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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.
| 5001. |
Find the value of sin^(-1) ( sin""(2pi)/( 3) ) |
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| 5002. |
The values of lambdafor which the matrix A =((lambda ,0 ,lambda),(lambda,0,-lambda),(0 ,1,0)) is orthogonal is |
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Answer» `pm1` |
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| 5003. |
int_(0)^(pi//2) ln ((4+3 Sin x)/(4+3 Cos x))dx= |
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Answer» 1 |
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| 5004. |
Let L_(1) be a line with direction ratios (-2,-1,2)andL_(2) be the line joining the points (1,2,3)and(3,2,1), If theta is the angle between the lines L_(1)andL_(2) then |sintheta| equals: |
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Answer» `1//3` |
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| 5005. |
The magnitude of the projection of the vector a=4i-3j+2k on the line which makes equal angles with the corrdinates axes is |
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Answer» `SQRT2` |
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| 5006. |
Evaluate the following integrals int e^(sinx) (x cos x - sec x tan x) dx |
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| 5007. |
If m and M respectively denote the minimum and maximum of f(x)=(x-1)^2+3 for x in[-3,1], then the ordered pair (m, M) is equal to |
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Answer» `(-3, 19)` |
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| 5008. |
The transformedequation of x^3 -6x^2 +5x +8=0byeliinatinsecondtermis |
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Answer» `x^3 +7X+2=0` |
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| 5009. |
Find int(sin2xcos2xdx)/(sqrt(9-cos^(4)(2x))) |
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| 5010. |
Networks of Blood Capillaries and Large Lymph vessel is present in :- |
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Answer» Villi |
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| 5011. |
The area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 is equal to |
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| 5012. |
Find the correct statement for the following : |
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Answer» If `alpha` and `BETA` are the roots of `X^2+3x+7=0` then this equationwhose roots are `alpha+1` and `beta+1` is `x^2+x+5=0` |
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| 5013. |
If x=-5+4i then x^4+9x^3+35x^2-x+4= |
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Answer» 0 |
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| 5014. |
C_(1): x^(2) + y^(2) = 25, C_(2) : x^(2) + y^(2) - 2x - 4y -7 = 0 be two circle intersecting at A and B then |
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Answer» Equation of common CHORD is `x + 2y - 9 = 0` |
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| 5015. |
If veca is a unit vector and (vecx-veca).(vecx+veca)=255 then find |vecx| |
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Answer» 81 |
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| 5016. |
2 dice are rolled then the probability of getting both even or different is |
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Answer» `(1)/(3)` |
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| 5017. |
IfS=Sigma_(n=1)^(oo) (""^(n)C_(0)+""^(n)C_(1)+""^(n)c_(2)+..+""^(n)C_(n))/(""^(n)P_(n)) then S equals |
| Answer» Answer :d | |
| 5018. |
Find the number of onto functions from a set {1, 2, 3, 4, 5} to another set {a_1,a_2,a_3,a_4} such that f^(-1)(a_1)={2} |
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| 5019. |
int_(0)^(1) (sin theta (cos^(2) theta- cos^(2) pi//5) (cos^(2) theta ^(2) 2 pi //5))/(sin 5 theta)d theta |
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| 5020. |
If int e^(alpha x) ( ( 1- beta sin x )/(1 - cos x ) ) dx = -e^x cot x/2+c,then (alpha^2 + beta^2)/(2 alpha beta)= |
| Answer» ANSWER :B | |
| 5021. |
Let z = 1 - t + isqrt(t^(2) + t + 2) , where t is a real parameter . The locus of z in the Argand plane is |
| Answer» Answer :A | |
| 5022. |
A die is loaded such that 1 turning upwards is 2 times as often as 6 and 3 times as any other face (2 or 3 or 4 or 5). The probability that we get a face with 6 when we throw such a die is |
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Answer» `(6)/(17)` |
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| 5023. |
int (dx)/(cos(x + 4) cos (x + 2)) is equal to |
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Answer» `(1)/(SIN 2) LOG |cos (x + 4)^(2)| + C` |
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| 5024. |
For reaction AtoB, the rate constant k_(1)=A_(1)e^(-Ea)//RT and for the reaction PtoQ, the rate constant k_(2)=A_(2)e^(-Ea_(2))//RT. If A_(1)=10^(8),andEa_(1)=600"cal/mol",Ea_(2)=1200"cal/mol", then the temperature at which k_(1)=k_(2) is (R=2cal/K-mol) |
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Answer» 600 K `(A_(2))/(A_(1))=e(Ea_(2)-Ea_(1))//RT` `10^(2)="Exp"{(600)/(RT)}"R=2cal/K-mol"` `2" ln "10=(600)/(2T)` `T={(300)/(2xx2.303)}K""]` |
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| 5025. |
Itis prescribed that the daily food ration for a patient must contains at least 100 units of vitamin A and120 unitsof vitaminB two kinds of foodF_(1)and F_(2)are avialablefor him food F_(2) contains 8 unitsof vitamin A and 12 unitsof vitamin B per gram and costs 20paiseper gramit is desired to determine a minimum cost dietr for the patient formulate theproblem as a linear programming problem and solve it graphically |
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| 5026. |
Find the values of 'alpha' for which 6 lies between the roots of the equation x^2 + 2(a - 3)x + 9 = 0 |
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| 5027. |
Examine if Rolle's theorem is applicable to the following functions : f(x) = cos x on [0,pi] |
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Answer» Solution :`f(x) = cosx on [0,pi]` Clearly f(a) doesnot EQUAL to f(B) hence Rolle.s theorem is not APPLICABLE. |
