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.

What is a logic gate? Name the three basic logic gates.

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Logic gatesperformbasic logicalfunctions and are the fundamental building blocks of digital integratedcircuits.

Mostlogic gatestake an input of two binary values, and output a single value of a 1 or 0.

These gates are the AND, OR, NOT,NAND, NOR, EXOR and EXNOR gates

deeply 🤗

2.

Hence, the Shake ts CtugaExample 35 A pole has to be erected at a point on the boundary of a circular park of diameter13 metres in such a way that the differences of its distances from two diametricallyopposite fixed gates A and B on the boundary is 7 metres. Is it possible to do it so? Ifyes, at what distances from the two gates should the pole be erected?

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Thank you so much but the question is "At what distances from the two gates should the pole be erected? "One is 5 m but what will be the other distance??

3.

15Use the angle sum property to prove that\angle A C D=\angle C A B+\angle A B C

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4.

८ है 1९4३ 2% ४ 9 ६2९4९] 1941:(० [8 0६ 1814 है 241० 24 ४ [2013 0४RoL (¢ [9 006 1ढ1% 216 9189 12॥24 9 24% ४ २०७३५ 0] 24%1- (५० [90 09 9106 फि "08

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Subhash can copy 50 pages in 10 hours.That means in 40 hours he can copy 50×4=200 pages.

Subhash and prakash together can copy 300pages in 40 hours.

That means prakash alone can copy 300-200=100 pages in 40 hours.

So to copy 30 pages prakash will take 40/100 ×30 = 12 hours.

5.

In a hexagon ABCDEF, side $ A B $ is a parallel to EF and $ \angle B : \angle C : \angle D : \angle E=5 : 4 : 2.1 $Find $ \angle B, \angle C, \angle D $ and $ \angle E $ .

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As AB || FE, FA becomes the tranversal line cutting parallel lines. So angle A + angle F = 180°.

sum of other four angles = 720° - 180°= 540°.So 6 x + 4 x + 2 x + 3 x = 15 x = 540°.x = 36°.

Angles B C D E are: 216°, 144°, 72°, 108°

6.

In a hexagon ABCDEF, side $A B$ is a parallel to EF and $\angle B : \angle C : \angle D : \angle E=5 : 4 : 2 : 1 .$Find $\angle B, \angle C, \angle D$ and $\angle E$ .

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As AB || FE, FA becomes the tranversal line cutting parallel lines. So angle A + angle F = 180°.

sum of other four angles = 720° - 180°= 540°.So 6 x + 4 x + 2 x + 3 x = 15 x = 540°.x = 36°.

Angles B C D E are: 216°, 144°, 72°, 108°

7.

\begin { equation } \begin{array}{r}{29} \\ {+\quad 21} \\ \hline\end{array} \end { equation }

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29 + 21 = 50

50 ......................

8.

By use of definition of limit, show that u 2x+3)-1

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9.

का खनिकलनन रा +By6X118

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x^3 + 3x^2 + 6x + 18= x^2(x + 3) + 6(x + 3)= (x^2 + 6)(x + 3

10.

\left( \begin array c c 2 & 3 \end array \right) \left( \begin array r r 1 & 2 \\ - 3 & 0 \end array \right) \left( \begin array l x \\ 3 \end array \right) = 0

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11.

\left| \begin{array} { r r r } { 1 } & { 2 } & { 9 } \\ { 2 } & { x } & { 0 } \\ { 3 } & { 7 } & { - 6 } \end{array} \right| = 180

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it's matrices

12.

ABC is a triangle right angled at C if AB=25 cm and AC =7 cm.find AC

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Using pythagoras theorem

(AB)²=(BC)²+(AC)²(25)²=(BC)²+(7)²625=(BC)²+49(BC) ²=625-49(BC)²=576BC=24

C is a right angleso AB^2=AC^2+BC^2BC^2=625-49=576so BC=24 cm

13.

In triangle ABC ,AB=5 ,AC=7 and x>BC>y find value of x and y

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14.

A = \left[ \begin{array} { r r r } { 3 } & { - 4 } & { 5 } \\ { - 6 } & { 7 } & { - 8 } \\ { 9 } & { 0 } & { x } \end{array} \right]

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15.

An almirah is sold at5,225 after allowing a discount of 5%. Find itsmarked p

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Marked Price = selling price/(1- (discount)/100)MP = 5225/(. 95)=5500

16.

17. Maximum exterior angle possible for a regularpolygon isa) 120(e) 360(b) 270*(d) 450°

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Answer:a)120°

17.

measure of each exterior angle of regular polygon of 12 side isA.20°B.15°C.30°D.168°

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Sum of all angles of regular polygon is 360Measure of each exterior angle =360/12 =30

thsnks😀😁😂

18.

( x + y ) p _ { 2 } = 56 \text { and } \quad ( x - y ) p _ { 2 } = 12 , \text { find } x \text { and } y

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19.

