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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.
| 7101. |
if A=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]and B=[{:(1,0,0),(0,1,0),(0,0,1):}],findwhetherAB=BA or Not . |
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Answer» `THEREFORE `ABExists. `AB=[{:(3,-1,2),(0,5,-3),(1,-2,7):}][{:(1,0,0),(0,1,0),(0,0,1):}]` `=[{:(3.1+00,0+1(-1)+0,0+02.1),(0+0+0,0+1.5+0,0+0+(-3).1),(1.1+0+0,0+1.(-2)+0,0+0+7.1):}]` `=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]` Now No of COLUMNS inB =No. of rows in A ` Therefore ` BA exists . `thereforeBA=[{:(1,0,0),(0,1,0),(0,0,1):}][{:(3,-1,2),(0,5,-3),(1,-2,7):}]` `=[{:(1.3+0+0,1(-1)+0+0,1.2+0+0),(0+0+0,0+1.5+0,0+1(-3)+0),(0+0+1.1,0+0+1(-2),0+0+1.7):}]` `=[{:(3,-1,2),(0,5,-3),(1,-2,7):}]` |
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| 7102. |
There are 8 intermediate railway stations between Vijayawada and Hyderabad. In low many ways can a train be stopped at 3 of these stations such that no two of them are consecutive. |
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| 7103. |
The order and degree of the differential equation ((d^(2)y)/(dx^(2)) + ((dy)/(dx))^(3))^(6//5) = 6y is |
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Answer» 2,1 |
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| 7104. |
The transverse axis of a hyperbola is of length 2a and a verlex divides the segment of the axis between the centre and the corresponding focus in the ratio 2 : 1. The equation of the hyperbola is |
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Answer» `5X^(2)-4y^(2)=5A^(2)` |
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| 7105. |
Which of the following statement is true Statement - I :1 +(1+2) /(2!) + (1+2+3)/(3!) + ......oo = (3e)/2 Statement - II :1 +(3) /(1!) + (5)/(2!) + 7/(3!)+9/(4!) + ......oo = 3e Statement - III :1 +(3) /(2!) + (7)/(3!) + 15/(4!) + ......oo = e(e-1) |
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Answer» I, II TRUE |
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| 7106. |
The vector equation of a plane passing through three points hati+hatj-2hatk, 2hati-hatj+hatk" and " hati+2hatj+hatk is |
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Answer» `BARR.(9hati-3hatj-hatk)=14` |
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| 7107. |
A particle moves in a line with velocity given by (ds)/(d t) = s+1. The time taken by the particle to cover a distance of 9 metre is |
| Answer» Answer :B | |
| 7108. |
Which of the following sentences are propositions and which are not ? Write with reason :It was raining yesterday. |
| Answer» Solution :It was RAINING yesterday. It is not a proposition as it is not KNOWN to which DAY yesterday MEAN. | |
| 7109. |
100 persons are arranged in a row. In how many ways can 5 pairs of consecutive persons can be selected, so that each pair must be seperated by atleast one person |
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| 7110. |
If n(A) = 4, then number of equivalence relations is |
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Answer» 10 |
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| 7111. |
A factory has two Machines - I and II. Machine - I produces 60% of items and Machine -II produces 40% of the items of the total output . Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine -II are defective . If an item is drawn at random what is the probability that it is defective ? |
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| 7112. |
Find the derivative of f given by f(x)= tan^(-1) x assuming it exists. |
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| 7113. |
Observe the following lists {:("List-I","List-II"),((A) 1-(1)/(2)+(1)/(3)-(1)/(4)+(1)/(5)+...oo,(1)(2)/(3)+ (1)/(2)log2),((B)(1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+...oo,(2)log_(e )2),((C )(1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))...oo,(3)-log_(e )((4)/(5))),((D)1+(1)/(3.3^(3))+(1)/(5.3^(5))+...oo,(4)log_(e )((5)/(4))),(,(5)-log_(e )(1-(1)/(n+1))):} The correct match for List - I from List -II is |
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Answer» `{:(A,B,C,D),(2,4,1,5):}` |
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| 7114. |
