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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.
| 10851. |
If the area ofthe regionbounded by twocurvesy=x^2 andy=x^3is (k)/(6) then k=……. |
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Answer» `1/3` |
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| 10852. |
A computer solved several problems in succession. The time it took to solve each successive problem was the same number of times smaller than the time it took to solve the preceding problem. How many problems were suggested to the computer if it spent 63.5 min to solve all the problems except for the first, 127 min to solve all the problems except for the last one, and 31.5 min to solve all the problems except for the first two? |
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| 10853. |
Let H be the orthocentre of triangle ABC. Then angle subtended by side BC at the centre of incircle of Delta CHB is |
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Answer» `(A)/(2)+90^(@)` `=(B+C)/(2)+90^(@)` 
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| 10854. |
Solve : tan^(-1)2x+tan^(-1)3x= (pi)/(4) |
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| 10855. |
If vec(a) and vec(b) are two vectors such that |vec(a) xx vec(b)| = vec(a).vec(b), then what is the angle between vec(a) and vec(b). |
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| 10856. |
Let f(x) ={{:( [x],-2le xle -(1)/(2) ),( 2x^(2)-1,-(1)/(2)lt xle2):}and g(x) =f(|x|)+|f(x)|, where[.]represents thegreatest integerfunction . the number of pointwhere g(x)is discontinuous is |
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Answer» 1 |
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| 10857. |
If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is (pi)/(3). |
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| 10858. |
Let f(x) ={{:( [x],-2le xle -(1)/(2) ),( 2x^(2)-1,-(1)/(2)lt xle2):}and g(x) =f(|x|)+|f(x)|, where[.]represents thegreatest integerfunction . the numberof pointwhereg(x)is non - differentiableis |
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Answer» 4 |
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| 10859. |
Let f(x) ={{:( [x],-2le xle -(1)/(2) ),( 2x^(2)-1,-(1)/(2)lt xle2):}and g(x) =f(|x|)+|f(x)|, where[.]represents thegreatest integerfunction .the numberof pointwhere|f(x)| is non- differentiable is |
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Answer» 3 |
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| 10860. |
If |z-z_(1)|^(2)+|z-z_(2)|^(22)=|z_(1)-z_(2)|^(2) represents a conic C, then for any point P having affix z on the conic C Statement 1:, The distance between the orthocentre of Delta PAB and the centre of conic is (1)/(2)|z_(1)-z_(2)| because Statement 2: (z_(2)-z)/(z_(1)-z) is purely imaginary |
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Answer» STATEMENT - 1 is True, Statement - 2 is True, Statement-2 is a correct EXPLANATION for Statement-1 |
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| 10861. |
Let f be a twice differentiable functin such that f''(x) - f(x) and f''(x) -g(x) If h (x) = [f (x) ]^(2) + [g (x)]^(2) ,h(1) =8 then h(2)= |
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Answer» 1 |
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| 10862. |
Let a_(n) denote the term independent of x in the expansion of [x+(sin(1//n))/(x^(2))]^(3n), then lim_(xto oo)((a_(n))n!)/(""^(3n)P_(n)) equals |
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Answer» 0 |
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| 10863. |
Choose the correct answer. int_(1/3)^1 (x-x^3)^(1/3)/x^4 dx = |
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Answer» 6 |
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| 10864. |
Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,find fog |
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| 10865. |
The roots of the equation ax^(3)+bx^(2) +cx+d=0, are alpha_(1), alpha_(2), alpha_(3) and roots of g(z)=az^(3) +(f''(y)z^(2))/(2!) +(f'(y))/(1!) z+f(y)=0 are beta_(1), beta_(2), beta_(3), then alpha_(1)-beta_(1) equals |
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Answer» `alpha_(2)-beta_(2)` |
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| 10866. |
If sum_(r=0)^(n) (n)/(""^(n)C_(0))= sum__(r=0)^(n) (n^(2)-3n+3)/(2.""^(n)C_(r)), then |
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Answer» `N = 1` `:. n/2 = (n^(2)-3n+3)/(2)` or `n = 1,3` |
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| 10867. |
In the following graph, state the absolute and the local maximum and minimum values of the function. |
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Answer» Solution :x = 1, 4, 6are the POINTS of local maxima, and thelocal MAXIMUM values are` f(1) = 2, f(4) = 4 andf(6) = 3`. x = 5, 7are the points of local MINIMA, and the local minimum values are` f(5) = 2, f(7) = 1` . x = 2 is the point of absolute minima and the local minimum value isf(2) = 0. x = 8is thepoint of absolute maxima and the absolute maximum value isf (4) = 5. |
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| 10868. |
If a, b in R satisfy the equation a^(2)+4b^(2)-4=0, then the minimum value of (2a+3b) will be |
| Answer» ANSWER :B | |
| 10869. |
Prove that the points P(3,2,-4),Q(5,4,-6) andR(9,8:-10) are collinear. Find the ratio in which the point Q divides the line segment PR. |
| Answer» Solution :Give that P = `(3, 2, -4) Q = (5, 4, -6), R = (9, 8, -10)` D. rs. Of PQ are `lt2,2,-2gt` D. rs. Of QR are `lt4,4,-4gti.e.,lt2,2,-2gt` Thus D.rs. Of PQ and QR are same. So P,Q,R lie on the same STRAIGHT LINE. HENCE P , Q, R are collinear.(PROVED) | |
| 10870. |
If C and D are two events such that CsubsetD and P(D) ne0, then the correct statement among the following is |
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Answer» `1//3` |
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| 10871. |
If m is a natural such that m le5, then the probability that the quadratic equation x^2+mx+1/2+m/2 =0 has real roots is |