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| 5028. |
Let the position vectors of the points A, B and C be vec(a),vec(b)andvec(c) respectively. Let Q be the point of intersection of the medians of the triangle ABC. Then vec(QA)+vec(QB)+vec(QC)= |
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Answer» `(vec(a)+vec(B)+vec(C))/(2)` |
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| 5030. |
If the complex numbers z_1,z_2 " and " z_3 represent the vertices of an equilateral triangle such that |z_1|=|z_2|=|z_3|," then " z_1+z_2+z_3=0 |
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Answer» `rArr z_1,z_2,z_3` lie on a CIRCLE with CENTRE at origin `rArr` Circumentre = CENTROID `rArr ""0=(z_1+z_2+z_3)/(3)` `thereforez_1+z_2+z_3=0` |
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| 5031. |
If f(x).f((1)/(x))=f(x)+f((1)/(x)), and f(3)=82, then int(f(x))/(x^(2)+1)dx= |
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Answer» `X^(3)-x+2tan^(-1)x+c` |
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| 5032. |
Find the derivative of x from the first principle, where f is given by f(x)=x+(1)/(x) |
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| 5033. |
Choose the correct answer. Answer all the questions, [Answers are in bold]If p+iq= (2-3i)(4+2i) then q is …. |
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Answer» 14 |
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| 5034. |
A value of k such that the straight lines y-3kx+4=0 and (2k-1)x-(8k-1)y-6=0 are perpendicular is |
| Answer» Answer :A | |
| 5035. |
Evalute the following integrals int (cos sqrt(x))/(sqrt(x)) dx |
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| 5036. |
Let u(x)" and "v(x) be differentiable functions such that u(x):v(x)=7. If : u'(x):v'(x)=p" and "y'(2)=7," then: "(p+q):(p-q)= |
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Answer» 1 |
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| 5037. |
If the sum of the roots of x^(3)+px^(2)-qx+r=0 is zero, then pq is equal to |
| Answer» ANSWER :A | |
| 5038. |
Find the area of the triangle formed by two tangents drawn from (3,5) to the circle x^(2)+y^(2)=16 and the chord of contact of (3,5) |
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| 5039. |
Integrate the rational functions (x)/((x+1)(x-1)) |
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| 5040. |
Find |vec(a)xxvec(b)|, if a=hat(i) -7hat(j)+7k and b=3hat(i)-2hat(j)+2hat(k). |
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Answer» Solution :It is GIVEN that `a=hat(i)-7hat(j)+7hat(k) and b=3hat(i)-2HAT(j)+2hat(k)`. `therefore vec(a)xxvec(b)=|(hat(i),hat(j),hat(k)),(1,-7,7),(3,-2,2)|=(-14+14)hat(i)-(2-21)hat(i)-(2-21)hat(k)=0hat(i)+19hat(j)+19hat(k)`. `rArr |axxb|=SQRT(0^2+(19)^2+(19)^2)=sqrt(2xx(19)^2)=19sqrt(2)`. |
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| 5041. |
A line in 3-dimensional space makes an angle theta(0ltthetalepi//2) with both the x and y-axis. Then the set of all values of theta is the interval: |
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Answer» `(0,(PI)/(4)]` |
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| 5042. |
Find the value of k if the equation (k+1)x^(2)+2(k+3)x+(k+8)=0 as have equal roots. |
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| 5043. |
Let p: roses and red and q: The sun is a star. Then the verbal translation of (~p)vvq is |
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Answer» Roses are not RED annd the SUN is not a star |
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| 5044. |
Based on the data in the table above, which of the following statements must be true? I. For every 3 men who applied to a same state collage, 2 women applied to a same state collage. II. If a female student is selected at random the probability that she did not apply to a 2-year collage is greater than 75%. III. Of the students who applied to a same state collage, 40 % were females |
| Answer» Answer :D | |
| 5045. |
Evalute the following integrals int 2^(x)cos x dx |
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| 5046. |
A particle moves along the curve 6y = x^(3)+2 . Find the points on the curve at which the y coordinate is changing 8 times as fast as the x - coordinate. |
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| 5047. |
Three vectors of magnitudes a, 2a and 3a are along the directions of the diagonals of three adjacent faces of a cube that meet in a point. Then the magnitude of their sum is |
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Answer» 4a |
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| 5048. |
A biologist places a colony consisting of 5000 bacteria into a petri dish. After the intial placement of the bacteria at time t = 0, the biologist measures and estimates the number of bacteria present every halfhour. This data was then fitted by an exponential curve of the form y=c.2^(kt) where c and k are constants, t is measured in hours, and y is measured in thousands of bacteria. The scatterplot together with the exponential curve are shown below. Suppose that the data was fitted with a quadratic function of the form t^(2)+bt+c instead of an exponential function. Assume that the quadratic funtion agrees with the scatterplot at times t = 0 and t = 6. What is the t - coordinate of the vertex of the graph of the quadratic function? |
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| 5049. |
A biologist places a colony consisting of 5000 bacteria into a petri dish. After the intial placement of the bacteria at time t = 0, the biologist measures and estimates the number of bacteria present every halfhour. This data was then fitted by an exponential curve of the form y=c.2^(kt) where c and k are constants, t is measured in hours, and y is measured in thousands of bacteria. The scatterplot together with the exponential curve are shown below. According to the scatterplot, the biologist'smeasurements indicate that the number of bacteria present quadrupled in 6 hours, and the exponential curve passes through the corresponding data point at time t = 6. The exponential function also agrees with the initial number of bacteria. Compute ck. |
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