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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.
| 11551. |
if x,y,zare the distancesof the verticesofDelta ABCfrom its orthocentre thenx+y+z 'is |
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Answer» ` 2 (R+r)` |
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| 11552. |
Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the YZ-plane. |
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| 11553. |
Given that A and B are two events associated with a random experiment such that P(A)=0.5, P(B)=0.4 and P(AcupB)=0.7. Then match the following |
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Answer» <P> SOLUTION :`P(ACAPB)rarr0.2,P(barAcapbarB)rarr0.3,P(barAcupB)rarr0.7,P(barAcupbarB)rarr0.8` |
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| 11556. |
Find the values of theta and p, if the equation x cos+ y sin = p is the normal form of the line sqrt3x + y + 2 = 0 . |
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| 11557. |
If P(3,4,5), Q(4,6,3), R(-1,2,4), S(1,0,5) then find the projection bar(RS) on bar(PQ) |
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| 11558. |
Evaluate the following limits :Lim_(x to 0) (sqrt(x+2)-sqrt(2))/x |
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| 11559. |
Without using tables, give the value of each of the following : sec210^(@) |
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| 11560. |
If tan^(3) x + 3 lt 3 tan x + tan ^(2) xthen |
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Answer» `X in (N PI + (pi)/(3), n pi + (pi)/(2)) cup (n pi - (pi)/(3), n pi + (pi)/(4)), n in Z` |
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| 11561. |
If cos^(-1) x + cos^(-1) y + cos^(-1) z = 3pi, then |
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Answer» `X^(2)+y^(2)+z^(2)=2xyz` |
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| 11562. |
Does the point (-2.5, 3.5) lie inside , outside or on the circle x^(2)+y^(2)=25 ? |
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| 11563. |
Show that cot ""(A)/(2)+ cot "" ( B)/(2)+cot "" ( C ) /(2)= (S^(2))/( Delta ) |
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Answer» ` (DELTA )/( S^(2))` |
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| 11565. |
A person observes the top of a tower from a point A on the ground. the elevation of the tower from this point is 60^(@). He moves 60 m in the direction prpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45^(@). Then the height of the tower (in meters) is _____ |
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Answer» `60 SQRT((3)/(2))` |
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| 11567. |
Find the mean, variance and standard deviation using short-cut method Calculate the standard deviation and mean diameter of the circles. |
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| 11568. |
Show that equations of a circle with end points of diameter (x_(1),y_(1))and(x_(2),y_(2)) is same as the equation of circle with end points of diameter(x_(1),y_(2))and(x_(2),y_(1)). Give reason. |
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| 11569. |
The mean and S.D. of the income of the employers of two banks are as follows: Compare the coefficient of variation of the income of the employees of the two banks. |
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Answer» Solution :For bank A `barx_(1)=3200` `sigma_(1)=160` C.V. `=(sigma_(1))/(barx_(1))xx100=160/3200xx100=5` For bank B `barx_(2)=3500` `sigma_(2)=140` C.V. `=(sigma_(2))/(barx_(2))xx100=140/3500xx100=4` Hence the coefficient of variation for bank A's employees is more. |
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| 11570. |
Write each of the following statements in the form if then: You get a job implies that your credentials are good. |
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| 11571. |
Find distance between following pair of points : (-1, 3, -4) and (1, -3, 4) |
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| 11572. |
If bara,barb,barc are unit coplanar vectors, then find [ 2bara-barb2barb-barc2barc -bara]. |
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Answer» 0 |
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| 11573. |
The point B is image of a in the line x+y+4=0 and C is the image of B in the line 2x-y+2=0. If A =(1,2) then circum diameter of triangle ABC is |
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Answer» 12 |
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| 11574. |
Find the derivate of (2)/(x+1)-(x^(2))/(3x-1) |
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| 11575. |
verify whether the followingratiosare direction cosines of somevectoror not . ( i) 1/5, 3/5, 4/5(ii)1/sqrt2, 1/2, 1/2 4/3 ,0, 3/4 |
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Answer» (II) 1 (III)1 |
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| 11576. |
Assertion (A): The torque about the point 3vec(i)-vec(j) + 3vec(k) of a force represented by 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) is vec(i) + 2vec(j)-8vec(k) Reason (R ): The torque of a force F about a point P is vec(r ) xx vec(F ) where vec(r ) is the vector from the point P to any point vec(a) on the line of action of vec(F ) Which of the following is correct ? |
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Answer» Both (A) and (R ) are TRUE and (R ) is the CORRECT EXPLANATION of (A) |
