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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.
| 11251. |
Express each of the complex number given in the form of a+ib (1-i) - (-1+i6) |
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| 11252. |
Convert the following complex number in the polar form : (1+2i)/(1-3i) |
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| 11253. |
4 cards are drawn from a well - shuffled deck of 52 cards. What is the probability of obtaining 3 dimonds and one spead? |
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| 11254. |
Complete the table using calculator and use the result to estimate the limit. lim_(xrarr0)[sqrt(x+3) -sqrt3]/x |
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| 11256. |
Statement-I : If two of the lines represented by ax^(3) + bx^(2)y + cxy^(2) + dy^(3) = 0 (ane 0) make complementary angles with x-axis in anti-clockwise sense then slope of third line is a/d. Statement-II : If the slope of one of the line represented by ax^(2) + 2hxy + by^(2) = 0 is 'n' timesthe slope of another then ((1+n)^(2))/(n)=(h^(2))/(a b) Which of the above statement is correct : |
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Answer» only I |
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| 11257. |
Observe the following statements: Assertion (A) : If vertices of a triangle are A(vec(a)), B(vec(b)), C(vec(c )), then length of altitude through A is (|vec(a) xx vec(b) + vec(b) xx vec(c)+ vec(c ) xx vec(a)|)/(|vec(b)-vec(c )|) Reason (R ): Area of triangle is Delta = (1)/(2) (Base) (Height) = (1)/(2) |vec(AB) xx vec(AC)| |
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Answer» A, R are true, `R RARR A` |
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| 11258. |
If R is the circumradius of equilateral traingle DeltaABC then circumradius of the ex-central triangle is equal to |
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Answer» `(R)/(2)` |
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| 11259. |
......... Is the general form of the complex number of the point lies on real axis . (i.e. X axis) |
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| 11261. |
Find the nature of triangle formed by lines x^(2)-3y^(2)=0 and x=2 |
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| 11264. |
Assertion (A) : The maximum area of rectangle inscribed in a circle of radius '5' is 50 units Reason (R ) : The maximum rectangle inscribed in a circle is square |
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Answer» Both (A) and (R) are TRUE and R is correct explaination of A |
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| 11265. |
Compute the limit of Lt_(x to3)(x^2-8x+15)/(x^2-9) |
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| 11266. |
Differentiate the following functions: (7)/( x^( (2)/(3) ) ) |
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| 11267. |
If the incircle of a triangle ABC passes through the circum centre then cosA + cosB + cosC = |
| Answer» Answer :C | |
| 11268. |
If (1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n in N prove that (a) 3 C_0- 8C_1+13C_2-18C_3+...."upto" (n+1) term=0 if n ge 2 (b ) 2C_0+2^2(C_1)/(2)+2^3(C_2)/(3)+2^4C_(3)/4+....+2^(n+1)(C_n)/(n+1)=(3^n+1-1)/(n+1) ( c)C_0^2+(C_1^2)/2+C_2^2/3+....+C_n^2/(n+1)=((2n+1)!)/(((n+1)!)^2) |
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| 11269. |
If a, b, c are in G.P. and x, y are arithmetic means of a, b and b, c respectively, then (1)/(x)+(1)/(y) is equal to |
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Answer» `(2)/(B)` |
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| 11270. |
If the vectors (a, b, c), (b, c, a) and (c, a, b) are linealy dependent then |
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Answer» `a^(3)+B^(3)+C^(3)=3abc` |
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| 11271. |
Find the points on the X-axis, whose distances from the line (x)/(3) + (y)/(5) =1 are 4 units. |
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| 11273. |
The solution set of sin x lt 1 is |
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Answer» R |
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| 11274. |
A committee of 6 is to be chosen from 10 men and 7 women. So as to contain atleast 3 man and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee ? |
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| 11275. |
If P(1+^t//_sqrt2,2+^t//_sqrt2) be any point on a ine then range of values of t for whic the point P lies between the parallel line x+2y=1 and 2x+4y=15 and intergral value of t is |
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Answer» `-(4sqrt2)/5lttlt(5sqrt2)/6` |
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| 11277. |
Let 'P' be a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with foci S (ae , 0) and S'(-ae,0) . IfA is the area of the triangle PSS' , then the maximum value of A (where e is eccentricity and b^(2)=a^(2)(1-e^(2)))is |
