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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.
| 11051. |
All the permissibel of b ,if a=0 S_(2) is a subset of (0,pi) |
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Answer» `(N PI , n in Z) and (m pi+(-1))^(m) (a sin b) , m in Z)` |
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| 11052. |
If overline(a), overline(b), overline(c) are non-coplanar vectors and lambda is a real number, then [[lambda(overline(a)+overline(b)), lambda^(2)overline(b), lambdaoverline(c)]]=[[overline(a), overline(b)+overline(c), overline(b)]] for |
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Answer» EXACTLY three VALUES of `LAMBDA` |
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| 11053. |
If p:0 is a natural number q:5 is a factor of 10, then |
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Answer» <P>`p implies~q and ~PTOQ` are TRUE |
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| 11054. |
Evaluate the following inegrals int(sec^(2)x)/(sqrt(a+btanx))dx,a,b are positive real numbers |
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| 11055. |
Evalute the following integrals int x^(2) sin^(-1) xdx |
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| 11056. |
If f(x) = f'(x) + f''(x) + f'''(x) + ….and f(0)=1, then f(x) = |
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Answer» `e^((x)/(2))` |
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| 11057. |
Evaluate the following integrals int_0^1(e^x-e^(-x))/(e^x+e^(-x))dx |
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Answer» SOLUTION :`int_0^1((e^x-e^(-x))/(e^x+e^(-x))DX)` `int_2^(e+(1/e))dt/t=[Int]_2^(e+1)` `In(e+(1/e)-In2)=(In(e^2+1)/(2E))` |
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| 11058. |
CHOOSE THE ADD MAN OUT : |
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Answer» `(3/5)^x = x -x^2 -9` |
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| 11059. |
Find sum to infinite terms of the series 1 + 2 ((11)/(10)) + 3 ((11)/(10)) ^(2) + 4 ((11)/(10)) ^(3) +……… |
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| 11060. |
Write the equation of the plane x+3y-7z+2=0 in the intercept from. |
| Answer» SOLUTION :The EQUATION of the PLANE through x-axis and y-axis is xy-plane WHOSE equation is z=0. | |
| 11061. |
The radical centre of the circles x^2+y^2-x+3y-3=0 , x^2+y^2-2x+2y-2=0, x^2+y^2+2x+3y-9=0 |
| Answer» ANSWER :A | |
| 11062. |
If A and B are symmetric matrices , prove that AB-BA is a skew symmetric matrix. |
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| 11063. |
Evaluate the definite integral in exercise overset((pi)/(4)) underset(0) tan x dx |
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| 11064. |
Three numbers are chosen from 1 to 20. The probability that they are not consecutive is |
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Answer» `(186)/(190)` |
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| 11065. |
Discuss the continuity of sine function. |
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| 11066. |
If the vectors p hati + hatj+ hatk, hati i+ q hatj + hatk and hati + hatj + r hatk ( p ne q ne r ne 1) are coplanar, then the value of pqr-(p + q + r) is : |
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Answer» 2 |
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| 11067. |
The range of a random variable X = {1, 2, 3,…} and the probability distribution of X is given by P(X = n) = (k(n +1))/(2^(n)) (n = 1, 2, 3,…) find k. |
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| 11068. |
A circle of the coaxal system with limiting points (0,0) and (1,0) is |
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Answer» `x^(2)+ y^(2) - 2x = 0 ` |
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| 11069. |
Find the difference of percentage ionic character in N-F & B-F bond by using Hanny Smith Equation (EN of B=2, N=3 , F=4) |
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| 11070. |
Area of rhombus is ......., where diagonals are a=2hat(i)-3hat(j)+5hat(k) and b=-hat(i)+hat(j)+hat(k) |
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Answer» `SQRT(21.5)` `a=2hati-3hatj+5hatk" and"b=-hati+hatj+hatk` `:.""` AREA of RHOMBUS `= 1/2|axxb|` `=1/2|-8hati-7hatj-hatk|=1/2sqrt(114)=sqrt(28.5)` |
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| 11072. |
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females. |
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| 11073. |
The order and degree of the differential equation ((dy)/(dx)) ^(1//3) -4 (d ^(2)y)/(dx ^(2)) -7x=0 are alpha and beta, then the value of (alpha +beta) is: |
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Answer» 3 |