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| 11577. |
If x so large prove that sqrt(x^(2)+25)-sqrt(x^(2)+9)=(8)/(x) nearly. |
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| 11578. |
U= [-2,1], A= {x : x in N, x^(2)+x -2=0} then A'="……….". |
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Answer» `[1, 2]` |
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| 11579. |
Observe the following statements : Statement-I : The angle between the line x=y=z and the plane x+y+z=4 is 90^(@). Statement-II : A tetradedron has vertices O(0,0,0),A(1,2,1),B(2,1,3)andC(-1,1,2). Then the angle between the faces OABandABC is cos^(-1)((19)/(35)). |
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Answer» Only I |
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| 11580. |
Consider function f(x)=x^(4)-14x^(2)+24x-3=p {:("Column - I","Column -II"),((A)"two negative real roots",P"for" pgt120),((B) "two real roots of opposite sign","for"-8leple-5),((C)"four real roots","for"3ltplelt120),((D)"no real roots","for"p lt-8 or -5ltplt3):} |
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| 11581. |
If 5f (x)+3f ((1)/(x))=x+2,y=xf(x),then the value of ((dy)/(dx))(x=1) =……… |
| Answer» Answer :C | |
| 11582. |
The points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. AB produced cuts the y-axis at P and CB produced cuts the x-axis at Q. Find the co-ordinates of the points P and Q. Find the equation of the straight line joining the mid-points of Ac and OB (where O is the origin), and verify that this line passes through the mid- point of PQ. |
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| 11583. |
If A(5, 4) and B(7, 6) are points in a plane, then the set of all points P(x, y) in the plane such that AP : PB = 2:3 is |
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Answer» a CIRCLE |
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| 11584. |
Let A= {1, 2, 3}, B= {3, 4} and C= {4, 5, 6}. Find (A xx (B uuC) |
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| 11585. |
Five mangoes and 4 apples are in a box . If two fruits are chosen at random, find the probability that one is a mango and the other is an apple . |
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| 11587. |
If x sin alpha + y sin2a + z sin 3a = sin4a x sin b + x sin 3b = sin 4b, x sin c + y sin 2c + z sin 3c = sin 4c. Then the roots of the equation t^(3)-(z/2)t^(2)-((y+z)/(4))t+((z-x)/8)= 0 , a b , c ne n pi , are |
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Answer» `sin a , sin B, sin c` |
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| 11588. |
Equation of the plane passing through the point (3,4,5) and parallel to the plane barr.(2bari+barj-bark)=6 is |
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Answer» `barr.(2bari+barj-bark)=-13` |
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| 11589. |
Evaluate : (a) 0.9bar7 (b) 0.2345 |
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| 11590. |
Are the following pairs of statements negations of each other: The number x is not a rational number. The number x isa rational number. |
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| 11591. |
State the equation of the line which has the y-intercept 2 and slope 7 |
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| 11592. |
Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd. |
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Answer» If a NUMBER x is not odd, then x is not a PRIME number. The converse is If a number x in odd, then it is a prime number |
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| 11593. |
The (p+q)th term and (p-q)th terms of a G.P. are a and b respectively. Find the pth term. |
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| 11594. |
If (2,-2),(-1,2),(3,5) are the vertices of a triangle then the equation of the side not passing through (2,-2) |
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Answer» `x+2y+1=0` |
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| 11595. |
Three athletes A, B and C participate in a racecompetition. The probability of winning for Aand B is twice of winning for C. Then. theprobability that the race is won by A or B, is |
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Answer» `(2)/(3)` |
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| 11596. |
The smallest and the largest values of tan^(-1)((1-x)/(1+x)),0lexle1 are |
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Answer» `0, PI` |
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| 11597. |
If the equation of the base of an equilateral triangle is x+y=2 and the vertex is (2,-1), then find the length of the side of the triangle. |
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| 11598. |
The area of the triangle with vertices (1,2,3), (2,5,-1), (-1,1,2) is |
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| 11599. |
An angle is increasing at a constant rate. The rate of increase of tan when the angle is pi//3 is |
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Answer» 4 C |
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| 11600. |
If a particle moves alonga straight line by S = 4t^(2) - 8t + 3 and the time at which the particle comes of rest is 't' seconds then '2t' is |
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Answer» 2 |
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