| Answer» Answer :C | |
| 11278. |
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm ( Use pi=22/7) |
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| 11279. |
A flag staff of length 'd' stands on tower of height h. IF at a point on the ground the angle of elevation of the tower and top of the flag staff be alpha, beta then h= |
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Answer» `(dcotbeta)/(Cotalpha-Cotbeta)` |
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| 11280. |
Sum of the series 1-(1)/(2)+1/(2^2)-1/(2^3)+............oo=......... |
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| 11281. |
a,b,c and d are 4 observations . Their mean and median is zero then b = -c. |
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| 11282. |
If sin h x = (3)/(4) then sin h (3x) = |
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Answer» `(61)/(16)` |
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| 11283. |
Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and {0,1,2,3,4,5,6,7,8,9,10} |
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| 11284. |
If a= cos theta+ i sin theta, then find the value of (1+a)/(1-a) |
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| 11285. |
The negation of p^^(q implies ~r) is ……. |
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Answer» <P>`~p^^(q^^r)` |
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| 11286. |
If A(1,2,3), B(6,7,7), C(9,9,0) are three points, then the foot of the perpendicular drawn from the point A to the joining the points B and C is |
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Answer» (3,5,7) |
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| 11287. |
Consider , f(x) = x^(lnx) and g(x) = e^2x let alpha and beta (alpha lt beta) be two values of x satisfying the equation f(x)g(x). The product alpha beta equals : |
| Answer» ANSWER :C | |
| 11288. |
If A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(1//3)+sin^(-1)(3//5) then |
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Answer» `Agt((2PI)/3)` |
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| 11289. |
If A and B are two sets, suchthat n(A) = 115, n(B) = 326, n (A - b) = 47 , then write n (A cup B) |
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| 11290. |
2sin^(-1)x=cos^(-1)(1-2x^(2)) is true for |
| Answer» Answer :C | |
| 11291. |
Consider , f(x) = x^(lnx) and g(x) = e^2x let alpha and beta (alpha lt beta) be two values of x satisfying the equation f(x)g(x). If lim_(x to beta) (f(x) - cbeta)/(g(x) - beta^2) exists and is equal to l then the value of (c - l) is equal to |
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Answer» `4 - E^2` |
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| 11292. |
Two sides of a triangles are given by the roots of the equationx^(2)- 3 ( sqrt2+ 1)x +9sqrt2=0andthe angle between the sides is45^(@), then the triangle is |
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Answer» ISOSCELES |
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| 11293. |
Consider , f(x) = x^(lnx) and g(x) = e^2x let alpha and beta (alpha lt beta) be two values of x satisfying the equation f(x)=g(x). If h(x) = (f(x))/(g(x)) then h'(alpha) is equal to : |
| Answer» ANSWER :D | |
| 11294. |
When x in [-6,8] the maximum value of (x+6)^4(8-x)^3 is |
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Answer» `6^4"8^3` |
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| 11295. |
A card is drawn from a pack of cards . Findthe probability that it is a club |
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| 11296. |
If -pi/2 lt alpha lt pi/2, then prove that tan^(-1)((3sin2alpha)/(5+3cos2alpha))+tan^(-1)((tanalpha)/4)= |
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Answer» `ALPHA` |
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| 11297. |
cos 2x=(sqrt(2)+1)(cos x - (1)/(sqrt(2))), cos x ne (1)/(2) rArr x in |
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Answer» `{2 n PI pm (pi)/(3): n in Z}` |
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| 11298. |
If a, b, c are in A.P. and p is the A.M. between a and b and q is the A.M. between b and c, show that b is the A.M. between p and q. |
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| 11299. |
For x in (0,(5pi)/(2)) define, f(x)= overset(x) underset(0) int sqrt(t) sin t dt then f has |
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Answer» local MINIMUM at `pi` and local MAXIMUM at `2PI` |
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| 11300. |
Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the feet of the perpendicular from the origin on the variable line L has the equation |
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Answer» `2(x^2+y^2)-3x-4y=0` |
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