age of a man is twice the square of the age of his son. Eight yearshence, the age of the man will be 4 years more than three times theage of his son. Find their present ages.ICBSE 2009C |
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Answer» Let the sons'age be = x father's age = 2x^2 8 years later... son = x+8 Father = 2 x^2 +8 Since the difference between father and son age is 4. According to question, 2x^2 + 8 - 3 ( x+8) = 4 2x^2 + 8 - 3x - 24 = 4 2x^2 -3x - 20 = 0 2x^2 + 8x - 5x - 20 = 0 2x ( x +4) -5 (x+4) = 0 (2x-5)(x+4) = 0 x+4 = 0 x = -4 ( age cannot be negative so we leave out the negative sign ) so son's age is 4. father age = 2x^2 = 32 answer |
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| 9. |
\lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}, a+b+c \neq 0 |
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Answer» lim x--> (ax²+bx+c)/ (cx²+bx+a)put x = 1(a+b+c)/ (a+b+c) = 1. |
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| 10. |
A = \left[ \begin{array} { c c } { 3 } & { 6 } \\ { 5 } & { - 4 } \end{array} \right] \cdot B = \left[ \begin{array} { c c } { 7 } & { 8 } \\ { 5 } & { 6 } \end{array} \right] \Rightarrow 2 A + 3 B = |
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| 11. |
A triangle with integral sides has perimeter 8 unitsThe area of the triangle is____sq u1) 2(2) 2√2(4) 3(3) 3√2 |
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Answer» Let integral sides of triangle be a, b, c a + b + c = 8 => a + b = 8 - c => sum of 2 sides a+ b = 8–1 =7 a+ b = 8 - 2 = 6 a + b = 8- 3 = 5 a+ b can not be 4, 3, 2, or 1 ( as the sum of 2 sides > third side) . & perimeter given is 8. Out of sums given above, only possible sum will be 6 or 5 Reason: If sum a+ b = 7 , sides a, b, c are to be 6, 1, 1 or 5,2 , 1or 4, 3, 1 which are not possible. As the sum of any 2 sides of a triangle > third side. If a + b = 6, sides a,b,c are to be 5,1,2 or 4, 2, 2 or 3,3,2 . First 2 triplets won't be possible. The same reason as given above. If a+ b = 5, sides a,b,c are to be 4, 1, 3 or 3, 2, 3 . Here first triplet is not possible. Similarly the sum a+ b won't be equal to 4, 3, 2, & 1 as the sum of 2 sides should be > third side So, finally the sides of triangle are3, 3, 2 It will be an isosceles triangle with equal sides 3 & base = 2 So perpendicular length from the vertex to the base = √( 3² - 1²) = √8 ( as perpendicular will bisect the base) Area = 1/2 * base * altitude Area = 1/2 * 2 * √8 =√8 =2√2 unit² I di d not understand I di d not understand |
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| 12. |
10. Three sides of a triangle are (2x + y) units, (3x - y) units and (x + 3y) units.perimeter. |
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Answer» Perimeter = Sum of sides = (2x + y) + (3x - y) + (x + 3y) = (6x + 3y) units Perimeter is the sum of all sideshence=(2x+y)+(3x-y)+(X+3y)=6x+3y units (6x+3y ) is the correct answer of the given question |
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| 13. |
NCERerfect square ? If not, find the smallcomesPage No.:youvaDateSubtract at 2b-cfrom 2a73b +6 |
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| 14. |
O years ago, age of B was 10 times of theage of C. If ratio of their present ages is 4: 1. What is the age of B at present ?(1) 10 year(3) 60 year(5) of these [R.O. 1989, RRB 2008]12. 1(2) 40 year(4) 80 year |
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Answer» (B-10)=10(C-10)B-10=10C-100B-10C=-90B/C=4/1B=4C4C-10C=-90-6C=-90C=15so.B=4×15=60 |
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7. Find all the zeros of the polynomialand-2- 34x? - 4x+120, if two of its zeros are 2ICBSE 2008) |
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| 16. |
3.Five years ago, a man was seven times as old as his son, while five year henceman will be four times as old as his son. Find their present age., themult |
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| 17. |
Five years ago, a man was seven times as old as his son, while five year hence, theman will be four times as old as his son. Find their present age3.multipli |
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| 18. |
Four years ago the father 3 times the age of his son. At present the sum of father's age and son's age is 56 |
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Answer» The answer is 172 years old the answer is 172 years old the answer is 172 years old |
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| 19. |
