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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. |
\operatorname { tan } 30 ^ { \circ } \times \operatorname { tan } \square ^ { \circ } = 1 |
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Answer» tan 30° x tan 60°=1tan 30° = 1/√3tan 60°=√3(1/√3)(√3)=1Ans:tan 60° |
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| 2. |
\sec ^{2} \theta-\frac{\sin ^{2} \theta-2 \sin ^{4} \theta}{2 \cos ^{4} \theta-\cos ^{2} \theta}=L |
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| 3. |
\frac{\cos ^{2} \theta}{\cot ^{2} \theta-\cos ^{2} \theta}=3, \text { then find }^{4} \theta |
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| 4. |
\sec ^{2} \theta-\frac{\sin ^{2} \theta-2 \sin ^{4} \theta}{2 \cos ^{4} \theta-\cos ^{2} \theta}=1 |
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| 5. |
14 NITIQ.35: Amit started walking positioning his back towards the sun. After sometime, he turned left, then turned right and towards the left again. In whichdirection is he going how?(a) North or South(b) East or West(c) North or West(d) South or West |
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| 6. |
Find the median for the following frequency distributionMarks obtained (x)17 20 22 15 3025Number of students (f) 59 4 3 10 6 |
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| 7. |
Fig.8.8/12. In Fig. 8.88, PQ is a chord of a circle and PT is the tangent at Psuch that zQPT6INCERT EXEMPLAR)Then, find ZPRQ女" |
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Answer» Given,PQ is a chord of a circle with center O. Also, ∠QPT = 60°.let x be the point on the tangent PT. Now, ∠QPT + ∠QPX = 180° [Linear pair] ⇒ ∠QPX = 180° - ∠QPT = 180° - 60° = 120° Again, ∠QPX = ∠PRQ [Alternate segment theorem] ⇒ ∠PRQ = 120° |
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| 8. |
CHYEXemplarProblenFind whether= 1 , x¡5 has real roots. If real roots exist, fi3them.INCERT Exemplar Prob |
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| 9. |
INCERT EXEMPLAR]A window of a house is h metre above the ground. From the window, the angles ofelevation and depression of the top and bottom of another house situated on theopposite side of the lane are found to be a and B respectively. Prove that the height ofthe house is h (1 + tan a tanſ) metres.INCERT EXEMPLAR |
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Answer» hope it helps u tanx=DC/hCoty; DC=h.tanx coty______(1) ; we see height of another house is BD; BFLD=BC× CD; BD=h+h tand cot y/h(1+ tand coty) |
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| 10. |
sExample 6. Without nctual dieision, prove that 2x+ x 2x 2 is divisible byINCERT Exemplar) |
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Answer» First of all, x^2-3x+2=>x^2-2x-1x+2=>x(x-2)-1(x-2)=>(x-2)(x-1)Therefore,(x-2)(x-1)are the factors.i) (x-2)x-2=0=>x=2So,p(x)=2p(x)=2x^4-5x^3+2x^2-x+2p(2)=2(2)^4-5(2)^3+2(2)^2-2+2=32-40+8= -40+40=0Hence,it proves that (x-2) is a factor .ii) (x-1)=>x-1=0=>x=1So,p(x)=1p(x)=2x^4-5x^3+2x^2-x+2p(1)=2(1)^4-5(1)^3+2(1)^2-1+2=2-5+2-1+2=6-6=0Hence,it proves that (x-1) is a factor. Like my answer if you find it useful! |
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| 11. |
Q. 3. If in two triangles ABC and PQR,INCERT EXEMPLAR]BC CA then=-thenQR PRPQ |
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Answer» Correct answer is(A)ΔPQR ~ΔCAB please like the solutionboth will be congruent triangle |
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| 12. |
,-12,will be-77? Find the sum of this A.P. upto the-,ermi- 77.-3. The sum of first n terms of an A.P. whose first term is 8 and the common difference isto the sum of first 2n terms of another A.P. whose first term is - 30 and20 is equalcommon difference is 8. Find nINCERT EXEMPLAR74 The students of a schooldid |
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Answer» Sum of first n terms Sn=n/2[2a+(n-1)*d]n/2[2×8+(n-1)×20]=2n/2[2×-30+(2n-1)×8]16+20n-20=2(-60+16n-8)-4+20n=2(-68+16n)-2+10n=-68+16n66=6nn=11 What is value of n in second AP bro |