let f: R to R be a function such that f(2-x)= f(2+x) and f(4-x)=f(4+x), for all x in R and int_(0)^(2)f(x)dx=5. Then the value ofint_(10)^(50) f(x) dx is |
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Answer» 125 |
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| 7115. |
If x=3 cos t and y = 4 sin t, then (d^(2) y)/(dx^(2)) at the point (x_(0), y_(0))=((3)/(2) sqrt(2),2sqrt(2)), is |
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Answer» `(4 SQRT(2))/(9)` |
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| 7117. |
Integration by partial fraction : int(dx)/(4 sin^(2)x+5cos^(2)x)dx=...+c |
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Answer» `(1)/(sqrt(5))tan^(-1)((2tanx)/(sqrt(5)))` |
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| 7118. |
Find the area of the smaller part of the circle x^2+y^2=a^2 cut-off by the line x= (a)/(sqrt(2)). |
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| 7119. |
If vecalpha =x(vecx xx vecb) + y(vecb xx vecc) + z(vecc xx veca) and [veca.vecb.vecc]=1/8, then x+y+zis equal to: |
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Answer» `8vecalpha.(veca+VECB +VECC)` |
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| 7120. |
Find the point on the curve y = x^(2)-3x+2 where tangent is perpendicular to y =x . |
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| 7121. |
A: underset(x to oo)"Lt" x sin""1/x=0 R: If underset(x to a)"lt" f(x)=0 and g(x) is bounded on a deleted neighbourhood ofa then underset(x to a)"Lt" f(x) g(x)=0 |
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Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A |
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| 7122. |
Find the domain of sqrt(9-x^(2)) |
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| 7123. |
Findthe areaof theregionenclosedbetweenthe twocircles: x^2 +y^2 =4 and (x-2)^2+y^2 =4. |
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| 7124. |
Assertion (A) : Ifalpha , beta,gammaare the rootsofx^3 -x-1=0thenalpha^3 + beta^3 + gamma^3 =1Reason (R ):If a +b+c=0 thena^3+ b^3+c^3= 3abc |
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Answer» bothA and RaretrueR ISTHE correctexplanationof A |
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| 7126. |
If the origin and the points P(2, 3, 4),Q(1, 2, 3) and R(x, y, z) are co-planar, then |
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Answer» x - 2y - Z = 0 |
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| 7127. |
If a, b, and c are in A.P., then which one of thew following is not true? |
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Answer» `K/a, k/b` NAD `k/C` are in H.P. |
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| 7128. |
Solve the following inequlities (i) sqrt(x-1) lt x-3 (ii) sqrt(x-3) gt sqrt(7-x) (iii) sqrt (x^(2)+4x+9) gt x +2 (iv) 4-x lt sqrt(2x-x^(2)) (v) root3((x-4)(x-6)) gt 2 (vi) sqrt(x^(2)+3x+5) lt sqrt(x^(2)+x+1) (vii) sqrt((1)/(x^(2))-(3)/(x)) lt (1)/(x)-(1)/(2) (viii) (sqrt(2x^(2)+7x-4))/(x+4) le (1)/(2) (ix) (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0 |
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| 7130. |
If x != 1, then (2x^2 + 4x + 2)/((x + 1)^2) = |
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Answer» 0 |
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| 7131. |
Represent the set in Roster form: A={(x,y):(x,y)"is the co ordinate of point of intersection of line "y=x and " curve "y=e^x}. |
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| 7132. |
if twocurves y=2 sin ((5pi)/6)x and y=alphax^(2)-3ax+2alpha+1 touch each other at some point then thevalue of (sqrt(3alpha))/(5pi) " is "(0le x le (18)/(5)) |
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| 7133. |
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective ? |
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Answer» `((9)/(10))^(5)` |
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| 7134. |
Ifcos alpha+ cosbeta=0= sinalpha + sinbeta ,then cos2 alpha+ cos2 betaisequalto |
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Answer» `- 2 sin( ALPHA + beta) ` |
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| 7135. |
If S_(n)=(1-"tan"^(4)(pi)/(2^(3)))(1-"tan"^(4)(pi)/(2^(4)))……….(1-"tan"^(4)(pi)/(2^(n))). The value of lim_(nto oo)S_(n) is |
