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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.
| 6051. |
If a matrix has 7 elements, write all possible orders it can have. |
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| 6052. |
x^2 + x + 1 is a factor of ax^(3) + bx^2 + cx + d = 0, then the real root of above equation is (a,b,c,d in R) |
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| 6053. |
Find the transpose of each of the following matrices : (i)[{:(5),((1)/(2)),(-1):}] (ii)[{:(1,-1),(2,3):}] (iii)[{:(-1,5,6),(sqrt(3),5,6),(2,3,-1):}] |
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Answer» (II) `=[{:(1,2),(-1,3):}]` (III) `=[{:(-1,sqrt(3),2),(5,5,3),(6,6,-1):}]` |
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| 6054. |
Find Order and Degree of given differential equationy"' + 2y'' + y' = 0 |
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| 6055. |
If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y |
| Answer» SOLUTION :`y=500E^(7X)+600e^(-7x)dy/dx=7(500e^(7x))-7(600e^(-7x)),(d^2y)/dx=49(500e^(7x)+49(600e^(-7x)=49y` | |
| 6056. |
If A and B are such events that P(A) gt 0 and P(B) ne 1, then P(A'//B')= ....... |
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Answer» `1- P(A//B)` |
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| 6057. |
A rectangular box has sides 3,4 and x and a volume of 18. What is the value of x? |
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| 6058. |
If lim_(xto0) (x^asin^bx)/(sin(x^c)), which a,b,c in R -{0} and, [.] denotes the greatest integer function, then |
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Answer» `a+C=b` |
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| 6059. |
The range of x of which the expansion of (2-3x^2)^(-11/2)is valid is |
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Answer» `(-SQRT(2/3), 2/3)` |
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| 6060. |
Two dice are rolled simultaneously . The probability that the sum of the two numbers on the dice is a prime number , is |
| Answer» Answer :A | |
| 6061. |
Given that, for all real x, the expression(x^(2)-2x+4)/(x^(2)+2x+4)lies between (1)/(3) and 3. The values which the expansion (9*3^(2x) +6*3^(x)+4)/(9*3^(2x)-6*3^(x)+4) lies are |
| Answer» Answer :a | |
| 6062. |
A plane passes through (1,1,1). It is perpendicular to the line (x-1)/(3)= (y-1)/(0) - (z-1)/(4) Then the distance of this plane from the origin is............ |
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Answer» `3/4` |
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| 6063. |
Find the distance of the point (1, -2, 3) from the plane x-y+z=5 measured along a line parallel to x/2=y/3=z/(-6). |
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| 6064. |
The tables give the distribution of grades for 21 students in two different college mathematics classes. For purposes of making statistical calculations, A=4, B=3, C=2, D=1, and F=0. Which of the following statements is true about the data shown for these two classes? I. The standard deviation of grades is greater for class X. II. the standard deviation of grades is greater for class Y. III. The median letter grade is the same for classes X and Y. |
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Answer» I only |
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| 6065. |
int_(0)^(pi//2) sin 2x .tan^(-1)(sin x)dx= |
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Answer» `pi/2 -1` |
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| 6066. |
Integrationof certainirrational expressions int(dx)/(3sqrt((x+1)^(2)(x-1)^(4))). |
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| 6067. |
The total No. of possible isomers of the compound [Cu^(||)(NH_(3))_(4)][Pt^(||)Cl_(4)] are:- |
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| 6068. |
int sqrt(1-cosx)dx=......+c where 0 lt x lt pi |
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Answer» `-2 SQRT(2)cos((X)/(2))` |
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| 6069. |
Determine order and degree (if defined) of differential equations (y''')^(2) + (y'')^(4) + (y')^(5) + y^(6) = 0 |
