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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. |
If A is a square matrix and A^2=A" then |A|=…….. |
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Answer» 0 or 1 |
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| 2. |
I. The locus of the point of intersection of two perpendicular tangents to the circle x^(2)+y^(2)=a^(2)" is "x^(2)+y^(2)=3a^(2). II. The locus of the point of intersection of the perpendicular tangents to the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b^(2)" is "x^(2)+y^(2)=a^(2)+b^(2) |
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Answer» only I is true |
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| 3. |
int sqrt(x)/(sqrt(x)-3sqrtx)dx is equal to |
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Answer» `6{(x)/(6)+(x^(6//5))/(5)+(x^(1//2))/(2)+(x^(1//3))/(3)+log(x^(1//6-1))}+c` |
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| 4. |
Differentiate the following with respect to x: (e^(x)-1)/(e^(x)+1) |
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| 5. |
The work done by the force vecF=2hati-3hatj+2hatk in moving a particle from (3, 4, 5) to (1, 2, 3) is : |
| Answer» Solution :N/A | |
| 6. |
If the normal drawn at one end of the latus rectum of the ellipse b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2) with eccentricity 'e' passes through one end of the minor axis. Then, |
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Answer» `E^(4)+e^(2)=2` |
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| 7. |
Corner points of the feasible region for an LPP are ( 0,2) (3,0) ,(6,0),(6,8)and (0,5) Let Z=4 x + 6ybe the objective function. The minimum value of F occurs at? |
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| 8. |
Evaluate : int [ log (log x) +(1)/((log x)^(2)) ] dx |
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| 9. |
Consider the following statement. "If a triangle is equiangular, then it is an obtuse angled triangle." This is equivalent to I. a triangle is equiangular implies that it is an obtuse angled triangle. II. For a triangle to be obtuse angled triangle it is sufficient that it is equiangular. Choose the correct option. |
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Answer» Both are correct. |
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| 10. |
Volume of the parallelopiped having vertices at O equiv (0, 0, 0), A equiv (2, -2, 1), B equiv (5, -4, 4) and C equiv (1, -2, 4) is |
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Answer» 5 cu units `OB=5hati-4hatj+4hatk` and `OC=hati-2hatj+4hatk` VOLUME of parallelopiped`=["OA OB OC"]` `=|{:(2,-2,1),(5,-4,4),(1,-2,4):}|=2(-16+8)+2(20-4)+1(-10+4)` `=-16+32-6=10`cu units. |
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| 13. |
Find the number of ways in which 4 boys and 4 girls can be arranged along a row such that atleast one of the first 3 places must be arranged with a girl. |
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| 14. |
IfX-[[4,-5],[1,-3]]= [[0,1],[2,4]],then find the matrix X. |
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| 15. |
Let AOB be the positive quadrant of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with OA=a , OB=b . Then show that the area bounded between the chord AB and the arc AB of the ellipse is ((pi-2)ab)/(4) |
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Answer» `(PI AB)/(2)` |
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| 16. |
Five coins are tossed whose faces are marked 2 and 3 . Find the probability of getting sum 12. |
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| 18. |
Which of the following limits exists finitely? |
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Answer» `underset(xrarr0^(+))(lim)(x)^(log_(E)x)` So, limits does not exist finitely. (b) `underset(xrarr3)(lim)(x^(2)-9-sqrt(x^(2)-6x+9))/(|x-1|-2)` `=underset(xrarr3)(lim)(x^(2)-9-|x-4|)/(x-3)` Now, `f(3^(+))=underset(xrarr3^(+))(lim)((x^(2)-9)-(x-3))/((x-3))=underset(xrarr3^(+))(lim)((x+3)+1)=5` ALSO, `f(3^(-))=underset(xrarr3^(-))(lim)((x^(2)-9)+(x-3))/((x-3))=underset(xrarr3(-))(lim)((x+3)+1)=7` So, LIMIT does not exist. (c) `underset(xrarr3^(-))(lim)([x])^((1)/(x-1))underset(xrarr1^(+))(lim)^((1)/(x-1))=1` |
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| 19. |
Let the planes x-2y+kz=0 and x+5y-z=0 be perpendicular. Then the plane through (2,-2,-2) and perpendicular to the given planes also passes through the points |
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Answer» `(0,5,8)` |
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| 20. |
In triangle ABC, which of the following is not true.a)oversetrarr(AB)+oversetrarr(BC) + oversetrarr(CA) =oversetrarr0b)oversetrarr(AB) +oversetrarr(BC) - oversetrarr(AC) =oversetrarr0c) oversetrarr(AB) + oversetrarr(BC) -oversetrarr(CA) = oversetrarr0d)oversetrarr(AB) - oversetrarr(CB) +oversetrarr(CA) =oversetrarr0 |
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Answer» `oversetrarr(AB)+oversetrarr(BC) + oversetrarr(CA) =OVERSETRARR0` |
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| 21. |
IF thelinex-y=-4kis a tangent to theparabolay^2= 8x at P , thenthe perpendiculardistance ofnormalat Pfrom( k , 2k)is |
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Answer» `(5)/(2sqrt(2))` |
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| 22. |
Normal at point P(x_1,y_1), not lying on x-axis, to the hyperbola x^2-y^2=a^2 meets x-axis at A and y-axis at B. If O is origin then: |
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Answer» Circumcentre of TRIANGLE OAB at P |
