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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. |
Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}. Let Z = X + Y, then What is P(Z is the product of two prime numbers) equal to? |
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Answer» Solution :Z=product of two PRIME number `Z=x+y=7+6=13` `n(E_(4))=3` `P(Z=9)=(n(E_(4)))/(P(B'))=(P(A)-P(AB))/(1-P(B))` |
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| 2. |
If 2 cards are drawn from a pack of cards then the probability of selecting both from same suit or both kings is |
| Answer» Answer :A | |
| 3. |
Which statement is correct about Glaucoma ? |
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Answer» Increased intra occuler PRESSURE due to increased amount of vitrous humor. |
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| 4. |
If p and q are the greatest values of ""^(2n)C_(r) and ""^(2n-1)C_(r) respectively, then |
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Answer» p=2q |
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| 5. |
Aradioactive isotopehas an ntitial mass 200 mg which two years later is 50 mg find the expression for the amount of the isotope remaining at any time what is its half life |
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| 6. |
Solution set of inequality xge0 is |
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Answer» half PLNE on the LEFT of Y-axis |
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| 8. |
which of the following is not a convex set? |
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Answer» `{(x,y):2X+2yle7}` |
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| 9. |
int sqrt(1+x^2) dx = is equal to |
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Answer» `X/2 SQRT(1+x^2) +1/2 log|x+sqrt(1+x^2)|+C` |
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| 10. |
49^(n)+16n-1 is divisible by |
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Answer» 3 |
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| 11. |
If a lt b lt 0 then int_(a)^(b) (|x|)/(x) dx= |
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Answer» `a-b` |
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| 12. |
Using differential find the approximate value ofsqrt( .036) |
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| 13. |
Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|=a^3 |
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Answer» |
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| 14. |
The value of i^(i^(-i…..oo)) = x + iy then x^(2) + y^(2) = |
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Answer» `E^(-PI y)` |
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| 15. |
Let f : [2, 4) rarr [1, 3) be a function defined by f(x) = x - [(x)/(2)] (where [.] denotes the greatest integer function). Then f^(-1) equals |
| Answer» Answer :B | |
| 16. |
To the height of a hill CD with its top as C, a horizontal line AB of length a is drawn along the foot of the hill. If angleCAB = alpha, angleCBA = beta, angleDAC = gamma, then CD is : |
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Answer» `(a SIN BETA sin GAMMA)/(sin(ALPHA + beta))` |
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| 17. |
Question 1-3 refer to the above scatterplot, which shows wrist and neck cicumference measurements, in centimeters, for 12 people. The line of beat fit is drawn. Q. What is the average increase in neck circumference per centimeter increase in wrist circumference, correct to the nearest tenth? |
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| 18. |
If A,B are two events such that P(A)=0.3, P(B)=0.4,P(AcupB)=0.6 Find P(A | B^c) |
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Answer» <P> SOLUTION :`P(A | B^c)=(P(A CAP B^c))/(P(B^c))=(P(A-B))/(1-P(B))``P(A)-(P(ACAPB))/(1-0.4)=(0.3-0.1)/0.6=0.2/0.6=2/6=1/3` |
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| 19. |
Question 1-3 refer to the above scatterplot, which shows wrist and neck cicumference measurements, in centimeters, for 12 people. The line of beat fit is drawn. Q. How many of the 12 people have an actual neck circumference that differs by more than 1 centimeters from the neck circumference predicted by the line of best fit? |
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Answer» |
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| 20. |
If veca*vecb=vecb*vec c=vec c *veca=0, then the value of [veca, vecb, vec c] is : |
| Answer» Solution :N/A | |
| 22. |
Show that the four points which the position: Vectors: 4hati + 8hatj + 12hatk, 2hati + 4hatj +6 hatk, 3hati + 5hatj + 4hatk, 5hati + 8 hatj + 5hatk are coplanar: |
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| 23. |
Find thevalues of the following : tan^(-1)sqrt(3)-sec^(-1)(-2) is equal to |
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Answer» `PI` |
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| 24. |
Integrate the following functions: tan^3 2x sec(2x) |
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Answer» Solution :`tan^3 2x sec 2x = tan^2 2x sec 2x tan 2x` = (sec^2 2x-1) sec 2x tan 2x` PUT t = sec 2x Then DT = 2 sec 2x tan 2x dx `gt sec 2x tan 2x = dt/2 THEREFORE `int tan^3 2x sex 2x dx = `int (t^2-1) dt/2` =1/2[t^3/3-t]+C` =`1/2[(sec^3 2x)/3 - sec2x]+c` |
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| 25. |
Solve the system of linear equations by matrix method : 2x-3y + 5z = 11, 3x + 2y - 4z = -5, x +y -2x =-3. |
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| 26. |
Examine the continuity of the function f(x)= 2x^(2)-1" at "x=3. |
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| 27. |
Rydberg atoms are nearly classical atoms in which electron is excitedto states corresponding to n = 10 , 2 0 or even 100. There are many difficulties in studying them. 1. The radius of their orbit will be very large. So at ordinary densities, their collisions will allow electrons to jump from one orbit to another without emitting radiation. 2. The energy levels at such value of n will be every close. So experiment on rydberg atoms should be done at very low temperatures and very low pressures. Consider a very dilute gas of hydrogen atoms that are excited to n = 10. Assume for this situation that the average centre to centre distance should be equal to diameter of rydberg atom. [Take wein constant = 2.88xx10^(-3) mK] If this energy were to come from a photon corresponding to maximum spectral emissive power of a blackbody, what would be the temperature of that black body. |