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| 11074. |
By the application of Simpson's one-third rule numerical integration, subintervals, the value of int_(0)^(1) (dx)/(1x)is |
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Answer» `(17)/(36)` ie, `h=(1-0)/(2)=(1)/(2)` `therefore underset(0)overset(1)INT (1)/(1+x)DX=(h)/(3)[(y_(0)+y_(2))+4(y_(1))]` `"At" x=0, y=1` `x=(1)/(2), y_(1)=(2)/(3)` `and x=1, y_(2)=(1)/(2)` `therefore underset(0)overset(1)int (1)/(1+x)dx=(1)/(2.3)[(1+(1)/2)+4((2)/(3))]` `=(1)/(6)[(3)/(2)+(8)/(3)]=(25)/(36)` |
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| 11076. |
If alpha,beta,gamma are the cube roots of p, p lt 0, then for any x, y and z the value of (xalpha+ybeta+zgamma)/(zbeta+ygamma+zalpha) is |
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Answer» `OMEGA` |
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| 11077. |
Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+, define ** by a**b=ab |
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Answer» Solution :If a and b are any two POSITIVE INTEGERS, AB is a unique positive INTEGER. Therefore, `**` is a binary operation. |
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| 11078. |
Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+, define ** by a**b=a-b |
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Answer» SOLUTION :We have 4,5 `in Z^+` but 4-5=-1 `cancelin Z^+` `THEREFORE ** ` is not a BINARY OPERATION |
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| 11079. |
If (AB)=B'A', where A and B are not square matrices , then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B. |
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| 11080. |
Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+, define ** by a**b=a |
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Answer» Solution :For any two positive INTEGERS a and b, a is a UNIQUE positive INTEGER `THEREFORE **` is a binary OPERATION |
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| 11081. |
Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on Z^+, define ** by a**b=|a-b| |
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Answer» Solution :For any TWO positive integers a and b, |a-b| is a UNIQUE positive INTEGER `therefore **` is a binary OPERATION |
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| 11082. |
Evaluation of definite integrals by subsitiution and properties of its : If theta_(1) and theta_(2) be respectively the smallest and the largest values of theta in (0,2pi)-{pi} which satisfy the equation, 2cot^(2)theta-(5)/(sintheta)+4=0, then int_(theta_(1))^(theta_(2))cos^(2)3thetad""theta is equal to : |
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Answer» `(2pi)/(3)` |
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| 11083. |
If P(B not) = 0.65, P(A cup B)= 0.85. A and B are independent then find P(A). |
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| 11085. |
Angle between vectors hati - hatj + hatk and hati + 2 hatj + hatk is : |
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Answer» `COS ^(-1) (1 )/(sqrr15)` |
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| 11086. |
If the speed of ball is 145 km//h and the perimeter of the ball is 22.4 cm along the seam and spin ratio of bumrah is 0.1 find angular speed approximately imparted to the ball: |
| Answer» Answer :A | |
| 11087. |
u= f (tan x), v= g(sec x), f'(1) =2 and g'(sqrt2)= 4" then " (du)/(dv)|_(x = (pi)/(4))=………. |
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Answer» `SQRT2` |
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| 11088. |
Evaluate the following integrals intxtan^(-1)x dx |
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| 11089. |
Show that the line x-2y + 4a = 0 touches y^(2) = 4ax. Also find the point of contact |
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| 11091. |
{:("Variate (x) ",0, 1, 2,3,... ,n ),("Frequency (f)", ""^(n)C_0, ""^(n)C_1, ""^(n)C_2,""^(n)C _3, ....,""^(n) C_n):} |
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Answer» ` SQRT((N+1)//2) ` |
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| 11092. |
