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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.
| 9051. |
Which of the following are examples of the null set Set of odd natural numbers divisible by 2 |
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| 9052. |
Sketch the graph of sin 2x in the intervals (0,pi). |
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| 9054. |
The total number of solutions of cos x = sqrt 1 - sin 2 x i n [0, 2 pi] is equal to |
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Answer» 2 |
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| 9055. |
For some constants a and b, find the derivative of (x-a)(x-b) |
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| 9056. |
If they are the tangents of a circle, write the radius of the circle |
| Answer» SOLUTION :`37sqrt13/52` | |
| 9057. |
Statement I : If A+B+C=pi (A,B,C gt 0) and the angle C is obtuse then tan A tan B lt 1.Statement II : If A, B, C are acute positive angles such that A+B+C=pi and cot A cot B cot C = Kthen K le (1)/(3sqrt(3))Which of the above statements is correct ? |
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Answer» Only I |
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| 9058. |
Consider the statement S and R S: Both sin x and cos x are decreasing in the interval ((pi)/(2),pi) R: If a differentiable function decreases in an interval (a,b) then its derivative also decreases in (a,b) which of the following is true . |
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Answer» BOT S and R are wrong |
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| 9059. |
The sum of the first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term of the A.P. is (1)/(3)Calculate the first term and the 13th term. |
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| 9060. |
Find the mean deviation about the median for the data : 13,17,16,14,11,13,10,16,11,18,12,17 |
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| 9061. |
bara.barb^(1)+barb.barc^(1)+barc.bara^(1)= |
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Answer» 0 |
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| 9063. |
Given that barx is the mean and sigma^(2)is the variance of n observations x_(1),x_(2),………….x_(n). Prove that the mean and variance of the observations ax_(1),ax_(2),ax_(3),………….ax_(n) are abarx and a^(2)sigma^(2) , respectively, (a!=0) |
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Answer» Solution :Mean of `N` OBSERVATIONS `barx=(x_(1)+x_(2)+…………..+x_(n))/n=(sumx_(i))/nimpliessumx_(i)=n.barx`………….1 Variance `SIGMA^(2)=(sum(x_(i)-barx)^(2))/n` `implies sum(x_(i)-barx)^(2)= nsigma^(2)`…………….2 Now mean of observation `ax_(1),ax_(2),………..,ax_(n)` `barx=(ax_(1)+ax_(2)+..............+ax_(n))/n=(a(x_(1)+x_(2)+..........+x_(n)))/n` `=(asumx_(i))/n=(a.nbarx)/n=abarx`............3 Hence PROVED. and variance `=((sumX_(i)-barX)^(2))/n=1/nsum(ax_(i)-abarx)^(2)` `=a^(2)sigma^(2)` Hence Proved. |
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| 9064. |
How many different selection of 4 books can be made from 10 different books, if (i) Two particular books are always selected. (ii) Two particular books are never selected. |
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| 9065. |
How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE ? |
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| 9066. |
The periodof x-[x] where[x]representstheintergralpart of x is |
| Answer» ANSWER :2 | |
| 9067. |
If f(x)=sinx,-pi//2lexlepi//2, then |
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Answer» f(X) is increasingin the INTERVAL `[-pi//2,pi//2]` |
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| 9068. |
Calculate the price index number by simple average of relative method for the data of Ex. 2. |
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| 9070. |
f(x)= bx^(2) + cx and d and f(x+ 1) - f(x)= 8x + 3 then……. |
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Answer» `B=2, C=1` |
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| 9071. |
Let y= x+(1)/(x).Find the rate of change of y w.r.t. x at x=2. |
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| 9072. |
Find a point at which origin is shifted such that transformed equation of 2x^(2)+y^(2)-12xy+16=0 has no term containing x and constant term. |
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Answer» Solution :Let origin be shifted to the point `(h,k)`. `:. "Put" x=X+h` and `y=Y+km` `2(X+h)^(2)+(Y+k)^(2)-12(X+h)+(Y+k)+16=0` `impliesX^(2)+2h^(2)+4hX+Y^(2)+k^(2)+2kY-12X-12h+Y+k+16=0` `implies 2X^(2)+Y^(2)+X(4h-12)+Y(2k+1)+(2h^(2)+k^(2)-12h+k+16)-0`……`(1)` The EQUATION will be INDEPENDENT of `X` if `4h-12=0` `implies h=3` The equation will be independent of CONSTANT term if `2h^(2)+k^(2)-12h+k+16=0` `implies18+k^(2)-36+k+16=0` `k^(2)+k-2=0` `implies (k+2)(k-1)=0` `implies k=-2` or `k=1` `:.` Required point is `(3,-2)` or `(3,1)` |
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| 9073. |
A(-1, 1), B(5, 3) are opposite vertices of a square. The equation of the other diagonal (not passing through A, B) of the square is |
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Answer» `2x-3y+4=0` |
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| 9075. |