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| 23. |
Examine the following functions for continuity : f(x)=1/(x-5),xne5 |
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| 24. |
There are 11 fruits in a basket of which 6 are apples, 3 mangoes and 2 bananas (fruits of same species are identical). How many ways are there to select atleast one fruit? |
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| 25. |
The vlaue of sinx+siny=a and cos x+cosy=b then cos(x-y)= |
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Answer» `(a^(2)+B^(2)+2)/2` |
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| 26. |
The solution of (dy)/(dx) = (2x -y)/(2y-x) is |
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Answer» `(y + X) (y + x)^(3) = CX^(4) e^(--4x)` |
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| 28. |
int_-a^a(x^5+2x^2+x)dx |
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Answer» SOLUTION :`int_-a^a(x^5+2x^2+x)DX=[x^6/6+(2x^3)/3+(2x^2)/2]_-a^a` =`1/6(a^6-a^6)+2/3(a^3+a^3)+(a^2-a^2)=(4a^3)/3` |
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| 29. |
Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(4-x)^2 |
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| 30. |
Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x,x^2,yz),(y,y^2,zx),(z,z^2,xy):}|=(x-y)(y-z)(z-x)(xy+yz+zx) |
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| 31. |
If y= ( sin^(-1) x)^(2) , show that (1-x^(2) ) (d^2 y)/( dx^2) - x (dy)/(dx) =2 |
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| 32. |
Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3 |
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| 33. |
Coefficient of x^(10) in e^(3x) is |
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Answer» `3^(10)` |
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| 35. |
The remainder when the polynomial x + x^3 + x^9 + x^27 + x^(81) + x^(243) is divided by x^(2)-1. |
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| 36. |
Evaluate: int(5x+3)/(sqrt(x^2+4x+10))\ dx |
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| 37. |
Given that vec(a).vec(b)=0 and vec(a)xx vec(b)=0. What can you conclude about the vectors vec(a) and vec(b) ? |
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| 38. |
Let A = R- {3} and B = R - {1}, consider the function f A rarr B defined by =((x-2)/(x-3))Show that f'is one-one and onto and hence find/ |
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| 39. |
If alpha, beta are the roots of x^(2) - x + 1 = 0 then the quadratic equation whose roots are alpha^(2015), beta^(2015) is |
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Answer» `x^2 -x+1=0` |
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| 40. |
If a ne b ne c, then solution of equation |{:(x-a,x-b,x-c),(x-b,x-c,x-a),(x-c, x-a,x-a):}|=0" "is: |
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Answer» `x=0` |
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| 42. |
If theta is the angle between two vectors vecaandvecb then veca*vecbge0 only when |
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Answer» `0ltthetalt(PI)/(2)` |
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| 43. |
Find all numbers a for each of which the least value of the quadratic trinomial 4x^2 - 4ax + a^2 - 2a + 2 on the interva 0 le x le 2is equal to 3. |
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| 44. |
Consider the following n ordered pairs of correspinding values of the two variables x and y. (x_(1),y_(1)), (x_(2),y_(2)), (x_(3),y_(3)), ...............(x_(n),y_(n)) Statement -1 : If byx and bxy are the two regression coefficients, then byx bxy le 1 Statement -2 : if e(x,y) is the karl pearson's coefficient of correlation, then e(x,y)=sqrt(byx bxy) which of the following is true? |
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| 45. |
int _(0)^(1) (x)/(x^(2)+1)dx |
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Answer» SOLUTION :`"Let "I= int_(0)^(1)(x)/(x^(2)+1)DX` `"Let" x^(2)+1=t rArr XDX=(dt)/(2)` `x=0 rArr t=1` `" and" x=1 rArr t=2` `:. I= int_(1)^(2) (1)/(t).(dt)/(2) =(1)/(2) int_(1)^(2) (1)/(t)dt =(1)/(2) [log |t|]_(1)^(2)` `=(1)/(2)[log |2|-log |1|]=(1)/(2)log 2.` |
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| 46. |
Prove that if the axes be turned through (pi)/(4) the equation x^(2)-y^(2)=a^(2) is transformed to the form xy = lambda. Find the value of lambda. |
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| 47. |
Find the equation of the circle which passes through (1,1) and cuts orthogonally each of the circles x^2+y^2-8x-2y+16=0 and x^2+y^2-4x-4y-1=0 |
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| 48. |
If AB and CD are two chord of a circle intersecting at right angles in P and O is centre, then overline(PA)+overline(PB)+overline(PC)+overline(PD)= |
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Answer» `2overline(PO)` |
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| 49. |
If n is even then C_0^2 - C_1^2+C_2^2-…....+(-1)^nC_n^2= |
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Answer» 0 |
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| 50. |
Let P_(1):x+y+2z-3=0 and x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1) and P_(2)=x-2y+z=4 be two planes. Also, let A(1,3,4) and B(3,2,7) be two points in space. The equation of plane which passes through line of intersection of P_(1)and P_(2) and upon which length of projection of the line segment AB is the greatest, is |
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Answer» `2x+3y+z+4=0` |
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