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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 5951. |
Let f(x) be a differentiable bounded function satisfayi 2f^(5)(x).f'(x)+2(f'(x))^(3).f^(5)(x)=f''(x) If f(x) is bounded in between y=k, and y=k^(2), Then the number of intergers between k_(1) and k_(2) is/are (wheref(-0)=f'(0)=0). |
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| 5953. |
Let ** be the binary opertion on N given by a **b=L.C.M. of a and b. Find (i) 5 **7, 20 **16 (ii) Is ** commutative ? |
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| 5954. |
The solution of (dy)/(dx) = sec (x +y) is |
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Answer» `sec (x-y) + tan (x +y) = ce^(2x + y)` |
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| 5955. |
A bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is takenn at random and a ball is drawn and noted to be green. The probability that it comes from bag B is |
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Answer» `(2)/(7)` |
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| 5956. |
Let A be 2xx2 matrix with non zero entries and let A^(2)=I where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elements of A and |A|= determinant of matrix A Statement-1 Tr(A)=0 Statement -2 |A|=1 |
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| 5957. |
IF 3 is a root of the function f(x)=x^2+13x+x and c is a constant, what is the value of c? |
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Answer» -48 |
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| 5958. |
Sum of absolute deviations about median is |
| Answer» Answer :A | |
| 5959. |
For the LPP: Maximize z=5x_1+7x_2 subject to x_1+x_2lt4 3x_1+8x_2le24. 10x_1+7x_2le35. xge0,yge0. Examine whether (10/3,11/5) is a feasible solution or not. |
| Answer» SOLUTION :Now `10/3+11/5=83/15le4`i.e.,(10/3,11/5)` does not SATISFY `x_1+x_2le4:THEREFORE(10/3,11/5)` is not a FEASIBLE solution. | |
| 5960. |
Distance between the two planes 2x+3y +4z =4 and 4x+6y +8z=12 is |
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Answer» 2 units |
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| 5961. |
Two circleseach of radius 5 units touch each other at (1,2)and 4x +3y = 10is their common tangent. The equation of that circle among the two given circles, such that some portion of it lies in every quadrant is |
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Answer» `X^(2) +y^(2) +6x +2Y +15 = 0 ` |
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| 5962. |
Find the points on the curve x^(2) + y 2 – 2x – 3 = 0 at which the tangents are parallel to the x-axis. |
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| 5963. |
A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: (a) Rs. 1800 (b) Rs. 2000 |
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| 5964. |
If overset(-)u=overset(-)a-overset(-)b, overset(-)v=overset(-)a+overset(-)b, |overset(-)a|=|overset(-)b|=2," then "|overset(-)u xx overset(-)v| is equal to |
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Answer» `2 SQRT(16-(overset(-)a.overset(-)b)^(2))` |
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| 5965. |
Given that for all real x, the expression (x^(2)-2x+4)/(x^(2)+2x+4) lies between (1)/(3) and 3 the values between which the expression (9tan^(2)x+6tanx+4)/(9tan^(2)x-6tanx+4) lies are |
| Answer» Answer :D | |
| 5966. |
If the function f(x) defined as f(x) = (x^(100))/(100) + (x^(99))/(99) +….+(x^(2))/(2) + x + 1, then f'(0) = |
| Answer» Answer :C | |
| 5967. |
"Verigy LMVT for " f(x) =-y^(2)+4x-5 " and " x in [-1,1] |
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Answer» Solution :`f(1) =-2 "",""f(-1) =-10` `RARR ""f(c) =(f(1) -f(-1))/(1-(-1)) ""rArr "" -2c +4=4 "" rArr "" c=0` |
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| 5968. |
Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1)/(3.2^(3))+….oo=log_(e )1//2 Statement-II : ((1)/(5)+(1)/(7))+(1)/(3)((1)/(5^(3))+(1)/(7^(3)))+(1)/(5)((1)/(5^(5))+(1)/(7^(5)))+….+oo=(1)/(2)log2 Which of the above is true |
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Answer» Only I |
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| 5969. |
The partial fractions of (x^(3)-5)/(x^(2)-3x+2) are |
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Answer» `x+3- (4)/(x-1)+(3)/(x-2)` |
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| 5970. |
Find the area under the given curves and given lines: (i) y = x_(2), x = 1, x = 2 and x-axis (ii) y = x^(4), x = 1, x = 5 and x-axis |
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| 5971. |