Assertion (A) : If f(x) , g(x) and h(x) are continueous on [a,b] and differentiable in (a,b) , then, the exists c in (a,b)such that |{:(f(a),g(a),h(a)),(f(b),g(b),h(b)),(f'(c ),g'(c ),h'(c )):}|=0 Reason ( R ) : Lagrange's Mean Value theorem is applicable on [a,b] for phi (x ) =|{:(f(a),g(a),h(a)),(f(b),g(b),h(b)),(f'(c ),g(x ),h(x )):}|=0 Then , which of the following is true? |
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Answer» Both A and R are TRUE and R is a correct explanation of A. |
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| 9077. |
The solution of the system of equations whose Augmented matrix is [(1,2,3,6),(2,4,1,7),(3,2,9,14)] is |
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Answer» `x=1,y=1,z=-1` |
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| 9078. |
Prove that (r_(1)(r_(2)+r_(3)))/(sqrt(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)))=a |
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Answer» a |
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| 9079. |
Number of vectors of unit length perpendicular to the vectors vec(a)= (1, 1,0) and vec(b)= (0, 1,1) is |
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Answer» 1 |
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| 9080. |
If x=-1 and x=2 are extreme points of f(x)=alpha log |x|+ betax^(2)+x then : |
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Answer» `alpha=-6, BETA=(1)/(2)` |
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| 9081. |
If cos theta - sin theta = (1)/(5), where 0 lt theta lt (pi)/(4), then{:(,"Column I",,"Column II"),((A),(cos theta+sin theta)//2,(p),(4)/(5)),((B),sin2theta,(q),(7)/(10)),((C ),cos2theta,(r ),(24)/(25)),((D),cos theta,(s),(7)/(25)):} |
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| 9082. |
If the radius of the incircle of a triangle withits sides 5k, 6k and 5 is 6, then k is equal to |
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Answer» 3 |
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| 9083. |
Find the derivative of w.r.to x 7 ^(x ^(3)+ 3x) |
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| 9085. |
Derive the equation for straight line in normal form.Hence find the equation of line p=2 and omega=60^@. |
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Answer» <P> |
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| 9086. |
The value(s) of x satisfying the equation sin^(-1)abs(sinx)=sqrt(sin^(-1)abs(sinx)) is/are given by (n is any integer) |
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Answer» `NPI-1` |
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| 9087. |
If alpha = (2pi )/(7) , then tan alpha tan 2 alpha + tan 2 alpha tan 4 alpha + tan 4 alpha tan alpha = |
| Answer» ANSWER :D | |
| 9088. |
Find themaximum and theminimum values ofthe followingfunctionover R. (i) sin^(2) X (ii)7 cos x-24 sin x + 5 (iii)3 sin x-4cos x (iv)3 cos(4x -5) + 4 (v ) (sinx+ cos x) (vi)5 sin x + 12 cosx + 13 (vii)(3 sin^(2)x+ 4) (ix)5 sin x +12 cos x -13 |
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| 9089. |
Evaluate the following limits in lim_(xrarr3)(x^(4)-81)/(2x^(2)-5x-3) |
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| 9090. |
Angle between the lines x + y = 0 and y = 5 is ........... |
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| 9092. |
The value of the lambda, if the lines (2x + 3y + 4) + lambda( 6 x - y + 14) =0 are {:("Column- I","Column - II"),("(i) Parallel to Y -axis is","(a)" lambda = (-3)/(4) ),("(ii) Perpendicular to" 7x + y -4 =0 "is" , "(b)" lambda = (-1)/( 3) ),("(iii) Passes through (1, 2) is","(c)" lambda = (-17)/( 41) ),("(iv) parallel to X -axis is","(d)" lambda = 3):} |
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| 9093. |
If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) If f(x) = x^3 +x^2 +log_ex and g is inverse of f then 6'g(6) is equal to |
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Answer» 1 |
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| 9094. |
A verrical pole subtends an angle tan^(-1)"1/2 at a points P on the ground. The angle subtended by the upper half the pole at P is |
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Answer» `tan^(-1).(1)/(4)` |
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| 9096. |
What is the geometric property possessed by the straight lines of each system given by 9x + 6y = k |
| Answer» SOLUTION :A FAMILY of PARALLEL LINES | |
| 9097. |
The value of 2 sin 15^(@).cos75^(@) |
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Answer» `(2+SQRT(3))/2` |
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| 9098. |
Given statements (a) and (b). Identify the statements given below as contrapositive or converse of each other. If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi. |
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Answer» (II) CONVERSE |
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| 9099. |
If f:[0, oo) to [0,oo) is defined by f (x) = (x)/(1+ x) , then f is |
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Answer» one-one and onto |
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| 9100. |
Given statements in a and b. Identify the statements given below as contrapositive or converse of each other. If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram (ii) If the diagonals of the quadrilateral bisect each other then it is a parallelogram. |
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Answer» (II) CONVERSE |
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