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| 13. |
Identify the types of tria5 cm |
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Answer» Here AB=BC=CA=5cm Since all the sides are equal it is called equilateral triangle equilateral triangle it has all side equal to its other equilateral triangle AB=BC=CA=5cmall side are side are equal it is a equilateral triangle In above figure,AB=BC=CA=5cm.As we know that ,A triangle which have all sides are equal are known as equilateral triangle. |
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| 14. |
um, ))anld1, 15) is 10, find the value ofx.2. Find the values of y for which the distance between the points P(2,-3) and Q(10,units. |
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| 15. |
verify : sin60 =2tan 30/1+ tan square 30 |
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| 16. |
1: Uing the formula, tan 2A 1anr find the valtue of tan 60, it2tan A find the value of tan 60°, it1 - tan Abeing given that tan 30 |
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| 17. |
2tan 30. ¥ का भाग है1+ tan® 30A) sin 60 (B} cos 60tan 60° (D) sec 60F |
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Answer» tan 30 = 1/√3Then,2tan30/(1+tan^2 30) =2×1/√3/(1+(1/√3)²)=2/√3/(1+1/3) in brackets by taking 3 as lcm we get=2/√3/ (3+1/3)=2/√3 / 4/3=2/√3×3/4=3/2√3 (3 can be written as√3×√3)=√3×√3 / 2√3=√3/2= sin 60 (A) is correct option |
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| 18. |
2tan²60°+3scc60°-4sin²30°-2tan45° |
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Answer» tan60 = √3 , tan²60 = 3sec60 = 2 , sec²60 = 4sin30 = 1/2 , sin²30 = 1/4tan45 = 1 , tan²45 = 1 so the value is 2*3+3*4-4*(1/4)-2 = 6+12-1-2 = 15. |
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| 19. |
(cosec^2*(90^circ - theta) - tan(theta)^2)/((4*(cos(42^circ)^2 %2B cos(48^circ)^2))) - 2*sin(38^circ)^2*tan(30^circ)^2*sec(52^circ)^2/(70^circ*cosec^2 - tan(20^circ)^2) |
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| 20. |
-3*1/(2*(65^circ*cosec^2 - tan(25^circ)^2))*sin(54^circ)^2*cot(30^circ)^2*sec(36^circ)^2 %2B (sin(theta)^2 %2B sin(90^circ - theta)^2)/((3*(-cot(29^circ)^2 %2B sec(61^circ)^2))) |
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| 21. |
(((cos(30^circ)^2 %2B cos(60^circ)^2)/(90^circ*cosec^2 - cot(90^circ)^2))*((-sin(30^circ)^2 %2B 1)/(sin(45^circ)^2 %2B 1)))/((sin(60^circ)*tan(30^circ))) |
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Answer» 4/5 is the correct answer |
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| 22. |
(5*cos(60^circ)^2 %2B 4*sec(30^circ)^2 - tan(45^circ)^2)/(sin(30^circ)^2 %2B cos(30^circ)^2) |
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| 23. |
The value of a machine depreciates by 10% annually. If the present value of the machine is Rs.100000, what will be it's value after 2 years? |
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Answer» tq |
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| 24. |
12.-The value of a machine depreciated at the rate of 8% p.a. If the value of the machineis now75,000, what will be its value after 2 years? |
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Answer» Solution Value of the machine after 2 years = Rs.[75000*(1- 8/100)^2]= Rs.75000*92*92/100*100= Rs. 63480 |
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| 25. |
पद 1641. R IR L .. र ही नर कर >>20 + 30 नकिक(2x + 5y) X 3X |
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| 26. |
months. How much rent did it pay?Area of a triangle is x,square units. If the sides of this triangle be doubled, then the area of the new triaunits. Prove that x1 : = 1 : 4. Also, find the percentage increase in area7.square |
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| 27. |
A circle of radius 5 units touches the co-ordinates axesin the first quadrant. If the circle makes one completeroll on x-axis along the positive direction of x-axis,find its equation in the new position. |