Consider f : {1, 2, 3} rarr {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. find f^(-1) and show that (f^(-1))^(-1) = f |
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Answer» Solution :`F = {(1,a), (2,B), (3,C)} ` `f^(-1) = {(a,1), (b,2), (c,3)}` `(f^(-1))^(-1) = {(1,a) (2,b), (3,c)}= f` `THEREFORE (f^(-1))^(-1) = f` |
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| 5972. |
Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]] |
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Answer» SOLUTION :`[[1,OMEGA,omega^2],[omega,omega^2,1],[omega^2,1,omega]]=[[1+omega+omega^2,omega,omega^2],[omega+omega^2+1,omega^2,1],[omega^2+1+omega,1,omega]]` (REPLACING `C_1` by `C_1+C_2+C_3`) =`[[0,omega,omega^2],[0,omega^2,1],[0,1,omega]]=0(because 1+omega+omega^2)` |
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| 5973. |
Equation of a plane bisecting the angle between the planes 2x-y+2z+3=0 and 3x-2y+6z+8=0 is |
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Answer» 5x-y-4z-45=0 |
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| 5974. |
If omega is a cube root of unity , then |{:( 1 , omega , 2 omega^(2)) , (2, 2omega^(2) , 4 omega^(3)) , (3 , 3 omega^(3) , 6 omega^(4)):}|= |
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Answer» 1 |
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| 5975. |
Given that the two numbersappearing on throwing two dice are different. Find the probabilityof the event 'the sum of numbers on the dice is 4'. |
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| 5976. |
Evaluate:int_(0)^(pi/2)(sqrttanx+sqrtcotx) dx. |
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| 5978. |
Find the area enclosed between the curves y= sin pi x, y = x^(2)-x and the line x=2 |
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| 5979. |
Differentiate y=a^x |
| Answer» SOLUTION :`y=a^xlogy=koga^X=xloga` Differentiatingthroughoutw.r.tx, we GET `1/yd/DX="x"xx0+logaxx1=loga(DY)/(dx)=yloga=a^xloga(dy)/(dx)(x^x)=x^x(1+logx).d/dx(a^x)_2=a^2-loga` | |
| 5980. |
Ifx= 2+ 3^(2//3)+ 3^(1//3) , then the value of the expressionx^(3)-9x^(2)+18x-10 is equal to _____ |
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| 5982. |
if (3x+2)/((x+1)(2x^(2)+3))=(A)/(x+1)+(Bx+C)/(2x^(2)+3') " then " A- B + C= |
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Answer» 1 |
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| 5983. |
Solve graphically -3x + y gt 0 |
Answer» SOLUTION :
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| 5984. |
Find the area of the region bounded by the curve y=x^2 and the line y=4. |
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| 5985. |
Let f: R to R be defined by f(x) = int_(0)^(1) (x^2 + t^2) /( 2-t) dt. Then the curve y=f(x) is |
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Answer» an ellipse |
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| 5986. |
Find m and n if P(m+n,2)=56,P(m-n,2)=12 |
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Answer» SOLUTION :`""^(m+n)P_2=56,""^(m-n)P_2=12` `or,((m+n)!)/((m-n-2)!)=12` `or,(m+n)(m+n-1)=8xx7`(m-n)(m-n-1)=4xx3` `:. (m+n)=8 ,m-n=4` `:. M=6,n=2` |
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| 5987. |
If f(x) = underset(nrarroo)lim(x^(n)-x^(-n))/(x^(n)+x^(-n)),0ltxlt1,ninN then int(sin^(-1)x)f(x) dx is equal to |
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Answer» `-[sin^(-1)x+sqrt(1+x^(2))]+C` |
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| 5988. |
Out of 2n tickets numbered 1,2 …..2n, 3 are chosen at random. The probability that the numbers on them are in A.P is |
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Answer» `(2)/(2n-1)` |
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| 5989. |
If X is a poisson variatesuch that P(X = 0) = P(X = 1) = K, then the show that K = 1//e |
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| 5990. |
int_(0)^(pi//2) (8+7 cos x )/((7+8 cos x)^(2))dx is equal to |
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Answer» `1//7` |
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| 5991. |
Sixty points lie on a plane, out of which no three points are collinear. How many straight lines can be formed by joining pairs of points ? |
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Answer» Solution :Sixty points LIE on a PLANE, out of which no.3 points are collinear. A straight LINE required two points. The number of straight lines formed by joining 60 points is `""^60C^2 = (60!)/(2xx58!)=(60xx59)/2=1770` |
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| 5992. |
If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then prove that a^(2)cos^(2)alpha+b^(2)sin^(2)alpha= p^(2). |
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Answer» <P> |