The volumeofarightcircularcone is 9856 cm. If the diameter of the base is 28 cmfind0) height of the cone(ii curved surface area of the done"(ii) slant height°ftheaofthedone

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20.

A semicircular sheet of diameter 28 cm is bent to make a conical shape. Findthe volume of this cone so formed.18.

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21.

A serni-circular sheet of metal of diameter 28 cm is henl into an open couical cup.Find the depth and capacity of the cup

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Radius, r = 14 cmCircumference of semi circle = πr= (22/7) x 14 = 44 cmThis becomes circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cmThe radius of semi circular sheet = slant height of conical cupThat is l = 7 cmWe know that r2+ h2= l2142+ h2= 72196 – 49 = h2h2= 147Therefore, h = 7√3 cmThat is depth of the conical cup is 7Ö3 cmCapacity of cup = (1/3)πr2h = (1/3) x (22/7) x 72x 7√3 = 622.37 cu cm

22.

A semicircular sheet of diameter 28 cm is bent to form an openconical cup. Find the capacity of the cup. (Use sqrt 3 1.732.)

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diameter =d = 28 cmRadius= r = 14 cmCircumference of semi circle = πr= (22/7) x 14 = 44 cm

so the circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cm

The radius of semi circular sheet = slant height of conical cupwhich isl = 7 cmAs,r2+ h2= l2

142+ h2= 72

196 – 49 = h2

h2= 147

hence; h = 7√3 cm

depth of the conical cup= 7√3 cm

Capacity of cup = (1/3)πr2h

= (1/3) x (22/7) x 72x 7√3

= 622.37 cu cm approx

23.

10 A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. Determine thdepth and capacity of the cup.

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Slant height of the conical cup, 'l' = radius of the semi-circular sheet, R = 14 cmLet radius and height of the conical cup be 'r' and 'h' respectively.Circumference of the base of the cone = Length of arc of the semi-circleOr, 2πr = (1/2)2πROr, 2πr = (1/2)(2π)(14)Or, r = 7 cmNow, we know that l² = h² + r²(14)² = (h)² + (7)²h² = 196 - 49h =√147Height or depth of the conical cup = 12.124 cmNow, capacity of the conical cup = 1/3πr²h= 1/3*22/7*7*7*12.124= 13069.672/21Capacity of the conical cup = 622.365 cu cm

24.

2. Using opposite angles test for parallelogram, prove that every rectangle is a parallelogra

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Firstprovethat ABM ≡ CDMusingthe SAS congruencetest. (alternateanglesare equal): Hence ABCD is aparallelogram, because one pair ofoppositesides are equal and parallel. ... Hence ABCD isrectangle, because it is aparallelogram withone rightangle.

25.

9. The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelograis 60°. Find the angles of the parallelogram.

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26.

What is the value of z in the figure shown below?3.6 3.6X1183.8 3.8

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x=30°(alternate angle)

27.

निम्नलिखित बहुपदों के सम्मुख अंकित मान बहुपद के शून्यक है, सत्यापित कीजिए।(i) p(x) = -1; 3 = 1, -1 (i) p(*) =2x+1; 3=-(iii) p(31) = 4x +5;=(iv) p(x) = 33; 3 = 0(v) p(3) = (x-3)(x+5); x=3, -5(vi) p(3) = ar+b; x =-(vi) P(x) =3x’ -1; 3=-६६(vi) p(५) =3x+2; ४====\

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i) x^2-1; x=1, -1; (1)^2-1=1-1=0, (-1)^2-1=-1=1; (ii)2x-1; x=-1/2; 2(1/2)-1=1-1=0, (iii)4x+5; x=-5/4; 4(-5/4)+5=-5=5=0; (iv)3x^2; x=0; 3(0)^2=3(0)=0; (v)=( x-3)( x+5); x=3, -5; (3-3)(3+5)=0(8)=0; x=-5; (x-3)(x+5)=(-5-3)(-5+5)=('8)(0)=0;(vi)ax+b; x=-b/a; a(-b/a)+b=a(1/a)=0;

(vii); 3x^2-1; x=-1/V3; 1/V3; 3(-1/V3)^2-1=3(1/3)-1=0; 3(1/V3)^2-1=3(1/3)-1=0; p(x)=3x+2; x=-3/2; =3(-3/2)+2=0

28.

construct a parallelogram ABCD in which AB -5.2 cm, BC 4.7 cmand AC 7.6 cm.

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29.

\left(p^{4}+0 p^{3}-2 p^{2}+0 p+9\right) \div(p+3)

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30.

| x3 (x+p}} (xp)310. If x, y, z are all different a11. z are all different and yº (y + p)3 (y - p)31 = 0, prove that| 23 (2+ p)3 (2-p)3 |p2(x + y + z) = 3xyz.od koThen operat

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31.

- 3 p ^ { 2 } + 3 p q + 3 p x \text { from } 3 p ( - p - a - r )

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3p(- p - a - r ) - (-3p²+3pq+3px)-3p² -3pa -3pr + 3p² -3pq -3px-3pa-3pr-3pq-3px-3p(a+r+q+x)

thank you

32.