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| 28. |
\left. \begin{array} { l l } { 82 } & { 7 } \\ { 32 } & { 2 } & { 09 } \end{array} \right. |
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| 29. |
P. If <C = 106" and <D= 56" ,tina zrrb.9. The angles of a quadrilateral are 110, 75, 53 and x. Findtvalue of x. |
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| 30. |
: A boy starts walking straight towards East. After walking 75 metres, he turns to the left andwalks 25 metres straight. Again he turns to the lefAgain he turns to the right and walks a distance of 10 metres. Again he turns to the leftcovers 35 m. Finally he turns to the left and covers 35 m. How far is he from the starting point?(A) 25 metres(C) 115 metrest and walks a distance of 40 metres straight.and(B) 50 metres(D) of these19. Malti walked 12 metres towards West, then turns to her right and walked 8 metres andthen turns to her left and walked 6 metres. Finally she turns around and walked 12 m straight.What is the shortest distance (in metres) between her starting point and the present position?(A) 30(C) 10(B) 20(D) none of these |
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Answer» please also help me in solving 18th ques. ok... give me time to solve thanku very much for helping me |
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| 31. |
The number of cards collected by Rina, Mina, and Tina are in the ratio 1:3:5 respectively. If Rina hasa collection of 45 cards, find the number of cards with Mina and Tina. |
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Answer» Let the no. of cards be x , 3x and 5x Rina has = 45 cards Cards with Rina = x = 45Cards with Mina= 3x = 3*45=135 Cards with Tina = 5x = 5*45=225 Ans : The number of cards with Rina,Mina and Tina are 45,135 and 225. |
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| 32. |
topology |
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Answer» Topology is the study of geometrical properties and spatial relations unaffected by the continuous change of shape or size of figures. thanks |
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| 33. |
Theorem M2: Burpose the topology space oneach space Xx & given by a basi Bu Acollection of all sets of the form I Bx whereB& E Bd for each & will serve as thebasis for the box to pology on Testthe collection of all sets of the same form.when where BatB fos finitely many.indexes d E B = Xd for all the remainingmany indexes, ne will serve as a basis forthe product topology TEXASen |
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Answer» Call your starting integern:n+(n+1)+(n+2)=1923n+3=1923n=189n=63So your integers are:63+64+65=192 n +( n+1) + ( n+2)=192; 3n + 3 = 192; 3n = 192-3=189; n= 189/3=63; n+(n+1)+(n+2)=1923n = 192-3=1893n+3=192n=189/3=63 |
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| 34. |
S for SUPER COMPUTERSUPER COMPUTER is themost powerful computer.PARAM is the first IndianSuper Computer. |
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Answer» What is your question here? |
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| 35. |
POLYNOMIALS373 Ir the zeroes of the polynomial 2-3++ 1 area- b, a,a+ b, find a and b.İftwo zeroes ofthe polynomíalx4-6x3-26x2+138x-35 are 2 yB, find other zeroes.5.Ifthe polynomial x4一6x3 + 1 6x2-25x + 1 0 is divided by another polynomial r-2x + k,the remainder comes out to be x + a, find k and a. |
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Answer» 3)X³-3x²+x+1The zeroes of the polynomial are (a+b),a, (a-b) Let α=a-bβ=aγ=a+b α+β+γ=-x² coefficient/x³ coefficient a-b+a+a+b=-3/13a=-3a=-3/3a= -1 αβγ= -constant/x³ coefficient (a-b)(a)(a+b)=-1/1(a²-b²)(a)= -1[(-1)²-b²](-1)=-1(1-b²)= -1/-11-b²=11-1=b²b²=0b=√0=0Therefore, a=-1 and b=0 |
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| 36. |
13. Given that 2 is a zero of the cumbic polynomial 6x +v6r3+2x2 -10x - 4/2, find itsNCERT EXEMPLAR]other two zeroes.14.Given that w |
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| 37. |