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| 6070. |
f(x) is cubic polynomial which has local maximum at x = -1. If f(2) = 18, f(1) = -1 and f'(x) has local minima at x= 0, then (A) the distance between (-1,2) and (a, f(a)), where x =a is the point of local minima is 2sqrt5. (B) f(x) is increasing for xin[1,2sqrt5]. (C) f(x) has local minima at x=1. (D) the value of f(0)= 5. |
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Answer» the distance between (-1,2) and (a, F(a)), where x = a is the point of LOCAL MINIMA iis 2 sqrt5 |
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| 6071. |
If P(A) =3/5 and P(B)=1/5,find P(AnnB) if A and B are independent events. |
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Answer» <P> SOLUTION :`P(ANNB)`=P(A)P(B)=3/5xx1/5=3/25 |
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| 6072. |
Equation of the circel passing throuugh the intersection of ellipses (x^(2))/(a^(2))+ (y^(2))/(b ^(2))=1 and (x^(2))/(b ^(2))+ 1is- |
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Answer» `X ^(2) +y^(2)=a^(2)` |
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| 6073. |
Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A cap B^c) |
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Answer» <P> `P(AcapB^C)=P(A-B)=P(A)-P(AcapB)` `3/8-1/4=(3-2)/8=1/8` |
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| 6074. |
Consider the curves C_(1) = y - 4x + x^(2) = 0 and C_(2) = y - x^(2) + x = 0 The area of the region (in sq. units) bounded between the curves C_(1) = 0 and C_(2) = 0 is |
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Answer» `(121)/(6)` |
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| 6075. |
Two small blocks of mass m_A=30 kg & m_B =15 kg are connected with spring & kept on the wedge which is rotating about given axis as shown in figure. If blocks B remain in rest then minimum value of coefficient of friction between block A & wedge is mu_0, then the value of mu_0^2 is : |
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| 6076. |
If vec(a),vec(b),vec(c) are non-coplanar, non-zero vectors such that [vec(a),vec(b),vec(c)]=3,"then"{"["vec(a)xxvec(b),vec(b)xxvec(c),vec(c)xxvec(a)"]"}^(2) is equal to |
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Answer» 81 |
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| 6077. |
Discuss the continuity of the following functions: f(x)=sinx-cosx |
| Answer» Solution :SIN X and cos x are continuous functions SINCE DIFFERENCE of continuous functions is continuous , f is continuous | |
| 6078. |
Discuss the continuity of the following functions: f(x)=sinx+cosx |
| Answer» Solution :sin x and cos x are CONTINUOUS FUNCTIONS Sine SUM of continuous functions is continuous ,F is continuous | |
| 6079. |
Let S_(1)=underset(0 le i lt j le 100)(sumsum)C_(i)C_(j), S_(2)=underset(0 le j lt i le 100)(sumsum)C_(i)C_(j) and S_(3)=underset(0 le i = j le 100)(sumsum)C_(i)C_(j) where C_(r ) represents cofficient of x^(r ) in the binomial expansion of (1+x)^(100) If S_(1)+S_(2)+S_(3)=a^(b) where a, b in N, then the least value of (a+b) is |
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Answer» `66` `=('^(100)C_(0)+^(100)C_(1)+^(100)C_(2)+...+^(100)C_(100))^(2)` `=(2^(100))^(2)=2^(200)` Now `S_(1)+S_(2)+S_(3)=2^(200)=4^(10)=16^(50)=32^(40)=256^(25)=…=a^(b)` HENCE least value of `(a+b)=16+50=66` |
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| 6080. |
Solution of xy - (dy)/(dx) = y^(3)e^(-x^(2)) is |
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Answer» `E^(-X^(2)) = y^(2)(2x-c)` |
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| 6081. |
Integral part of 7 + 4sqrt3)^n is (n in N) |
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Answer» an EVEN NUMBER |
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| 6082. |
Thereare 3 copies of eachof 4differentbooks. Thenumber ofwaysthattheycan bearrangedin ashelfis |
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Answer» `(12!)/(3!)^(4)` |
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| 6083. |
If A (t) = int_(-1)^(t) e^(-|x|) dx, then lim_( t to oo) A (t) is equal to |
| Answer» ANSWER :A | |
| 6084. |
