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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.
| 951. |
If A and B are two events associated with a random experiment such that P(A)=0.3, P(B)=0.2 and P(AcapB)=0.1, then the value of P(AcapB') is ……. |
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| 952. |
If 4nalpha = pi then the numerical value of tan alpha tan 2alpha tan 3 alpha ......tan (2n-1) alphais equal to |
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Answer» `-1` |
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| 953. |
Find the equation of the parabola whose vertex is at the point (-2,2) and whose focus is (-6,-6). |
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| 955. |
Let f(x) be any function. Observe the following lists {:("List-I","List-II"),("A)"f^1(a)=0 and f^(11)(a)lt0" then","1) f(x) is increasing at x = a"),("B)"f^1(a)=0 and f^(11)(a)gt0" then","2) f(x) has maximum value at x = a"),("C)"f^1(a)ne0" then","3) f(x) has neither max.nor.minimum"),("D)"f^1(a)gt0" then","4) f(x) has minimum value at x = a"),("","5) f(x) is decreasing at x = a"):} |
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Answer» A-4,B-2,C-3,D-5 |
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| 956. |
The solution set of the equation sin^(-1)x=2tan^(-1)x is |
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Answer» `{1,2}` |
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| 957. |
From the following data compute 3 yearly moving averages. Plot original and trend values on the same graph. {:("Year",2006,2007,2008,2009,2010,2011,2012,2013,2014,2015),("Value",50,36.5,43.0,44.5,38.9,38.1,32.6,41.7,41.1,33.8):} |
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| 958. |
Consider a real valued function f(x) satisfying 2f(xy)=(f(x))^(y)+(f(y))^(x) AA x , y in R and f(1)=a where a != 1 then (a-1)sum_(i=1)^(n) f(i)= |
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Answer» `a^(n+1)+a` |
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| 960. |
Find the volume of the parallelopiped having co-terminus edges bari+barj+bark, bari-barj,bari+2barj-bark. |
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Answer» 2 |
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| 961. |
Let P (3,2,6) be a point in space and Q be point on the line vecr = (hati - hatj + 2 hatk) + mu ( - 3 hati + hatj + 5 hatk). Then the value of mu for which we vector vec (PQ) is parallel to the pplane x - 4y + 3z =1 is |
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Answer» `1/4` |
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| 962. |
cos^(2)5^(@)+cos^(2)10^(@)+cos^(2)15^(@)+.....+cos^(2) 90^(@)= |
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Answer» 7 |
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| 963. |
f(x) = (sin (x-a))/(x -a) , x ne , f(a) = 0 , f(x) at x = a is |
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Answer» discontinuous |
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| 964. |
A ray of light leave the point (3,4) reflects off the y-axis towards x-axis and again after reflection from x-axis finally arrives at the point (8,2) then the abscissa of point where the reflected ray meets x-axis and the ordinate of point where the refleced ray meet y-axis is |
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Answer» `26/11` |
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| 965. |
If the projection of the vector bari+barj+bark " on the vector " abari+barj+2bark " is " 5//3, then a = |
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Answer» 7 |
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| 966. |
If x acute angle and sin(x + 10^(@)) = cos (3x - 68^(@)) then find x in degree. |
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| 967. |
(v) Let y= sqrt{(1+x)/(1-x)} find dy/dx |
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| 969. |
State the equation of the line which has the y-intercept 2 and is inclined at 45^(@) to the x-axis |
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| 970. |
If D is the mid-point of the side BC of triangle ABC and AD is perpendicular to AC, then |
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Answer» ` B^(2)= a^(2) - c^(2) ` |
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| 971. |
For the frequency distribution |
Answer»  `SD=SQRT((Sigmaf_(i)d_(i)^(2))/N-((Sigmaf_(i)d_(i))/N)^(2))` =sqrt(137/60-(37/60)^(2) ) `sqrt(2.2833-(0.616)^2) `=sqrt(2.2833-0.3794)` `sqrt(1.9037)=1.38` |
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| 972. |
For the frequency distribution |
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Answer» `x-2+x+x^(2)+(x+1)^(2)+2X+x+1=60` `rArr "" 2x-2+x^(2)+x^(2)+1+2x+2x+x+1=60` `rArr ""2x^(2)+7x=60` `rArr2x^(2)+7x-60=0` `rArr2x^(2)+7x-60=0` `2x^(2)+15x-8x-60=0` `rArr "" x(2x+15)-4(2x+15)=0` `rArr ""(2x+15)(x-4)=0` `x=-(15)/(2),4` `rArr""x=(-15)/(2)`  Mean `=A+(Sigma f_(i)d_(i))/(Sigmaf_(i))=3+((-12)/60)=2.8` `sigma=sqrt((Sigmaf_(i)d_(i)^(2))/(Sigma_(f_(i)))-((Sigmaf_(i)d_(i))/(Sigmaf_(i)))^(2))=sqrt(78/60-((-12)/60))^(2)` `sqrt(1.3-0.04)=sqrt(1.26)=112` |
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| 973. |
Evaluate the following limits : Lt_(xto0)(4^(x)-9^(x))/(x(4^(x)+9^(x))) |
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| 975. |
If a = Cos theta - Sin theta, b = Cos^(3) theta - Sin^(3) theta, then |
