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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.
| 8551. |
If S.D of x_1,x_2, x_3 , ...x_n issigma , then find S.D of-x_1 , -x_2 , -x_3 , .....-x_n ? |
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| 8552. |
The sum of the binomial coefficients of the 3rd, 4th terms from the beginning and from the end of (a+ x)^n is 440 then n = |
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Answer» 10 |
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| 8553. |
Lt_(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))] |
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Answer» 1 |
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| 8554. |
Identify the incorrect option ("log"_10 3=0.4771) |
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Answer» `log_3 log_2 28 lt log_4 log_4 255` |
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| 8555. |
(veca+vecb).(vecb+vecc)xx (veca+vecb+vecc) is equal to |
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Answer» 0 |
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| 8556. |
An figure given below consisting of two equal and externally tangent circles inscribed in an ellipse. The eccentricity of the ellipse of minimum area is |
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Answer» `(1)/(SQRT(3))` |
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| 8557. |
If alpha, beta are the roots of lambda(x^(2)+x)+x+5=0 and lambda_(1), lambda_(2) are the two values of lambda for which alpha, beta areconnected by the relation (alpha)/(beta)+(beta)/(alpha)=4, then thevalue of (lambda_(1))/(lambda_(2))+(lambda_(2))/(lambda_(1))= |
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Answer» 150 |
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| 8558. |
Show that the points (2, 3, 4), (- 1, - 2, 1), (5, 8, 7) are collinear. |
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| 8559. |
S and T are the foci of an ellipse and B is an end point of the minor axis . IF /_\STB is equilateral then e = |
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Answer» `1/4` |
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| 8560. |
Let set A= {1,2,3,….50}. Set B is a subset of A and B has exactly 20 elements. If the sum of elements of all possible subsets of B is ""^(49)C_(19).xx 25 xx K |
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| 8561. |
Stating the reason if y is divisible by x then it is not necessary that x is divisible by y. Stating the reason x is divisible by x, AA x in A. |
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| 8562. |
Show that f(x) = |x-5| is continuous but not differentiable at x= 5 |
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| 8563. |
The relation between molarity (M) and molarity (m) is given by : (rho = density of solution (g/mL), M_(1) = molecular weight of solute) :- |
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Answer» `m = (1000M)/(1000rho -M_(1))` |
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| 8564. |
Let f(x)=-2 sin x, if x le (-pi)/(2), f(x)=a sin x+b," if "(-pi)/(2), f(x)=a sin x+b," if "(-pi_/(2) lt x lt pi/2, f(x)=cos x" if "x ge pi//2. The value of d and b so that f(x) is continuous everywhere are |
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Answer» a=0,b=1 |
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| 8565. |
A function f is differentiablein theinterval 0 le x le 5 suchthat f(0) =4& f(5) =- If g (x) =(f(x))/(x+1),thenprovethat there exists some c in (0,5) such that g(c)=-(5)/(6) |
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| 8566. |
If three dice are rolled, find the probability of showing all different numbers. |
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| 8567. |
int(x+1)/(sqrt(1+x^(2)))dx=... |
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Answer» `SQRT(1+x^(2))+TAN^(-1)x+c` |
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| 8568. |
If |vec(a)|=10,|vec(b)|=2 and vec(a).vec(b)=12 then find |vec(a)xx vec(b)|. |
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| 8569. |
Findthe areaenclosedby theparabola (y-2)^2 = x -1 , x -axisand thetangent to theparabolaat (2,3) pointsis …….Sq. units |
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Answer» 9 |
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| 8570. |
If int(dx)/(sqrt(1-x^(2)))=sin^(-1)x-=f_(1)(x) (say) and int(dx)/(sqrt(1-x^(2)))=-cos^(-1)x-=f_(2)(x) (say), then |
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Answer» `f_(1)(x)=f_(2)(x)` |
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| 8571. |
Verify that the given function (explicit or implicit) is a solution of the correseponding differential equation : y = Ax: xy' = y( x ne 0) |