The value of int_(-1)^(1)g(x)-g-(-x)+[x]dx where [.] is the greatest function and g(x) continuous and differentiable for all x is ______________ |
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| 6085. |
underset(0)overset(pi//4)(int)log(1+tanx)dx=..... |
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| 6086. |
If A={x//x^(2)-5x+6=0},B={2,4},C={4,5}, then Axx(B nn C)= |
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Answer» `{(2,4),(3,4)}` |
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| 6087. |
Find the vector equation for the line passing through the points (-1, 0, 2) and (3, 4, 6). |
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| 6088. |
The probability that A speaks truth is (4)/(5), while this probability for B is (3)/(4). The probability that they contradict each other when asked to speak on an event is ………. |
| Answer» Answer :A | |
| 6089. |
Find the area of the region enclosed by the curves y=x^(2) and y = 2x |
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| 6090. |
if Delta (x) = |{:(tan x,,tan (x+h),,tan(x+2h)),(tan(x+2h),,tan x,,tan(x+h)),(tan(x+h),,tan(x+2h),,tanx):}|, " then " Thevalue oflim_(h to 0).(Delta (pi//3))/(sqrt(3)h^(2)) " is" |
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Answer» 144 `rArr underset( h to 0)("LIM") .(Delta)/(h^(2)) =|{:(tan x,,sec^(2) x,,2SEC^(2) x),(tan x,,-2sec^(2) x,,-sec^(2) x),(tan x,,sec^(2)x,,-sec^(2) x):}|` `= |{:(0,,0,,3sec^(2)x),(0,,-3sec^(2)x,,0),(tan x,,sec^(2)x,,-sec^(2)x):}|` `= tan x sec^(4) x` `rArr underset( h to 0)(" lim ") .(Delta (pi//3))/(sqrt(3)h^(2)) =144` |
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| 6091. |
0.10x + 0.20y = 0.18(x + y) Clayton will mix x milliliters of a 10% by mass saline solution with y milliliters of a 20% by mass saline solution in order to create an 18% by mass saline solution. The equation above represents this situation. If Clayton uses 100 milliliters of the 20% by mass saline solution, how many milliliters of the 10% by mass saline solution must he use? |
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Answer» 5 Choices A, C, and D are incorrect and may result from CALCULATION errors. |
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| 6092. |
Let sum of n, 2n, 3n, terms of an A.P are S_(1), S_(2), S_(3) respectively. Prove that S_(3) = 3 (S_(2) - S_(1)). |
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| 6093. |
The ratio in which the line 3x+4y+2 = 0 divides the distance between 3x + 4y + 5 = 0 and 3x + 4y - 5 = 0 |
| Answer» Answer :B | |
| 6094. |
The number of unit vectors which are collinear with non zero vector bar(a) is …………… |
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Answer» Exactly ONE |
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| 6095. |
Let f(x)=lim_( n to oo) n^2 (x^("1/n"^2) -1), x gt 0. If f satisfies f(xy)=4kf(x)+f(y) for x , y gt 0, then k is equal to |
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| 6096. |
If the tangents at two points (1, 2) and (3, 6) as a parabola intersect at the point (-1, 1), then the slope of the directrix of the parabola is |
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Answer» `SQRT2` |
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| 6097. |
L = (1, 3), L^(1) (1, -1) are the ends of latus rectum of a parabola. A is the vertex of the parabola then area of DeltaALL^(1) in sq. units is |
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Answer» 2 |
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| 6098. |
Locus of midpoints of chords of circles x^(2)+y^(2)-4x-2y-4=0 which are perpendicular to the line 4x-3y+10=0 is |
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Answer» `4x-3y+5=0` |
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| 6099. |
The system of equations {:(x+2y+3z=4),(2x+3y+4z=5),(3x+4y+5z=6):} has …………… solutions |
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Answer» INFINITE |
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| 6100. |
The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of vectors 2hati+4hatj-5hatk and lambda hati+2hatj+3hatk is equal to one. Find the value of lambda. |
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