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Answer» `1/5` |
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| 10872. |
Find the coefficient ofx^(4) in ((2+3x)^(3))/((1-3x)^(4)) |
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| 10873. |
intsqrt(1+sin2x)dx |
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Answer» SOLUTION :`intsqrt(1+sin2x)DX` =`intsqrt(sin^2x+cos^2x+2sinxcosx)dx` =INT`SQRT(sinx+cosx)^2dx` =`int(cosx+sinx)dx` =`sinx-cosx+C |
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| 10874. |
Using the equality (sin (n + (1)/(2))x)/( 2 sin""(pi)/(2))=(1)/(2) + cos x + cos 2 x + . . . . . + cos nx |
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| 10875. |
If e^(y) (x+ 1)=1, show that (d^(2)y)/(dx^(2))= ((dy)/(dx))^(2) |
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| 10876. |
What are the total number of pokemon used, except dittos, by both Red and Blue? |
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Answer» 6,7 
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| 10877. |
If f(x) =|underset((x)/(1+x^(2))""(a)/(1+a^(2))""(b)/(a+b^(2)))underset(xe^(x) " "ae^(e)""be^(b))(sin^(3) ""sin^(3)a""sine^(3)b)| Where 0 lt a lt b lt2 pi. Then show that the equation f(x) =0 has atlest oneroot in the interval (a,b) |
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| 10878. |
if the function f(x) ={ (1- cos2x)/( 1- cos x) ,x ne 0 iskforx =0 is continuous at x=0 then the the value of k is |
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| 10879. |
If y+(y^(3))/(3)+(y^(5))/(5)+…oo=2[x+(x^(3))/(5)+(x^(5))/(5)+…oo] then |
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Answer» `X^(2)y=2x-y` |
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| 10880. |
The line (x-4)/1=(y-2)/1=(z-k)/2 lies exactly on the plane 2x-4y+z=7 , then the value of k is : |
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Answer» -7 |
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| 10881. |
Evaluate the integral underset(0)overset(1)int x^(7//2)(1-x)^(5//2) dx |
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| 10882. |
If z = x + iy is a complex numbers z for which |z +i//2|^(2) = |z - i//2|^(2) then the locus of z is |
| Answer» ANSWER :A | |
| 10884. |
Find the area of the circle 4x^2+4y^2=9 which is interior to the parabola x^2=4y. |
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| 10885. |
Prove that : int_(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0 |
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| 10886. |
Let f(x) be differentible on [1, 6] and f(1)=-2. If f(x)has only one root in (1, 6) then thereexists c in (1,6) such that |
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Answer» `F'(C)=(1)/(10)` |
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| 10887. |
(d)/(dx) (x^(2) + sin^(2) x)^(3) =……. |
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Answer» `3(X^(2) + SIN^(2)x)` |
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| 10888. |
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -1), (4, 3, -1) |
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Answer» the direction ratios of the `2^nd` line are 4-3, 3-5, 1-+1 i.e., 1, -2, 0 SINCE `2xx1+1xx-2+1xx0 = 2-2+2 = 0`, the two LINES are perpendicular |
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| 10889. |
underset(x to 0)"Lt" ([1^(2)x]+[2^(2)x]+[3^(2)x]+....+[n^(2)x])/(n^(3))= |
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Answer» x/2 |
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| 10890. |
If the circles x^(2) + y^(2) -2x -2y -7 =0 and x^(2) + y^(2) + 4x + 2y + k = 0 cut orthogonally, then the length of the common chord of the circle is |
| Answer» Answer :B | |
| 10891. |
Which of the following statement pattern is a tautology? |
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Answer» <P>`p VV (Q to p)` |
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| 10892. |
Each of the following defines a relation of N : x. y is square of an integer x,y inN. Determine which of the above relations are reflexive , symmetric and transitive . |
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| 10893. |
Let f(x)= "max" {sin x, cos x, (1)/(2)}. Determine the area of the region bounded by y= f(x), x-axis and x= 2pi |
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| 10894. |
Integrate the following inte^(x^3)x^2dx |
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Answer» Solution :`INTE^(x^3)x^2 dx` [PUT `x^3=t` then `3x^2dx=dt` or `x^2dx=1/3(dt)` `inte^tcdot(1/3)dt=(1/3)e^t+C=(1/3)e^(x^3)+C` |
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| 10895. |
The two lines of regression for a bivariate distribution (X,Y) are 3 x + y = 7 and 3x + 5y = 11 . Find the regression coefficient b_(yx) |
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| 10896. |
IF cos A=(-60)/61 and tan B=-7/24 and neither A nor B in the second quadrant, then the angle A+B/2 lies in the quadrant |
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Answer» 1 |
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| 10897. |
Number of ways in which 12 identical balls can be put in 5 different boxes in a row, if no box remains empty is |
| Answer» Answer :C | |
| 10898. |
A straight line which makes equal positive intercepts on X and Y axes and which is at a distance 1 unit from the origin intersects the straight line y=2x+3+sqrt2 at (x_0,y_0). Then 2x_0 +y_0 is equal to |
| Answer» Answer :B | |
| 10899. |
In the first box there re tickets marked with numbers 1,2,3,4 . In the second box there are tickets marked with number 2,4,6,7,8,9. If a box is chosen and a ticket is drawn from it at random, the probability for the number of the ticket to be 2 or 4 is |
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Answer» `9//12` |
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| 10900. |
If y = 36^(log_(6)x), then (dy)/(dx) is |
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Answer» 2x |
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