In the adjoining figure, r:y:z 5:4:6. If XOYis a straight line, find the values of x, y and z.zo

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5k+4k+6k=180;15k=180k=12Then the angles are x=5(k)=5(12°)=60° and y=4(k)=4(12°)=48° and z=6(k)=6(12)=72°

I

33.

2 p + \frac { 1 } { p } = y \quad p ^ { 3 } + \frac { 1 } { \gamma p ^ { 3 } } = ?

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2p+1/p=42p+1=4p2p=1∴p=1/2

p3+1/8p3=(1/2)^3+1/8(1/2)^3=1/8+1/ 8(1/8) =1/8+1=9/8

Bhai Apne to Google Ka ans paste kardiya

34.

4. What should be subtracted from 3x3 8x2+4r 3, so that the resulting expression hasx + 2 as a factor?

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-67 should be subtracted to make the polynomial have a factor (x+2)

35.

A shopkeeper sells an article at 12% loss. If2he sells it for Rs. 92.50 more then he gains,6%.What is the cost price of the article?A. Rs. 510C! Rs. 575B. Rs. 500D. Rs. 600

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Let cost price be CP

If article sold at loss of 12 1/2 %SP1 = CP(1 - 25/200)SP1 = 7CP/8

If article sold for Rs 92.50 more

7CP/8 + 92.50 = CP(1 + 6/100)53CP/50 - 7CP/8 = 92.50(212 - 175)CP/200 = 92.5037CP = 18500CP = 185000/37 = 500

(B) is correct option

and

36.

A shopkeeper sells 6 eggs for30. What would be the cost of 10 eggs?

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cost of 6 eggs=30cost of 1 egg=30/6=5cost of 10 eggs=5×10=50

37.

drilateral ABCD, the bisector of ZC andLD intersect at OProve that 2COD =-(ZA + 2B)

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Angle COD= 180°- 1/2angle C-1/2 angle D=180°-1/2(angle C+D)----------(1)

Angle (A+B+C+D)=360°

AngleC+D= 360°- AngleA- angle B--------------(2)

Substituting (2) in (1)

Angle COD= 180°-1/2(360°- angle A- Angle B)

Angle COD= 180°-180°+1/2 Angle A + 1/2 Angle B= 1/2(Angle A+ Angle B)

thanks

38.

3.In a quadrilateral ABCD, the bisector of ZC andZD intersect at OProve that COD A +4B)

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1

39.

Write the given set in roaster form 1)seven basic sounds of sargam

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Solution :

Let set A is seven basic sounds

of a sargam .

List form of set A :

i ) In Carnatic music :

A = { Sa , Ri , Ga,Ma,Pa,Dha,Ni }

ii ) In Hindustani classical :

A = { Sa, Re, Ga, Ma, Pa, Dha, Ni }

40.

M. Prove that <МОС--nLe.21. The bisectors of ZB and ZC of an isosceles AABC with AB- AC intersecteach other at a point O. Show that the exterior angle adjacent to LABCis equal to ZBOC.I in line through P, parallel to BA

Answer»

If you find this solution helpful, Please like it.

thankhs

but ext angle ABD +angle B=180

41.

10. In triangle ABC, LA-4B-15° and 2B-ZC-30°, find ZA.4B and ZC.

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1st

2nd

42.

EXERCISE 6.3In Fig. 6.39, sides QP and RQ of A PQR are produced to points S and T respectively.If SPR 135° and Z PQT 1100, find 4 PRQIn Fig. 6.40, LX = 62°, XYZ = 54°. IfYO and ZO are the bisectors of< XYZ andLXZY respectively of A XYZ, find ZOZY and 2 YOZ.3. In Fig. 6.41, ifAB | DE, BAC 35° and ZCDE 53°, find L DCE.P0135B.▽35062°110530RYFig. 6.39Fig. 6.40Fig. 6.414. In Fig. 6.42, if lines PQ and RS intersect at oint T urhth

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43.

17. OB and OC bisect ZB and ZC respectiely. If ZB=ZC, can you say that triangle OBC is isosceles.Justify you answer stating the axiom used.

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44.

BE ACcinDE BIn the given figure, DBL BC, DEL AB and AC丄BC Prove thatA.

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45.

zo m

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46.

I.Distance of the centre of mass of a solid uniforvertex is zo. If the radius of its base is R and its height is h, thenZo is equal to(a) n(2015 Main)3h4Sh4R3/h8R

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option A ,

47.

22. In the given figure, ABL BC, GF丄BC andDE LAC. Prove that AADE ~ ΔGCF.

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48.

(1) Write the symbolic statements in words for

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Representing the symbol statement given we have:- 4/3 is an element of set Q.

49.

(1) Write the symbolic statements in words for EQ

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Statement :4/3 belongs to set of rational number

50.

4(1) Write the symbolic statements in words for eQ

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Statement :

4/3 belongs to set of rational numbers