55. If b cos θ-a, then prove that cosec θ + cot()[CBSE 2015]b+ a1-cos θa12 |
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| 20. |
Find the angle between Y-axisand the line yx- |
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| 21. |
\lim _{n \rightarrow \infty} h a\left[a^{h}+a^{2 h}+a^{3 h}+\dots+a^{nh}\right] |
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| 22. |
\lim _{x \rightarrow 2} \frac{x^{n}-2^{n}}{x-2}=80and if n is a positive integer, find n |
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| 23. |
\lim _ { x \rightarrow 2 } \frac { x ^ { n } - a ^ { n } } { x - 2 } = 80 \text { and } n \in N , \text { find } n |
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| 24. |
34. If one small square in the grid isof area 4 sq, units, what is theperimeter of the rectangle drawn onthe grid?(1) 12 units(2) 32 units(3) 8 units(4) 24 units |
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11. If the area of four walls is 256sq.units and the ratio of its perimeter to its height is1) Perimeter 8 units3) Length-6 units2) Height of the room32 units4) Width 4 units |
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Answer» Let height =xGiven area=256 cm squareA.t.q.Length=5(height)L=5xBreadth=3(height)B=3x Curved surface area of cuboid= 2(l+b)hGiven area=256 cm square2(5x+3x)×x=2562(8x)×x=256 16x^2=25616x^2-256=0Taking 8 common8(2x^2-32)=02x^2-32=0By factorization2x^2+0x-32=02x^2+8x-8x-32=0Taking common2x(x+4)-8(x+4)=0(x+4)(2x-8)=0x+4=0,,,,,2x-8=0x=-4,,,,,x=4Sides can't be -ve so x=4Height=4cmLength =5xLength=5×4=20Breadth=3xBreadth=3×4=12L=20B=12H=4 |
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The ages Of A and B are in the ratio 4:3. Eight years ago, their ages we7. Find their present ages.3. Eight years ago, their ages were in the ratio 10: |
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| 27. |
Product of Pragati's age 2 years ago and 3years hence is 84. Find her present age. |
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| 28. |
4. The sum of the reciprocals of Rehman's ages, (in years) 3 years agonow isFind his present age. |
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Answer» Rehman is half year old |
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| 29. |
Practice Set 2.6Product of Pragati's age 2 years agoand 3 years hence is 84. Find her present a |
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Answer» suppose present age of pragati is x so (x-2)(x+3) = 84 x*x + x -6 = 84 x*x + x - 90 = 0 (x+10)(x-9) = 0 x=-10 or 9 |
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488Secondary School Mathematics for Class 1015. In the given figure, a circle with centre O,is inscribed in a quadrilateral ABCD suchthat it touches the side BC, AB, AD andCD at points P, Q R and S respectivelyIf AB 29 cm, AD = 23 cm, <B-90, andDS=5cm then find the radius of thecircleICBSE 2008, 13]16. In the given figure, O is the centre of thecircle and TP is the tangent to the circle froman external point T. If 4PBT 30, prove thatBA: AT 2:1.30[HOTS! [CBSE 2015]바 --0--h |
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Answer» Please specify the question that needs to be answered and post again |
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| 31. |
Practice Set 2.6uct of Pragati's age 2 years ago and 3 years hence is 84. Find her present age. |
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Answer» Answer: present age of Pragati = 9 years Step-by-step explanation: Let at present: Pragati age = x years 2 years ago: Pragati age = (x-2) years After 3 years: Pragati age = (x+3) years according to the problem given, Product of ages = 84 => (x-2)(x+3)=84 => x(x+3)-2(x+3)=84 => x²+3x-2x-6-84=0 => x²+x-90=0 Splitting the middle term,we get => x² +10x-9x-90=0 => x(x+10)-9(x+10)=0 => (x+10)(x-9)=0 => x+10=0 Or x-9 = 0 => x = -10 Or x = 9 Now, age should not be negative. Therefore, present age of Pragati = 9 years •••♪ |
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- . -4.7The sum of the reciprocals of Rehman's ages. (in years) 3 years ago and 5 years fromx+4 X-7 30now is Find his presente |
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Answer» abhi time nhi hai baad me bataunga |
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circle.ICBSE 2008, '13]16. In the given figure, O is the centre of thecircle and TP is the tangent to the circle froman external point T. If <PBT-30, prove thatBA: AT 2:1.[HOTS] [CBSE 2015] B2015 B30 |