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Answer» `a^(3)-3a+2b=0` |
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| 976. |
If f(x)=x^(n-1)+x^(n-2)+….+1,-1ltxlt1 then f'(x)=……. |
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Answer» `(1)/((x-1)^(2))` |
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| 977. |
If D is maximum interval of [0, pi]such that the function f (x) = |sin x|is an injection on D, then find D. |
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| 978. |
Let L _(1) : (x -1)/( 1) = (y+1)/(2) = (z-2)/(2) L _(2) : x - 2y -1 =0lamda y - z + 2pi : 2x + y-z =0 If the line L _(1) is perpendicular to the line L_(2) then lamda equals |
| Answer» ANSWER :B | |
| 979. |
Let f(x) ={:{( sin x +cos x, 0 lt x lt (pi)/(2) ),(a, x = pi//2) , ( tan ^(2)x + cosecx , pi//2lt xlt pi ):} then its odd extension is |
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Answer» `{:{(-tan^(2)X-cosec",",-PI lt x lt - pi/2),(-a",",x= - pi//2),(-sin x + cos x",",-pi//2 lt x lt 0):}` |
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| 981. |
There are two identical boxes containing respectively. 6 black and 4 red balls, 2 black and 2 red balls. An urns is chosen at random and a ball is drawn from it (i)find the probability that the ball is black,(ii)if the ball is black,what is the probability that it is from the first urn? |
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Answer» (II)`(6)/(11)` |
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| 982. |
If ("Cos"alpha, "Sin"alpha,0),(cos beta, sin beta,0), (cos gamma, sin gamma, 0) are vertices of a triangle then circum radius R is |
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| 984. |
How many different numbers of six digits can be formed with the digits 3,1,7,0,9,5 (without repetition)(i) How many of them are divisible by 10(ii)How many of them will have zero in the ten's place ? |
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| 985. |
For three vectors bar(p), bar(q) and bar(r)" if "bar(r)=3bar(p)+4bar(q) and 2bar(r)=bar(p)-3bar(q) then |
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Answer» `ABS(BAR(r)) lt 2abs(bar(q)) and bar(r), bar(q)` have the same direction |
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| 986. |
Solve the following equations and write general solutions sec x cos 5x+ 1 = 0, 0 lt x lt 2pi |
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| 987. |
DeltaABC be an equilateral triangle whose orthocentre is the origin 'O'. If bar(OA)=bar(a), bar(OB)=bar(b)" then "bar(OC) is |
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Answer» `BAR(a)+bar(B)` |
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| 988. |
A balloon which always remains spherical has a variable diameter 3/2 (2x+1). Find the rate of change of its volume with respect to x. |
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| 989. |
Consider the points A(1,2,8), B(0,3,4), C (1,1,3) and D(2,0,7) Find the mid points of AC and BD |
| Answer» SOLUTION :`(1,3/2,11/2), (1,3/2,11/2)` | |
| 990. |
The price relative to base 100 of a set of commodities are as given in the following tabe : Find the index number usingsimple average of price relatives . |
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| 991. |
The vertices of trianglePQR are P(2,1),Q(-2,3) and R(4,5). Find the equation of the median through the vertex R. |
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| 992. |
For alpha = pi //7 which of the following hold (s) good ? |
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Answer» `TAN ALPHA tan 2 alpha 3 alpha = tan 3 alpha - tan 2 alpha - tan alpha ` |
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| 993. |
Vertices of the triangle ('t' being parameter) are given in list-I and locus of the respective centroids is given in list-II. Match the two lists. The correct matching is |
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Answer» `{:(A,B,C,D),(V,III,ii,i):}` |
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| 994. |
The standard deviation for the following data isn = 10 , sum x = 60, sum x^2 = 1000 |
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Answer» 8 |
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| 995. |
Write down the negation of following compound statements. A triangle has either 3-sides or 4-sides. |
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| 996. |
Consider the fuunctionh_2( x) =f(|g|) and h_2( x) = |f( g(x))| Which of the following is not true about h_1(x)? |
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Answer» It is a PERIODIC function with period `pi` |
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| 997. |
If theta is a parameter . Find the equation of the locus of a moving point , whose coordinates are (a(theta - sin theta),a(1- costheta) |
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| 998. |
Find the orthocentre of the triangle whose vertices are (5,-2),(-1,2),(1,4). |
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| 999. |
If A = {4,5,6,8,9}, B = {4,5,8} and C = {3,4,8,9} Find A cap B andB cap C |
| Answer» SOLUTION :{4,5,8},{4,8} | |
| 1000. |
Sketch roughly the lines satisfying the givenconsition and writeits equation angleof inclination = 150^(@) and distance from the origin= 3 units . |
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