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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.
| 1251. |
f(x)=sqrt(x-[x]) is discontinuous at |
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Answer» square of integers |
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| 1252. |
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is i. 9 ii) 12. |
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| 1253. |
Find the derivative of the w.r.t.x (sin (x +a ))/( cos x ) |
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| 1254. |
A variable triangle ABC is inscribed in a circle of diameter x units. At a particular instant the rate of change of side 'a' is x/2 time the rate of change of the opposite angle A then A = |
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Answer» `pi//2` |
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| 1255. |
If( 1 + x ) ^(n) =a_(0) + a _(1) x +a_(2) x^(2)+ ………. + a_(n)x^(n), then showthat(i)a_(0) - a_(2) + a_(4) - a_(6) + ……… = 2^(n//2) cos. (npi)/4 (ii)a _(1)a_(3) + a_(5) - a_(7) + …….. = 2^(n//2) sin . (npi)/4 |
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| 1256. |
A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies ((x-10)(x-50))/(x-30)ge0,then P(A) is: |
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Answer» `0.20` |
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| 1257. |
If cosec^(-1)(cosecx) and cosec(cosec^(-1)x) are equal functions, then the maximum range of value of x is |
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Answer» `[-(pi)/2,-1]UU[1,(pi)/2]` |
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| 1258. |
Solve the following equations: (i) sin 5x-sin x=cos 3x (ii) 2 cos^(2) theta+3 sin theta-3=theta (iii) cos theta+cos 3 theta=2 cos 2 theta (iv) sin theta+sin 3 theta+sin 5 theta=0 (v) sin 2 theta-cos 2theta-sin theta+cos theta=0 (vi) sin theta+cos theta=sqrt3 (vii) sin theta+sqrt3 cos theta=1 (viii) cot theta+" cosec "theta=sqrt3 (ix) tan theta+tan (theta +pi/3) +tan (theta+(2pi)/(3))=sqrt3 (x) cos 2theta=(sqrt5+1)/(4) (xi) 2 cos^(2) x -7 cos x+3=0 |
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Answer» (vi) `pi/4(8n+1), n in Z` (vii) `2npi+pi//6 pm pi//3, n in Z` (viii) `2npi pm (2pi)/(3)-pi/3, n in Z` (IX) `sqrt3` (x) `npi pm pi/10, n in Z` (xi) `2npi pm pi//3, n in Z` |
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| 1259. |
Find the multiplicative inverse of each of the following complex numbers when it exists. (3+4i)/(4-5i) |
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| 1260. |
A(2, 0) and B(4, 0) are two given points. A point P moves so that PA^(2)+PB^(2)=10. Find the locus of P. |
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| 1261. |
If a matrix has 13 elements, then the possible dimensions (orders) of the matrix are |
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Answer» `1xx13` or `13xx1` |
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| 1262. |
If S_(n)=1 + (1)/(2) + (1)/(2) + …..+ (1)/(2^(n-1)), (n in N) then ……. |
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Answer» `S_(100) LT 100` |
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| 1264. |
Find the equation of a line passing through the points (-1,1) and (2,-4)? |
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| 1265. |
R = {(a, b): a in N, a lt 5, b= 4} write domain and range of R. |
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| 1266. |
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an are of length 22cm. (Use pi=(22)/(7)) |
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| 1267. |
Statement 1: In any DeltaABC he maximum value of r_(1)+r_(2)+r_(3)=9R//2 Statement 2: In any DeltaABC, R ge 2r |
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Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 |
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| 1269. |
358.6 xx 0.078 xx 0.5943 |
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| 1270. |
If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=lambda|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))| the value of lambda is |
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Answer» ABC |
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| 1271. |
If A =(1, 2, 3), B = (2, 3, 4)and AB isproduced upto C such that 2AB = BC, then C = |
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Answer» (5, 4, 6) |
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| 1272. |
bara,barb,barc are three vectors of equal magnitudes and each of them is inclined at an angle of 60^(@) to the others. If abs(bara+barb+barc) = sqrt6, " then find " absbara. |
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| 1273. |
L_1 : 3x+4y+8=0 , L_2 : 2x+7y-1=0If L_1,L_2 represents the sides AB and AC of the isosceles triangle ABC with =AC=2 then the coordinates of |
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Answer» `B " are " (28//5,-11//5)` |
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| 1274. |
Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (i) Parallel to the x-axis Line (k-3) x-(4-k^(2) ) y+k^(2) -7k+6=0. |
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| 1276. |
Find th transformed equation of 2x^(2) +4xy +5y^(2) =0 when the origin is shifted to the point (3,4). |
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| 1277. |
Write and simplify the term involving a^2 b^5 in(a - 2b)^4 (a+b)^3 |