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Answer» SOLUTION :y = AX `RARR y. = A` `rArr XY. = Ax = y ` `THEREFORE` y = Ax is a solution of xy.= y |
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| 8572. |
Find the numberof ways of preparing a garland with 3 yellow, 4 white and 2 red roses of different sizes such that the two red roses come together. |
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| 8573. |
int_(0)^(2pi)(sinx+|sinx|)dx= |
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Answer» 4 |
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| 8574. |
If x^(2)+3x+2=0, x^(2)+6x+k=0 have a common root then p= |
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Answer» 10 (or) 16 |
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| 8575. |
Integrate the following function : int(dx)/(7x^(2)+2x+10) |
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| 8576. |
A manufacturer is preparing a production plan on medicines A and B . There are sufficient ingredients availabe to make 20,000 bottles of A and 40 ,000 bottles of B but there are only 45,000 bottles into which either of the medicines can be put . Further it takes 3 hours to perpare enough material to fill 1000 bottles of A . It takes one hour to perpare enough material to fill 1000 bottles of B and there are 66 hours available for this operation . The number of constraints the manufacturer has is |
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Answer» 4 |
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| 8577. |
Determine whether the following functions are even or odd. {:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):} {:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):} |
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| 8578. |
Given two independent events, if the probability that exactly one of them occurs is 26/49and the probability that none of them occurs is 15/49, then the probabilityof more probable of two events is |
| Answer» Answer :A | |
| 8579. |
Let A = R - {3} , B = R - {1} . If f : A rarr B be defined f(x) = (x-2)/(x-3) AAx inA. Then show that f is bijective. |
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| 8580. |
If A=[[2/3, 1,5/3],[1/3, 2/3, 4/3],[7/3, 2, 2/3]] and B=[[2/5, 3/5, 1],[1/5, 2/5, 4/5],[7/5, 6/5, 2/5]] then compute 3A-5B |
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Answer» SOLUTION :`3A=[[2,3,5],[1,2,4],[7,6,2]]`, 5B=`[[2,3,5],[1,2,4],[7,6,2]]` 3A-5B=`[[0,0,0],[0,0,0],[0,0,0]]` |
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| 8581. |
Find the value of the following integral int_(0)^((pi)/(2)) cos^(7) x dx |
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| 8583. |
The volume of a cube is increasing at a rate of 9 cubic centimetres per second. How fast is the surface area increasing when the length of an edge is 10 centimeters ? |
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| 8584. |
Can the inverse of the following matric be found ? [[1,1],[1,1]] |
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Answer» SOLUTION :`ABSA = [[1,1],[1,1]]`=1-1=0 `THEREFORE A^-1` does not EXIST. |
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| 8585. |
(i) {:[( cos theta , -sin theta ),( sin theta , cos theta ) ]:}"" (ii) {:[( x^(2) -x+1,x-1),( x+1,x+1) ]:} |
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Answer» ` X^(3) , -x^(2) +2` |
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| 8586. |
Verify Rolles theorem for the function: f(x) = x^(2) + 2x -8,x in [-4,2] |
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| 8587. |
Can the inverse of the following matric be found ? [[1,0,0],[0,1,0],[0,0,1]] |
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Answer» Solution :`ABSA = [[1,0,0],[0,1,0],[0,0,1]]=1 ne 0` `THEREFORE A^-1` exists |
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| 8588. |
Evaluate : int (1)/(" cos (x+a) . sin (x+b)") " dx " |
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Answer» SOLUTION :`int (1)/(" cos (x+a) . SIN (x+b)") " dx "` `=(1)/(" cos(a-b)") int(1)/("cos (x_+a) . sin (x+b)")"dx "` `=(1)/(cos(a-b)).int{{"cos(a-b) -(x+b)}}/(cos(x+a).sin(x+b)) dx` `cos (x+b) cos (x+b)` `=(1)/("cos(a-b)") int (+"sin (x+a)sin (x+b))/(cos (x+a) sin (x+b)) dx` `=(1)/(cos(a-b)) int{(cos(x+a)cos(x+b))/(cos(x+a)sin(x+b))` `=(sin (x+a) sin(x+b))/(cos(x+a)sin(x+b))} dx` `=(1)/(cos (a-b)) int {COT(x+b)+tan(x+a)}dx` `=(1)/(cos(a-b)) [log |sin(x+b)| +log |sec (x+a)|] +c.` |
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| 8589. |
A vector vec(a)=alpha hati+2hatj+beta hatk(alpha, beta in R) lies in the plane of the vectors, vec(b)=hati+hatj and vec( c )=hati-hatj+4hatk. If vec(a) bisects the angle between vec(b) and vec( c ), then |
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Answer» `VEC(a)*hati+2=0` |
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| 8590. |