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| 5993. |
If the line (x-3)/(2) = (y +2)/(-1) = (z+4)/(3) is in the plane lx+ my-z = 9 then l^2 + m^2= ......... |
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Answer» 26 |
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| 5994. |
If (1 + cos theta + isin theta) (1 + cos 2 theta + isin 2theta) = x + iy then y = |
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Answer» `X TAN ((3theta)/(2))` |
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| 5995. |
Find Order and Degree of given differential equation(y''')^(2) + (y'')^(3) + (y')^(4) + y^(5) = 0 |
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| 5996. |
For what values of m the equation (1 + m)x^2 - 2(1 + 3m)x + (1 + 8m) = 0 has equal roots. |
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| 5997. |
I= int "In" ( sqrt( 1-x) + sqrt(1+x) )dx. |
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| 5998. |
A coin is tossed 4 times. Find the mean and variance of the probability distribution of the number of tails. |
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| 5999. |
You and your friend save as much money as possible by participating in the contest and fly to Athens. Exploring Athens you and all other teams come to Parthenon, the temple of Athena, who is the goddess of wisdom and intelligence. You also see many images of an owl. You learn from the guide that it is the “Athena Noctua”, also called the Minerva owl or the little owl. The guide also mentions some interesting stories of Athena’s wisdom and cleverness. The tourist guide at Parthenon takes you to an abandoned tunnel. And here you find an inscribed stone and a bowl of colored flowers. Suddenly you hear a deep and ancient gong ringing as you start reading the Stone Of Instructions. The instructions read as follows: Every person entering the Temple of Athena will be given a bowl with 15 red flowers and 12 yellow flowers. Each time the Gong of Time rings, he/she must do one of two things: 1. Exchange: If he has at least 3 red flowers in his bowl, then he may exchange 3 red flowers for 2 yellow flowers. 2. Swap: He may replace each yellow flower in his bowl with a red flower and replace each red flower in his bowl with a yellow flower. That is, if he starts with i red flowers and j yellow flowers, then after he performs this operation, he will have j red flowers and i yellow flowers. [You can leave the tunnel only when you make all the combinations (no. of red, no. of yellow) of flowers that are possible]. After how many operations will you have 5 each of red and yellow flowers? |
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Answer» 5 |
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| 6000. |
You and your friend save as much money as possible by participating in the contest and fly to Athens. Exploring Athens you and all other teams come to Parthenon, the temple of Athena, who is the goddess of wisdom and intelligence. You also see many images of an owl. You learn from the guide that it is the “Athena Noctua”, also called the Minerva owl or the little owl. The guide also mentions some interesting stories of Athena’s wisdom and cleverness. The tourist guide at Parthenon takes you to an abandoned tunnel. And here you find an inscribed stone and a bowl of colored flowers. Suddenly you hear a deep and ancient gong ringing as you start reading the Stone Of Instructions. The instructions read as follows: Every person entering the Temple of Athena will be given a bowl with 15 red flowers and 12 yellow flowers. Each time the Gong of Time rings, he/she must do one of two things: 1. Exchange: If he has at least 3 red flowers in his bowl, then he may exchange 3 red flowers for 2 yellow flowers. 2. Swap: He may replace each yellow flower in his bowl with a red flower and replace each red flower in his bowl with a yellow flower. That is, if he starts with i red flowers and j yellow flowers, then after he performs this operation, he will have j red flowers and i yellow flowers. [You can leave the tunnel only when you make all the combinations (no. of red, no. of yellow) of flowers that are possible]. What is the number of combinations you need to make to leave the tunnel? |
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Answer» 27 EXCHANGE : `R_(n) -Y_(n)=(R_(n-1)-3)-(Y_(n-1)+2)=(R_(n-1)-Y_(n-1)-5) Swap : `R_(n)-Y_(n) =(Y_(n-1)-R_(n-1))` From the above two statements it can be declared that (R, Y) can NEVER become (5,5) because the initial VALUE of R-Y is 3. Hence the value of ((R-Y) mod 5) REMAINS either 3 or 2 but never goes to 0. |
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