| Answer» Answer :B::C | |
| 7136. |
the slope of one ............... |
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Answer» It is also tangent to circle Hence `|sqrt(4m^(2)+1/2)/sqrt(m^(2)+1)|=1` `implies 4m^(2)+1/2 = m^(2)+1 implies 3m^(2) =1/2` `implies m^(2) =1/6 implies m = pm 1/sqrt(6) implies a=1, b=6` |
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| 7137. |
If P(-3, 2) is one end of focal chord PQ of the parabola y^(2)+ 4x + 4y = 0 then slope of the normal at Q is |
| Answer» ANSWER :A | |
| 7138. |
If |z + barz| + |z - barz| , then the locus of z is |
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Answer» a PAIR of straight lines |
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| 7139. |
Calculate the work that has to be done to stop an iron sphere of radius R rotating about its diameter with an angular velocity omega. |
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| 7141. |
If y^(x)= e^(y-x), then prove that (dy)/(dx)= ((1+ log y)^(2))/(log y) |
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| 7142. |
Evaluate the following integrals as the limits of sums int_(0)^(1) ( 5x+ 4) dx |
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| 7143. |
Consider the linear equations ax+by+cz=0, bx+cy+az=0 and cx+ay+bz=0. Match the conditions/expressions in Column I with statements in Column II. |
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Answer» `Delta = |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|` `""= -(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)` `""= -(1)/(2)(a+b+c)[(a-b)^(2)+ (b-c)^(2)+ (c-a)^(2)]` a. `a+b+c ne 0` and `""a^(2)+b^(2)+c^(2)-ab-bc-ca=0` or `""(a-b)^(2)+ (b-c)^(2)+ (c-a)^(2)=0` or `""a=b=c` THEREFORE, this question represents identical planes. b. `a+b+c=0` and `""a^(2)+b^(2)+c^(2)-ab-bc-ca ne 0` This means `Delta = 0 and a, b and c` are not all equal. Therefore, all equations are not identical but have infinite solutions. Hence, `""ax+by= (a+b)Z ""` (using `a+b+c=0`) and `""bx+cy= (b+c)z` `rArr""(b^(2)-ac)y=(b^(2)-ac)z rArr y=z` rArr `""ax+by +cy=0 rArr ax=ay` `rArr""x=y=z` Therefore, the equations represent the line `x=y=z`. c. `a+b+c ne 0 and a^(2)+b^(2)+c^(2)-ab-bc-ca ne 0` `rArr"" Delta ne 0` and the equations have only trivial solution, i.e., `x=y=z=0`. Therefore, the equations represent the planes meeting at a single point, namely origin. d. `a+b+c=0 and a^(2)+b^(2)+c^(2)-ab-bc-ca=0` `rArr"" a=b=c and Delta =0 rArr a=b =c =0` `rArr""` All equations are satisfied by all `x, y and z`. `rArr ""` The equations represent the whole of the three-dimensional space. |
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| 7144. |
Find the equation of all lines having slope -1 that are tangents to the curve y=(1)/(x-1), x ne 1. |
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| 7145. |
Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:(1,-1,2),(3,0,-2),(1,0,3):}] |
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| 7146. |
Let a.b ,gt 0 and Delta=|{:(,-x,a,b),(,b,-x,a),(,a,b,-x):}|, then |
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Answer» a+B-x is a FACTOR of `Delta` |
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| 7147. |
A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time. |
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| 7148. |
if abs({:(sinalpha, cosbeta), (cosalpha, sinbeta):})=1/2, where alpha, beta are acute angles, then find the value of alpha+beta.a) pi/3 b) (2pi)/3c) pi/2d)pi/4 |
| Answer» ANSWER :B | |
| 7149. |
Aman observes that the angle of elevation of the top of a tower from a point P on the ground is alpha.He moves a certain distance towards the foot of the tower and finds that the age of elevation of the top has doubled. He further moves a distance3/4of the previous and finds that the ele of elevation is three times that all. The angle is given by : |
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Answer» `sin alpha =3/4` |
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| 7150. |
3 integers are selected from the numbers 1 to 20. Then ........ is the probability that their product is an even number. |
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Answer» `(2)/(19)` |
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