Let E_(1) and E_(2)be two ellipse whsoe centers are at the origin. The major axes of E_(1) and E_(2) lie along the x-axis , and the y-axis, respectively. Let S be the circle x^(2)+(y-1)^(2)=2 . The straigth line x+y=3 touches the curves, S, E_(1) and E_(2) at P,Q and R, respectively . Suppose that PQ=PR=(2sqrt(2))/(3). If e_(1) and e_(2) are the eccentricities of E_(1) and E_(2) respectively, thent hecorrect expression (s) is (are) |
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Answer» `e_(1)^(2)+e_(2)^(2)=(43)/(40)` Sincex+y-3 is a tangent, `a^(2)+b^(2)=A^(2)+b^(2)=9` (using condition `c^(2)=a^(2)m^(2)+b^(2)` etc). POINT P lies on `x^(2)+(y-1)^(2)=2` Euation of normal to circle having slop 1 is `y-1=1x(x-0) or y-y+1=0` SOLVING this normal with tangent line we get point P(1,2) Now, `PA=PR=(2sqrt(2))/(3)` So, points on line `x+y-3=0` at distance `(2sqrt(2))/(3)` from point `P "are"(1+-(1)/(sqrt(2))(2sqrt(2))/(3),2+-(1)/(sqrt2)(2sqrt(2))/(3))` or `Q((5)/(3),(4)/(3)) and Q ((1)/(3),(8)/(3))` Now, `Q((5)/(3),(4)/(3))` lies on `E_(1)` So, `(25)/(9a^(2))+(16)/(9(9-a^(2)))=1` `rArr2525-25a^(2)+16a^(2)=9a^(2)(9-a^(2))` `rArra^(2)-10a^(2)+25=0` `rArr a^(2)=5 so b^(2)=4` `:. e_(1)^(2)=1(b^(2))/(a^(2))=1-(4)/(5)=(1)/(5)` Now, `((1)/(3),(8)/(3))` lies on `E_(2)` So, `(1)/(A^(2))+(64)/((9-A^(2))=9` `rArr9-A^(2)+64A^(2)=9A^(2)(9-A^(2))` `rArr-2A^(2)+1=0` `rArr A^(2)=1 "" so, B^(2)=8` `:. =1- =(1)/(8)=(7)/(8)` |
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| 8591. |
If int(cos^(2)x+sin2x)/((2cosx-sinx))dx=(-A)/(25)x-(2)/(5)log|2cosx-sinx|+(1)/(2-tanx)+C then A is equal to |
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| 8592. |
The value of int_(-pi/8)^(pi/8) x^(10) sin^(9) x dx is equal to |
| Answer» ANSWER :A | |
| 8593. |
If (3x)/((x-6)(x+a))=2/(x-6)+1/(x+a) " then "a= |
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Answer» 1 |
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| 8594. |
Let a plane pass through origin and be parallel to the line (x-1)/2=(y_3)/-1=(z+1)/-2 is such that distance between the plane and the line is 5/3. Then equation of the plane is/are |
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Answer» `x-2y+2z=0` |
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| 8595. |
If x^3, x^4, x^5 …….can be neglected then sqrt(x^2 + 16 ) - sqrt(x^2 + 9) = |
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Answer» `1 - (x^2)/(4)` |
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| 8596. |
If |z- z_1|^2 + |z-z-2|^2 = |z_1 - z_2|^2represents a conic C, then for any point P having affix z on the conic C STATEMENT1: The distance between the orthocentre of Delta PAB and the centre of conic is (1)/(2) |z_1 - z_2|. because STATEMENT 2 : ((n+1)a)/(x + a)is purely imaginary. |
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Answer» Statement -1 is True, Statement -2 ISTRUE,Statement -2 is a CORRECT EXPLANATION for Statement -1 |
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| 8597. |
Five person A,B,C,D and E are selected in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seatas get different coloured hats is ................... |
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Answer» So, there are following THREE cases of selecting hats are `2R+2B+1Gor 2B+2G+1Ror 2G+2R+1B`. To distribute these 5 hats first we will select a person which we can done in `3.^C_(1)` ways and distribute that the which is one of it's colour. and now the remaining four hats can be DISTRIBUTED in two ways. So, total ways will be `3xx.^5C_1xx2 =3xx5xx2=30` |
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| 8598. |
Let M be a set of (2 xx 2) non-singular matrices and R be a relation defined on set M such that R = {(A, B), A, B in M, A is inverse of B} then R is |
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Answer» Reflexive, symmetric but not Transitive Let `(A, B) in R IMPLIES A & B` are inverse of each other. `implies AB = I = BA` `implies BA = AB implies (B,A) in R` Now, Let `(A, B) in R implies AB = L = BA ""....(1)` `(B,C) in R implies BC = l = CB "".....(2)` From (1) & (2) (AB)(BC) = I `AB^(2)C = I` It is CLEAR that `AB^(2)C = I` is `AC = I`, if, `B^(2) = I` Which not possible of each matrix. |
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| 8599. |
Solve the following differential equations.dy/dx=y^2+2y |
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Answer» SOLUTION :`dy/DX=y^2+2yrArrdy/(y(y+2))=dx` `RARR INT(1/y-1/(y+2))1/2dy=intdx` `rArr1/2Iny/(y+2)=x+C` |
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| 8600. |
If f(x) = (x)/(1 + x) and g(x) = f(f(x)), then g(x) is equal to |
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Answer» `(1)/((2x + 3)^(2))` |
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