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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.
| 8251. |
If A and B are two events such that P(A)ne0 and P(B)ne1, then P(barA/barB)= |
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Answer» `1-P(A/B)` |
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| 8252. |
For the hyperbola (x^(2))/( cos ^(2) alpha )-(y^(2))/( sin ^(2) alpha )=1 Which of the following remains constant when alphavaries ? |
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Answer» ABSCISSAE of FOCI |
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| 8253. |
If A=[{:(3,-5),(-4,2):}], then find A^(2)-5A-14I. Hence , obtain A^(3). |
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| 8254. |
Differentiate w.r.t x the function 0 lt x lt (pi)/(2), cot^(-1) [(sqrt(1 + sin x) + sqrt(1-sin x))/(sqrt(1+ sin x)-sqrt(1-sin x))] |
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| 8255. |
Sum of the root of the equation 2sin^(2)theta+sin^(2)2 theta=2, 0lethetalepi//2 is |
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Answer» `pi//2` `IMPLIES(2SIN^(2)theta-1)cos^(2)theta=0` `impliessin^(2)theta=1//2)` or `cos^(2)theta=0` `impliestheta-pi//4` or `theta=pi//2` |
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| 8256. |
Divisibility by non-zero integers is |
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Answer» REFLEXIVE and SYMMETRIC |
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| 8257. |
Entropy change for reversible phase transition at contant pressur 'P' and temperature 'T' is calculated by the formula DeltaS=(DeltaH)/(T), where DeltaH is the enthalpy change for phase transition. For irreversible phase transitionDeltaS gt (DeltaH)/(T). Cosider a phase transition "Sn(white, s )" iff Sn ("gray, s") DeltaH^(@) at1 atm & 300K=- 2 kJ mol^(-1). The equilibrium temperature at 1 atm is 400 K. Assume C_(p,m)of Sn (white, s) and Sn (gray, s) are equal. DeltaG^(@) for above phase transition at 1 atm and 300 K is |
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Answer» `-500 J mol^(-1)` |
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| 8258. |
A straight line AB touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the ciecle x^(2)+y^(2)=r^(2), where b lt r lt a. PQ is a focal chord of the ellipse. If PQ is parallel is parallel to AB and cuts the circle in P and Q. find the of the pernepducular drawn from the centre of the ellipse to PQ hence. show that PQ=2b. |
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| 8259. |
Let P be the point on the parabola y^(2)=8xwhich is at a minimum distance from the centre C of the circle x^(2)+(y+6)^(2) =1 . Then the equation of the circle passing through C and having its centre at P is |
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Answer» `X^(2)+y^(2)-4x+8y+12=0` |
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| 8260. |
int(2xtan^(-1)x^(2))/(1+x^(4))dx=... |
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Answer» `[tan^(-1)X^(2)]^(2)+C` |
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| 8261. |
A : 3 sin x + 4 cos x = 7 has no solution R : a cos x + b sin x = c has no solution if |c|gt sqrt(a^(2)+b^(2)) |
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Answer» both A and R are true and R is CORRECT explanation of A |
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| 8262. |
Range of f (x) =(x^(2) x+2)/(x^(2) +x+1)(-oolt x lt oo) is- |
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Answer» `1 LE f (X) lt oo` |
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| 8263. |
Let f(x) = inte^(x)(x-1)(x-2)dx. Then f decreases in the interval |
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Answer» `(-OO, -2)` |
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| 8264. |
The vertices A, B, C of a triangle are (2, 1), (5, 2) and (3, 4) respectively. Then the circumcentre is |
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Answer» `((13)/(4), (-9)/(4))` |
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| 8265. |
If the straight line y=mx+c is parallel ot the axis of the parabola y^(2)=lx and intersects the parabola at (c^(2)/8,c), then the length of the latusrectum is |
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Answer» 2 |
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| 8266. |
If A=[{:((2)/(3),1,(5)/(3)),((1)/(3),(2)/(3),(4)/(3)),((7)/(3),2,(2)/(3)):}]andB=[{:((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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| 8267. |
If A=[{:(a,b),(b,a):}]andA^(2)=[{:(x,y),(y,x):}]then , x=……, y=……. |
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Answer» `x=a^(2)+B^(2),y=a^(2)-b^(2)` |
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| 8269. |
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X) |
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| 8270. |
If (d)/(dx) f(x) = g(x) then int_(a)^(b) f(x) g(x) dx= |
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Answer» `(F(B)-f(a))/(2)` |
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| 8271. |
ifh (x) = min {(2)/(f(x)) x^(2) |1 - |x||} then the number of points of non-differentiability h(x) is/are |
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Answer» 3 |
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| 8272. |
Let f(x+5)=2x+1,then find f^(-1) (2) |
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| 8273. |
Consider the following ststements. I. Solution set of the inequality -15lt(3(x-2))/(5)le0 is (-23,2] II. Solution set of the inequality 7le(3x+11)/(2)le11 is [1,(11)/(3)] III. Solution set of the inequality -5le(2-3x)/(4)le9 is [-1,1]uu[3,5] Choose the correct option |