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Answer» thanks |
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| 34. |
Q.18If the sum of zeroes of the quadratic polynomial 3x? - Kx + 6 is 3 then find the value of K.(CBSE 2008, 1 |
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Answer» k=-11 what is the ans. k=-11 thats the right answer |
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a+Ob-1=02(1)+ + 1-0bb3Hence, the required values are a 1 and b-3.TEST YOUR KNOWLEDGE 4.2T ANSWER TYPE PROBLEMSIs x =-3, a solution of the equation 2x2 + 5x + 3 = 0?Is --4, a solution of the equation 2x2+5x -12-0?Show that x =-3 is a solution of x2 + 6x + 9 = 0CBSE 2008[CBSE 2008]CBSE 2008]CBSE 2008)Showthat x =-2 is a solution of 3x2 + 13x + 14 = 0.Ifone root of the quadratic equation, 2x2 +kx -6 0 is 2, find the value of k.WER-I TYPE PROBLEMSmine if x = 3 is a root of the equation given below:242 -14x + 16. |
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Answer» Thanks |
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| 36. |
12. Fifteen years from now Ravi's age will be four times his present age. What is Ravi'spresent age? |
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| 37. |
14. How old is a man whose age fifteen years ago was two-fifths of what it will be in6 years? |
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| 38. |
i ulem2. Fifteen years from now Ravi's age will be four timpresent age?avi sage will be four times his present age. What is Ravi's |
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| 39. |
11. Evaluate: |
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| 40. |
Uwes uuring last year?3. A number exceeds 37684955 by 3615045. What is that number? |
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| 41. |
Consider the equation below.$(24 – 16x) = -3 (18x – 27)How many solutions does the equation have?Aone, x = 0Bone, x = -2Cno solutionsDinfinitely many solutions |
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Answer» infinitely many solutions |
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Which one of the following options is true, and why?y=3x+5 has0) a unique solution, (ii) only two solutions, infinitely many solutionsWrite four solutions for each of the following situationsPiarsa |
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Answer» Hi |
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| 43. |
. How many solutions are there for equation y x+2? |
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Answer» y = x + 2 is a linear equation in two variables .So , it has infinitely many solutions there are infinite answers for this question thank you😊 |
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| 44. |
के... 11- Evaluate Z + 3)£l दर |
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| 45. |
The magnitude of the resultant of two vectors of magnitudes 3 units and 4 units is 5 units. Whatis the angle between the two vectors?(a) 즈42(c) 34(d) π |
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| 46. |
1. 100 gm of butter make 14 cakes. How many cakes will 150 gm make? |
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Answer» 21 cakes trust me I'm correct |
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| 47. |
(3) 630 = 7(4) 200 - 150 = 5 x(5) 1 kg - 550 gm = |
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Answer» 3- 904- 106- 450 gm 3)904)106)450g is the right one 3)904)106)450gmis right answer (3)-ans-90(4)-ans-10(5)-ans-450 (3) 90(4) 10(5) 450gm 3) 90 -divide 630 with 74) 105) 450 4) 105) 450 3- 90 4-10 5-450 3- 904-1006-450gram answer 3-4-53-904-105-450gm (3)=90. (4)=10. (5)=450gm yhi sahi answer hoga 3)904)106)450g is correct answer 3- 90. 4-10. 5- 450gm 90*7=6305*10=50450gm |
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9.If potential at the surface of uniform sphere of mass M and radius R is zero. Then(a) potential at its centre would be(b) potetintial at infinity would be(c) potential at centre would be(d) potential at infinity would beGM2RGMGMGM |
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Answer» potential at infinity would be GM/R |
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\lim _ { x \rightarrow 1 \atop y \rightarrow 2 } \frac { 2 x ^ { 2 } y } { x ^ { 2 } + y ^ { 2 } + 1 } |
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| 50. |
\lim _{x \rightarrow 2} \frac{x^{2}-4}{\sqrt{3 x-2}-\sqrt{x+2}} |
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