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Answer» 5.3 K |
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| 28. |
Integrate the functions in exercise. (1)/(sqrt(9-25x^(2))) |
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| 29. |
Rydberg atoms are nearly classical atoms in which electron is excitedto states corresponding to n = 10 , 2 0 or even 100. There are many difficulties in studying them. 1. The radius of their orbit will be very large. So at ordinary densities, their collisions will allow electrons to jump from one orbit to another without emitting radiation. 2. The energy levels at such value of n will be every close. So experiment on rydberg atoms should be done at very low temperatures and very low pressures. Consider a very dilute gas of hydrogen atoms that are excited to n = 10. Assume for this situation that the average centre to centre distance should be equal to diameter of rydberg atom. [Take wein constant = 2.88xx10^(-3) mK] Assuming the atoms to fill up space like footballs filling up a room, how many atoms would fill up in a 1mxx1mxx1m room. (approx.) |
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Answer» `10^(20)` N is one LINE `= (1m)/(2xx53xx10^(-10))~~10^(8)` |
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| 30. |
A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for atmost 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at pofit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit ? |
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| 31. |
Solve the equation x^4 +4x^3 +5x^2 +2x -2=0giventhat-1 + sqrt(-1 ) isa root |
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| 32. |
If P=[[1,0,x],[3,0,1],[-1,-2,4]] is the adjoint of (3xx3) matrix A and |A|=4. Then x is : |
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Answer» 2 |
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| 33. |
Find the area of the region. {(x,y) : y28, 6x, x2+y27(6} |
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| 34. |
The vectors 5a + 6b + 7c, 7a - 8b + 9c, 3a + 20b + 5c are |
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Answer» COLLINEAR |
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| 35. |
Integrate the following functions : int(dx)/(1+sqrtx) |
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| 36. |
Let l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3),m_(3), n_(3) are direction cosine of three mutually perpendicular line OA, OB and OC.If the direction cosines of OP are proportional to l_(1)+l_(2)+l_(3), m_(1)+m_(2)+m_(3), n_(1)+n_(2)+n_(3)and angle made by OP with lines OA, OB, OC are respectively theta_(1), theta_(2), theta_(3), then |
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Answer» `theta_(1) LT theta_(2) lt theta_(3)` |
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| 37. |
IF""^(n) P_(r)=720,""^(n)C_(r)=120then(n,r)= |
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Answer» (7,4) |
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| 38. |
Q=17.6T The equation above shows the heat energy ,Q, in Joules that is absorbed by a 10g block of wood as temperature T. in degrees Celsius, increases. Which of the following best describes the meaning of the number 17.6 in this equation? |
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Answer» The heat ENERGY absorbed by the block of wood at a constant temperature |
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| 39. |
If f : A rarr B and g : B rarr C be the bijective functions , then (gof)^(-1) is .......... |
| Answer» Solution :N/A | |
| 40. |
Solve x^(2) - 4x - 21 ge 0 by algebric method and graphical method. |
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| 41. |
There are six periods in each working day of the school. In how manyways can one arrange 5 subjects such that each subject is allowed at leastone period? |
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Answer» 210 |
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| 42. |
Differentiate tan2x+sec2x |
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Answer» SOLUTION :`y=TAN2X+SEC2X` `dy/dx=d/dx(tan2x)+d/dx(sec2x)` `=sec^2 2X xxd/dx(2x)+sec2xcdot tan2x xxd/dx(2x)` `=2sec^2 2x+2sec 2x CDOT tan2x` |
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| 43. |
Which of the following differential equations has y = x as one of its particular solution? |
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Answer» `(d^(2)y)/(DX^(2))- x^(2)(dy)/(dx) + XY = x` |
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| 44. |
Let alpha=(2kpi)/(2025),beta=(2mpi)/(2026)"and " gamma=(2kpi)/(2027)where k,m,n in Z. A=((cosalpha,-sinalpha),(sinalpha,cosalpha)), B= ((cosbeta,-sinbeta),(sinbeta,cosgamma)) C=((sin gamma, -sin gamma),(sin gamma, cos gamma)) then det (A^(2025)+B^(2026)+C^(2027)) is equal to _______ |
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| 45. |
Prove statement "tan"^(-1) 1/7+ "tan"^(-1)1/13="tan"^(-1) 2/9 |
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Answer» SOLUTION :L.H.S. `="TAN"^(-1) 1/7 +"tan"^(-1) 1/13` `"tan"^(-1) ((1/7+1/13)/(1-1/7 -1/13))="tan"^(-1)((13+7)/(91-1))` `"tan"^-1(20/90) ="tan"^(-1) 2/9`=R.H.S. |
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| 46. |
Show that int_(0)^(1)tan ^(-1)x+tan^(-1)(1-x)dx=(pi)/(2)-log_(e)2 |
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| 47. |
Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohydrates. The corresponding values of rice are 0.05 gm and 0.5 gm respectively. Wheat costs Rs. 4 per kg and rice Rs. 6. The minimum daily requirements of proteins and carbohydrates for an average child are 50 gm and 200 gms respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost ? |
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| 48. |
The sum of the rational terms in expansion of (sqrt2+3^(1//5))^10 is |
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Answer» 41 |
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| 49. |
Form the quadratic equations whose roots are given below i) 7+-2sqrt5 ii) (a)/(b), (-b)/(a) (a!=0, b != 0) iii) (p-q)/(p+q), -((p+q)/(p-q)) (p != +-q) iv) -3 +- 5i v) 2, 5 vi) 2+sqrt3, 2-sqrt3 vii) -a+ib, -a-b |
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