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| 1278. |
If f:Rrrarr RR and g: RR rarr RR are defined by f(x)=|x| and g(x)=[x-3]" for "x in RR, then {g(f(x)):-8//5 lt x lt 8//5}= |
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Answer» `[0, 1]` |
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| 1279. |
Checkthe validity of the following statement" Square of an integer is positive ornegative " . |
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| 1280. |
Let g(x) be a function defined on [-1, 1]. If the area of the equilateral trianglewith two of its vertices at (0, 0) and (x, g(x)) is sqrt(3)//4, then the function g(x) is |
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Answer» `g(X)= pm sqrt(1-x^(2))` |
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| 1281. |
The minute hand of a watch is 1.5 cm long. How far foes its tip move in 40 minutes? |
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| 1282. |
63% of the Americans like cheese where as 76% like apples. If x% of the Americans like both cheese and apples then……… |
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Answer» `X= 39` |
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| 1284. |
Simplifyi) (sin 2theta)/(1+cos 2 theta) ii) (3 cos theta+cos3theta)/(3sintheta-sin3theta) iii) (sintheta+sin2 theta)/(1+costheta+cos 2theta) |
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Answer» ii) `COT^(3)THETA` iii)`tantheta` |
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| 1286. |
A die is tossed once . Whatis the probability of the number 8 coming up ? What us the probability of a number less than 8 coming up ? |
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| 1288. |
Write the contrapositive converse and inverse of the following statements: (i) if two lines are paralllel, then they do not interest in the same plane. (ii) something is hot implies that it has high temperature. (iii) if x is an odd number, then it is prime. (iv) if x is an even number, then it is divisible by 2. (iv) if the diagonals of a rectangle intersect at 90^@, then it is a rhombus. |
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Answer» Solution : (2). Contrapositive statements : (i) if two lines intersect in a plane , then they are not PARALLEL. (ii) if something has not HIGH temperature, then it is not hot. (iii) if x is not a prime NUMBER, then it is not odd. (iv) if x is not divisible by 2 then it is not even. (v) if a rectangle is not a RHOMUS, then its DIAGONAL does not intersect at `90^@`. Converse statements : (i) if two lines does not intersect in a plane, then they are parallel. (ii) if something has not high temperature, then it is hot. (iii) if x is not a prime number, then it is odd. (iv) if x is not divisible by 2, then it is an even number. (v) if a rectangle is a rhomus, then its diagonal intersect at `90^@`. opposite statements : (i) if two lines are not parallel, then they intersect in a plane. (ii) if something is not hot, then its temperatureis not high. (iii) if xis not an odd number,then it is not prime. (iv ) if x is not an even number, then it is not divisible by 2. (v) if the diagonals of a rectangle does not intersect at `90^@` then it is not a rhombus . |
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| 1289. |
Evaluate the following limits : Lt_(xto0)((1^(x)+2^(x)+.........+n^(x))/n)^(n/x) |
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| 1290. |
If f(x)= tan x - x then The least +ve value of 'x' for which f(x)=0 lies in the quadrant |
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Answer» `Q_(1)` |
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| 1291. |
Find the maximum or minimum values of the following functions. 4x - 3x^(2) - 4 |
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| 1292. |
Find the value of p,if the straight lines 6x-10y+3=0,kx-5y+8=0 are parellel. |
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| 1293. |
Consider a triangular pyramid ABCDthe positionvector of whose angular points are a(3,0,1) B(-1,4,1) C(5,2,3) and D(0,-5,4) Let G be the point of intersectionof the medians of triangle BCDThe lengths of the vector bar(AG) is |
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Answer» `sqrt(17)` |
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| 1294. |
Evaluate the following limits in lim_(xrarr-2)((1)/(x)+(1)/(2))/(x+2) |
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| 1295. |
Consider the function f(x) = (x^2 - 4)/(x - 2) Find the domain and range of f . |
| Answer» Solution :DOMAIN =R - {2}, RANGE = R - {4} | |
| 1296. |
If a, b, c, d are in G.P, prove that(a^n + b^n), (b^n + c^n), (c^n + d^n)are in G.P. |
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| 1297. |
A(2, 3), B(-3, 4) are two points. If a point P moves such that the area of DeltaPAB is 8.5 sq. units, then locus of P is |
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Answer» `X^(2)+10xy+25y^(2)-34x-170y=0` |
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| 1298. |
If x+y+z=xyz , " then " sum(3x-x^(3))/(1-3x^(2))= |
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Answer» `pi((3X-x^(3))/(1-3x^(2)))` |
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| 1299. |
The range of f(x)=(sin pi [x^(2)+1])/(x^(4)+1) is , where [.] is greatest integer function |
| Answer» ANSWER :D | |
| 1300. |
How do you distinguish between stable and unstable equilibrium? |
Answer» SOLUTION :
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