Explore topic-wise InterviewSolutions in Current Affairs.

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.

SL00EL १७15 0८0८ & जी [ gकुकी ey afng o 1 Jf pangy e 03] 1§ e lng) g के ८

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In series 120, 320, ? , 2070, 5196, 13007.5

Difference between successive terms is given by

320 = 120*2.5 + 20

So, Third term= 320*2.5 + 20= 160*5 + 20= 820

2.

10. By taking the values of a, b and c as 60, -10 and 2 respectively verify that:(a+b)+c+a+(b+c)

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3.

03Subtract the sum ofatom ( 31032 and 878

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4.

PROSESS CHCWrite an expression that represents theperimeter of the figure and simplify.2.0cmcm

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Perimeter is sum of all sideshence2/3x+x+1/X+6/x^2

5.

3. Au we prout OI (-16) Du wywy4. By what number should (-240) be divided to obtain 16?100

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Let the no be xSo-240/x=16-240=16xX=-240/16X=-15 ans.

let that no is x -240/x=1616x= -240x= -240/16= -15that no is -15

suppose _no is x,

-240/x = 16

-240 = 16 x

x = -240/15x = -15

the correct answer of this question is -15

6.

34. The figure below represents halfculindrical solid whose dimensionshown. What is the surfacearea?14 cm014 cm

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7.

then by chain rule find the value ofx—+ y—au +Z X 5ox "oy oz<“ का मान ज्ञात कीजिए।32. fu= [i‘yz 5 u- 5) हो तो श्रृंखला नियम से » _-+.]) oyयदि हा [¥y

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8.

B SRS I R 8- Y WY NS e - i Qua-32 Jrx?+gx4+5¥2=0Qua-33 :23 _ga x4+l = (2Qut —3% 2 30 = (20 =0Salve,QuL-3S

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9.

1. Express11) 20N40as a rational number with denominator(ul) -30THAI 35hdenomina

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10.

3x - 15x + 102x - 5Value: 33Find x

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3x-15+x+10+2x-5, 5x=15+5-10; 5x=10; x=10/5=2

3x-15+2x-5+x+10=180; 3x+2x+x+10-20=180; 6x=180-10=170; x=170/6=28.333

11.

उदाहरण 30 सिद्ध कीजिए कि AU B = AOB का तात्पर्य है कि A = B .

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AUB= all NUMBERS, A(~)B= different A

isme bahut mehnat ki hai please like to Kar do

AUB=all numbers,A(~)B=different A

12.

(C.B.S.E. 2005)25. The base BC of an equilateral triangle ABC lies on v-axis. The coordinates of point care(0-3). If the origin is mid-point of the base BC, find the coordinates of the points A and B.(C.B.S.E. 2005)

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fg

13.

12. A solid right cone and a solid hemisphere have the same base. The volume of the cone is doublehat of the hemisphere. Find the ratio of the height of the cone and the diameter of theemisphere.3) 2:14)3:1

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Volume of hemisphere=2/3*pi*r^3Volume of right cone = 1/3*pi*h*r^2

2Vh = Vc(Vh = volume hemisphere, Vc = volume cone)

4/3*pi*r^3=1/3*pi*h*r^2multiply by 3

4pi*r^3=pi*h*r^2

If they have the same base, their radii are the same. dividing both sides by pi*r^2 yields

4*r=h

2r=diameter, so r=d/2

4*d/2=h

2d=hhence ratio is 1:2

14.

Find the volume of a cylinder whose height is 10 cm and radius of base i5cm (π = 3.14)E.(

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given h=10cmr=5cmV=(pi)r^2 hV=3.14×5×5×10V=785cm cube

15.

Find the radius of the cylinder whose height is 15 cm and total surface area is 968 cm square

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16.

M.d. Calculate (i) the(b) The glven figure represents a hemisphere surmounted by a conical cone of wooheight of cone (ii) volume of the solid iii) surface area of solid. (6)

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17.

onthsnbase but on opposite sides. If volume of the solid is 32/3 Tt c.c. eland height oExample 7. A solid is made by joining a hemisphere and a conecone is 4 cm. Then find the base radius

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Let the required radius be rVolume of hemisphere+ Volume of cone = Volume of the solid⇒2/3​πr3+ 1/3​πr2h = 32/3​π⇒2r3+ 4r2= 32⇒r3+ 2r2= 16⇒r3+ 2r2- 16 = 0By replacing r with 2,we get the resultant as 0Therefore, the required radius is 2cm

18.

Show that the line segment joining the midpoint of the opposite sides of quadrilateral bisect each other

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19.

(ii) y- 9-216(v)10r- 30(vi)16-15x(xi) = 12(xiv)-8-1ions:(i) 81+5-21-31(v) 2x -1-14-

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y-9=21y=21+9y=30.