State True and False for the following (i) Integrating factor of the differential of the form (dx)/(dy)+p_(1)x=Q_(1) is given bye^(intP_(1)dy). (ii) Solution of the differential equation of the type (dx)/(dy)+P_(1)x=Q_(1) is given by x*IF=int(IF)xxQ_(1)dy. (iii) Correct substitution for the solution of the differential equation of the type (dy)/(dx)=f(x,y), where f(x, y) is homogeneous function of zero degree is y = vx. (iv) Correct substitution for the solution of the differential equation of the type (dy)/(dx)=g(x,y), where g(x,y) is a homogeneous function of the degree zero is x=vy. (v) Number of arbitrary constants in the particular solution of a differential equation of order two is two. (vi) The differential equation representing the family of circles x^(2)+(y-a)^(2)=a^(2) will be of order two. (vii) The solution of (dy)/(dx)=((y)/(x))^(1//3)"is "y^(2//3)-x^(2//3)=c (viii) Differential equation representing the family of curve y=e^(x)(Acosx+Bsinx)"is "(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0. (ix) The solution of the differential equation (dy)/(dx)=(x+2y)/(x)"is "x+y=kx^(2). (x) Solution of (xdy)/(dx)=y+xtan""(y)/(x)"is "sin((y)/(x))=cx (xi) The differential equation of all non horizontal lines in aplane is (d^(2)x)/(dy^(2))=0. |
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Answer» Solution :(i) True Given differential equation, `""(dx)/(dy)+P_(1)x=Q_(1)` `therefore""IF=e^(intp_(1)dy)` (ii) True (iii) True (IV) True (v) False There is no arbitrary constant in the particular solution of a differential equation. (vi) False We know that, order of the differential equation =number of arbitrary constant Here, number of arbitrary constant = 1 So order is one. (vii) True Given differential equation, `""(dy)/(dx) =((y)/(x))^(1//3)` `RARR""(dy)/(dx) =(y^(1//3))/(x^(1//3))` `rArr""y^(-1//3)dy=x^(-1//3)dx` On integrating both sides, we get `""inty^(-1//3)dy=intx^(-1//3)dx` `rArr""(y^(-1//3+1))/((-1)/(3)+1)=(x^(-1//3+1))/((-1)/(3)+1)+C'` `rArr""(3)/(2)y^(2//3)=(3)/(2)x^(2//3)+C'` `rArr""y^(2//3)-x^(2//3)=C'""["where",(2)/(3)C'=C]` (viii) True Given that, `""y=e^(x)(Acosx+Bsinx)` On differentiating w.r.t. x, we get `""(dy)/(dx)=e^(x)(-Asinx+Bcosx)+e^(x)(Acosx+(Bsinx)` `rArr""(dy)/(dx)-y=e^(x)(-Asinx+Bcosx)` Again differentiating w.r.t. x, we get `""(d^(2)y)/(dx^(2))-(dy)/(dx)=e^(x)(-Acosx-Bsinx)+e^(x)(-Asinx-Bcosx)+e^(x)(-Asinx+Bcosx)` `rArr""(d^(2)y)/(dx^(2))-(dy)/(dx)+y=(dy)/(dx)-y` `rArr""(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0` (ix) True Given that, `""(dy)/(dx)=(x+2y)/(x)rArr(dy)/(dx)=1+(2)/(x)*y` `rArr""(dy)/(dx)-(2)/(x)y=1` `""IF=e^((-2)/(x)dx)=e^(-2logx)=x^(-2)` The differential solution, `""y*x^(-2)=intx^(-2)*1dx+k` `rArr""(y)/(x^(2))=(x^(-2+1))/(-2+1)+k` `rArr""(y)/(x^(2))=(-1)/(x)+k` `rArr""y=-x+kx^(2)` `rArr""x+y=kx^(2)` (x) True Given differential equation, `""(xdy)/(dx)=y+xtan((y)/(x))` `rArr""(dy)/(dx)=(y)/(x)+tan((y)/(x))""`...(i) ltBrgt Put `""(y)/(x)=v" "i.e., y=vx` `rArr""(dy)/(dx)=v+(xdv)/(dx)` On SUBSTITUTING these values in Eq. (i), we get `""(xdv)/(dx)+v=v+tanv` `rArr""(dx)/(x)=(dv)/(tanv)` On integrating both sides, we get `""int(1)/(x)dx=int(1)/(tanv)dx` `rArr""log(x)=log(sinv)+logC'` `rArr""log((x)/(sinv))=logC'` `rArr""(x)/(sinv)=C'` `rArr""sinv=Cx""["where, C=(1)/(C')]` `rArr""sin(y)/(x)=Cx` (XI) True Let any non-horizontal line in a plane is given by `""y=mx+c` On differentiating w.r.t. x, we get `""(dy)/(dx)=m` Again, differentiating w.r.t. x, we get `""(d^(2)y)/(dx^(2))=0` |
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| 11093. |
Fundamental theorem of definite integral : int_(0)^(pi/4)tan^(100)xdx+int_(0)^(pi/4)tan^(102)xdx=........ |
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Answer» `(1)/(102)` |
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| 11094. |
If the value of a third order determinant is 12, then the value of ther determinant formed by replacing each element by its co-factor will be 144 |
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| 11095. |
From a point on the ground, if the angles of elevation of a bird flying at constant speed in a horizontal direction, measured at equal intervals of time are alpha, beta, gamma and delta, then |
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Answer» `COT^(2) BETA - cot^(2) gamma = 3 (cot^(2) alpha - cot^(2) delta)` |
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| 11096. |
Show that +:R×R→R and o:R×R→R defined as a∗b=∣a−b∣ and aob=a for all a,b∈R. Show that′ ∗′is commutative but not associative, 'o' is associative but not commutative. |
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| 11097. |
If z = (1 + 2i)/(1 - (1 -i)^(2)) then find Arg z |
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| 11098. |
Integrate the following functions : intsqrt(2ax-x^(2))dx |
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| 11099. |
Show thatthe function f(x) = {{:((x I n x)/(1-x) " at " 0 lt x lt 1),(0 "at" x = 0 ),(- 1 "at" x = 1 ):} is integrableon theinterval [0,1] |
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| 11100. |
IF 4x^2+4xy- ky ^2-12- 2y+8can bewrittenas theprodu oftwolinearfactors thenthe factorsare |
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Answer» `(2X + 3y+4 )(3X +5y +2)` |
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