p4.Ä°ftwo zeroes of the polynomial x4-6x3-26x2 + 138x-35 are 2-3, find other zeroes. |
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Answer» Thanks |
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| 38. |
) Find the product of all the zeroes of the cubic polynomial 6x3+2x2+x-6. |
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Answer» Product of zeroes is d/ahence here a =6 and d=-6henceproduct will be -6/6=-1 |
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| 39. |
(i) $ \frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}} $(ii) $ \sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ} $ |
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| 40. |
Find the remainder when the polynomial f(x) = 2x4-6x3 + 2x2-x + 2 is divided by (x + 2) |
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| 41. |
Obtain all other zeroes of the polynomial x4 + 6x3 + x2-24x-20, if two of its zeroes are+2 and -5 |
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| 42. |
14.Find all the zeroes of the polynomial 3x + 6x3 2x2 -10x -5 if two ofits zeroes are 2 and |
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| 43. |
lHat a6ap+p3-80(b) Find the remainder when the polynomial fx) 2x4-6x3+ 2x2-x + 2 is divided by x + 2. |
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| 44. |
16. What is the Highest Common Factor of 8,9 and 12?(A) 1(B) 72(C) 2(D) 3 |
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Answer» 72 is the HCF of the question The highest common factor (HCF) of 8,9 and 12 is 1. 1 is the correct answer of the given question option a is the correct answer of the given question 3 is कॉमन frctor because all digit division of 3 oh bro 1 is correct answer 1 is the correct answer 72 is the right answer of this question . the highest common factor 8,9 and 12 is 1 (A). 1) is the right answer its highest common factor is 3 3 is the highest common factor 72 is the right answer a) 1 is the right answer of the following , 72 is the correct answer me option (a) is correct answer option a is right answer option a is right answer Oppstion no D is correct 1 is the correct answer of this question B)72 is correct answer the hcf highest common factor is 72 72 is the correct answer me HCF of 8 9 & 12 is 1. 72 is the correct answer b) is the right answer of the following 72 is highest common factor 72 is the best answer a) is the right answer of the following 1 option is your correct answer D is the correct answer d is the correct answer 1 right answer hai factorial |
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| 45. |
Find the highest common factor of 36 and 84. |
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Answer» 12 is the correct answer hcf of 36 and 84 is 12 |
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| 46. |
1290. Find the highest common factor of 36 and 84(R.R.B(d) 18(a) 4(b) 6(c) 12 |
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| 47. |
factor ?which Highest common24, 60 48, 108 |
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Answer» 12 is the comman factor 12 is the highest common factor of 24, 60, 48,108 The highest common factor is 108 12 is the highest common factor 12 is highest common factor and best answer |
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| 48. |
Find the common factor(s) and the highest common tactor of the followingX³Y²,X⁴Y^5,XY^6 |
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Answer» x*x*x*y*y x*x*x*x*y*y*y*y*y x*y*y*y*y*y*y common factor = x*y*y |
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| 49. |
We have a basket full of apples, oranges and mangoes.If 50% are apples, 30% are oranges, then what per centare mangoes? |
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| 50. |
Sri Jyothi has a basket full of bananas, oranges and mangoes. If 50% are bananas,15% are oranges, then what percent are mangoes? |
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Answer» 35 percent is the answee4 |
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