20.

eral Mathematics :rite the reciprocal of a35nd the value of : 22 +33 +43.mplify : 8r - 10r²+ 6r:Ive the equations.7+ 5y - 3x

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the answer is 4r and it's power 3

4r³ is the correct answer of the given question

21.

(p^2+6pq+9q^2-9r^2)

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use (a+b)^2= a^2+b^2 +2abso given eq reduce to(p+3)^2 - 9r^2so (p+3-3r)(p+3+3r)

22.

13. Find the equation of the circle passing through (0,0)and making intercepts a and b on the co-ordinate axes.

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The circle intercept the co-ordinate axes at a and b. it means x - intercept at ( a, 0) and y-intercept at (0, b) .

now, we observed that circle passes through points (0, 0) , (a, 0) and (0, b) .

we also know, General equation of circle is x² + y² + 2gx + 2fy + C = 0

when point (0,0) (0)² + (0)² + 2g(0) + 2f(0) + C = 00 + 0 + 0 + 0 + C = 0 C = 0 -------(1)

when point (a,0) (a)² + (0)² + 2g(a) + 2f(0) + C = 0a² + 2ag + C = 0from equation (1) a² + 2ag = 0 a(a + 2g) = 0g = -a/2

when point ( 0, b)(0)² + (b)² + 2g(0) + 2f(b) + C = 0b² + 2fb + C = 0f = -b/2

now, equation of circle is x² + y² + 2x(-a/2) + 2y(-b/2) + 0 = 0 { after putting values of g, f and C }x² + y² -ax -by = 0

23.

(15)4331/(Set : B)Find the shortest distance between the lines:7-(i +2) +k) +af-j-k) and37OR

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24.

7oo sweets in the ratio 9 : 7 : 4. How many sweea wire of length 88 cm is cut into three pieces. The lengths of the pieces are in the rato2:3.6.Find theth of the (1) shortest piece (i) longest piece.

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wrong

25.

4. What will be the volume of a cylinder whose height h is equal to its radius?

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volume = πr²hwhen h= rit will be πr³

26.

the distance of the boat from the foot of lightAt a distance 2h meter from the foot of a tower of height h metre the top of the towerand a pole at the top of the tower subtend equal angles. Find the Height of the poleTouse5A house subtends a ri

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27.

very Snort Answer Type Questo1. Find the perpendicular distance of A(4.5, 13) from the Y-axis

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Perpendicular distance from y-axis = x coordinate of the pointGiven x coordinate of point is 4.5,Therefore, perpendicular distance of point A(4.5,13)from y-axis is 4.5

28.

The ratio of the measures of the sides of a triangle is 9:7:3. If the perimeterof the triangle is 266 inches, find the length of the shortest side. Show all work

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9 : 7 : 3Total units = 19 units19 u = 266 inches1 u = 266 / 19 = 14 inchesShortest side = 3 u3 u = 14 x 3 =42 inches

29.

13. Find the equation of the circle passing through (0,0)and making intercepts a and b on the co-ordinate axes.d br the intercents made by the circle on the co

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The circle intercept the co-ordinate axes at a and b. it means x - intercept at ( a, 0) and y-intercept at (0, b) .

now, we observed that circle passes through points (0, 0) , (a, 0) and (0, b) .

we also know, General equation of circle is x² + y² + 2gx + 2fy + C = 0

when point (0,0) (0)² + (0)² + 2g(0) + 2f(0) + C = 00 + 0 + 0 + 0 + C = 0 C = 0 -------(1)

when point (a,0) (a)² + (0)² + 2g(a) + 2f(0) + C = 0a² + 2ag + C = 0from equation (1) a² + 2ag = 0 a(a + 2g) = 0g = -a/2

when point ( 0, b)(0)² + (b)² + 2g(0) + 2f(b) + C = 0b² + 2fb + C = 0f = -b/2

now, equation of circle is x² + y² + 2x(-a/2) + 2y(-b/2) + 0 = 0 { after putting values of g, f and C }x² + y² -ax -by = 0

30.

Showline segment is the shortest.that of althat of all line segments drawn from a given pount not on it, the perpendicular

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Diagram for the question

We have a straight line AB.Take a point P not on AB, but some distance away. We draw PC the perpendicular on to AB meeting AB at C. We draw another line from P to D, where D lies on AB. We show that PD > PC, for any point D other than C.

In the triangle PCD, use the Pythagorean law for sides:PC² + CD² = DP²

Since CD² is positive and adds to PC², PC²+CD² > PC²Hence DP² > PC²

So DP > PC

SO PC, the perpendicular distance from an external point to a line segment, is the shortest

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31.

4.If the points (a, 0), (0, b) and ( l, l) are collinear then prove that-+-= 1 .

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32.

rnih terrn ofan А.Đ. is (2n+] ), what is the nmof its tirst three terms?

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The sum of n terms in an AP is given bys= n/2(2a+(n-1)d)wheres = sum of progressionn = number of termsa = value of first termd = difference between 2 terms

now, the first term in your question is 3 (2 x 1 + 1)so, a = 3second term is 5

third is 7, like that

so d = 2

Therefore, the sum of first n terms of the AP will be

n/2 [2 x 3 + (n-1) 2]simplifying, we get the sum as

n [3+n-1]

n (n+2)Hencen=33(3+2)=3*5=15

33.

TRIANGLES6.Show that of all the segments drawn from a given point not on it, the perpendicular line segment is theshortestTYERCISE 7.5 (Optional)*

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34.

Two parallelograms are on the same base and between the same parallels. The ratio oftheir area is

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35.

Find the area of the shaded part2. Find10 cmFind the area of the combined figjoining of two parallelograms.

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area of circles is 22/7×5×5=78.5714 is the right answer .....

78.5 is the right answer.....

the correct answer is 78.5

36.

5. What will be the ratio of areas of the two parallelograms which lie on same base and between thesame parallels?

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37.

A number p= a^2bq ,q=aqb a and b are prime number then prove l.C.m and h.C.f= pq

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lcm = a²bq

hcf = abq

38.

For the given shapes, which oneof the following statements is notcorrect?(1) Two of them are rhombuses.(2) Two of them are rectangles.(3) All are parallelograms(4) One of them is not aparallelogram

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two of them are rhombus (false) as one is kite shaped

39.

3. Draw AABC. Produce BA to X such that AX = AC. Join XC to show that BC < BX.

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thank you

40.

ar(AQC) ar (PBR).急. Diagonals AC and BD of a quadrilateralABCD intersect at O in such a way, thatar (AOD)- ar (BOC). Prove that ABCD is atrapezium.

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41.

Two parallel lines are crossed by a transversalWhat is the value of x?x=40x 70) x= 110x = 130

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42.

1. Every term of an infinite GP is thrice the sum of all the successive terms. If the sum of first two terms is 15, tthesum of theGP is-(A).20(B) 16(C) 28(D) 30

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no your answer is wrong

43.

22If the secood term of a GP is 2 and the sum of infinite ternes is &, then the tirst term is2) 6

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44.

In Fig. 10.39, A, B, C and D are four points on acircle. AC and BD intersect at a point E suchthat BEC 130° and Z ECD 20. FindLBACFig. 10.38130Fig. 10.39

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45.

SUBJECT6Solue the falling20-74 = 2834 d1-50 45111 =is2-60

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cghjpuyttfrbbhhjhjhhh

9x/7-6x=159x=105-90x90x-9x=10581x=105x=105/81x=35/27

2x-7x/1-5x=3+7x/4-5x-5x/1-5x=3+7x/4-5x-20x+25x*2=3-35x*235x*2+25x*2-20x-3=060x*2-20x-3=0

20+_√400-720X=--------------------------- 2×60

X=20+_√-320 --------------- 120 I hope it will help you👉👉👤

46.

Fig. 10.445. In Fig. 10.45, A, B, C and D are four pointson a circle. AC and BD intersect at a point Esuch that BEC = 130° and ECD = 20°Find Z BAC130Fig. 10.45

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Tq u

47.

Fig. 10.445 In Fig. 10.45, A, B, C and D are four pointson a circle. AC and BD intersect at a point Esuch that L BEC = 130° and < ECD = 20°.Find Z BAC130Fig. 10.45

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48.

square.From the given figure, prove that(i) BX AP2(i) AP + CR 2BQP is the mid-noint of the side AB of a19

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we know that sum of parallel sides is equal to twice of the line joining the mid points of non parallel sides.

you can use the mid point theorem and its conversefor solving the question.in triangle ACP,X is mid point of PC [converse of mid point theorem]also BX =1/2 AP [mid point theorem].(1)​similarly by using both theorems in triangle CRP,we can proveXQ=1/2 CR .(2)(1)+(2)= BX +XQ= 1/2(AP+CR)​this implies AP+CR=2 BQ

49.

In Fig.9.28, AP ||BQI| CR. Prove thatar (AQC)=ar (PBR).

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50.

So the remainder obtamil UITSo, 2t + 1 is a factor of the given polynomial q(t), that is a20+ 1.EXERCISE 2.31. Find the remainder when x' + 3x2 + 3x + 1 is divided by(1) x+1(ii) x-5(iii) x(iv) x+

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