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Answer» Only I and II are TRUE. |
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| 8274. |
Find the number of all 6-digit natural numbers having exactly three odd digits and three even digits. |
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| 8275. |
Find the projection of the vector veca=2hati+3hatj+2k on thevector vecb=hati+2hatj+hatk. |
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| 8276. |
Write the number of solution of the following system of equation. 2x+y=2 and -x-1/2 y=3 |
| Answer» SOLUTION :No solution | |
| 8277. |
A : sin 40^@ - sin 80^(@) + sin 160^(@) = 0 R :sin theta + sin(60^(@) - theta ) - sin (60^(@) + theta ) =0 |
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Answer» A is true , R is true and R is CORRECT EXPLANATION of A |
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| 8278. |
If the areas of the sectors in thecircle graphs are drawn in proportion to the percent shown, what is the measure, in degree, of the sector representing the number of high school with Pupil/Teacher ratio greater than 27 in 1999? |
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Answer» 21.6 |
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| 8279. |
Differentiate the following with respect to x: (e^(x)logx)/(x^(2)) |
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| 8280. |
Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the midpoint of the chords of the circle C that substend an angle of 2pi//3 at its centre is |
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Answer» `X^(2)+y^(2)=3/2` |
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| 8281. |
If a, b, c, ..., k are roots of the equation f(x) = 0, then the value of(f(x))/(x-a) +(f(x))/(x-b) +…+(f(x))/(x-k) is |
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Answer» 2 |
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| 8282. |
Do both parts of problem 2 if 4 cards are drawn at random. |
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Answer» SOLUTION :4 CARDS are drawn one after another. As they are of DIFFERENT suits, we have their PROBABILITY `=52/52xx39/51xx26/50xx13/49` As the cards are of different DENOMINATIONS,we have their probability `= 52/52xx48/51xx44/50xx40/49` |
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| 8283. |
If Z= ((sqrt3 +1)^(3) (3i + 4)^(2))/((8+ 6i)^(2)) then |Z| is equal to |
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Answer» 3 |
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| 8284. |
f:[0,1)toR be a non increasing function the for alpha epsilon(0,1) |
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Answer» `alpha int_(0)^(1)f(x) DX le int_(0)^(alpha)f(x)dx` Put `x=alphat` `:. int_(0)^(alpha) f(x)dx=alpha int_(0)^(1)f (alpha t)dt ge alpha int_(0)^(1)f(t)dt` as `alpha epsilon(0,1)` ALSO `alpha int_(0)^(1) f(t)dt ge alpha^(2) int_(0)^(1)f(t)dt` `:. int_(0)^(alpha)f(x)dxgealpha^(2)int_(0)^(1)f(x)dx` |
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| 8285. |
Write the value of int(cosx-sinx)/(sinx+cosx)dx. |
| Answer» SOLUTION :`INT(cosx-sinx)/(sinx+cosx)dx=int(DT)/t` where SIN x+cos x=t `RARR(cosx-sinx)`dx=dt=In | t| +C=In |sin x+cos x|+C | |
| 8286. |
Statement I: If A+B+C=pi and cos A =cos B cos C then cot B cot C=1/3 Statement II : If 5 sin B=sin (2A+B) then 2tan(A+B)=3 tan A Which of the above statements is correct? |
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Answer» only I |
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| 8288. |
int(e^(2x)-1)/(e^(2x)+1)dx=... |
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Answer» `(E^(2X)-1)/(e^(2x)+1)+C` |
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| 8289. |
If A =[[1,3],[2,4]] ,then A.(Adj. A) = |
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Answer» `[[0,-2] , [-2,0]]` |
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| 8290. |
If f(x)=x tan^(-1) x," then "lim_(x to 1)(f(x) - f(1))/(x-1)equals to |
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Answer» ` (PI +3)/4` |
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| 8291. |
S is defined on N xxN by ((a,b) , (c,d) in S hArr a +d = b +c ........ |
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Answer» S is REFLEXIVE , but not symmetric |
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| 8292. |
(bar(a)xx bar(b))^(2) = …………….. |
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Answer» `|{:(BAR(a).bar(B),bar(a).bar(a)),(bar(b).bar(b),bar(b).bar(a)):}|` |
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| 8293. |
Let sqrt(3)hati+hatj,hati+sqrt(3)hatj" and "betahati+(1-beta)hatj respectively be the position vectors of the points A, B and C with respect to the origin O. If distance of C from the bisector of the acute angle between OA and OB is (3)/(sqrt(2)), then the sum of all possible values of beta is(a) 1(b) 3(c) 4(c) 2 |
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Answer» 1  CLEARLY, angle bisector divides the sides AB in OA:OB, `i.e., 2 : 2 =1 : 1""[using angle bisector theorem]` So, D is the mid-point of AB and hence coordinates of D are `((sqrt(3)+1)/(2),(sqrt(3)+1)/(2))` Now, eauation of bisector OD is `(y-0)=(((sqrt(3)+1)/(2)-0)/((sqrt(3)+1)/(2)-0))(x-0)impliesy=x` `impliesx-y=0` According to the problem, `(3)/(sqrt(2))=CM=|(beta-(1-beta))/(sqrt(2))|` [Distance of a point `P(x_(1),y_(1))` from the line `ax+by+c=0" is "|(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))|]` `implies""|2beta-1|=3implies2beta=+-3+1` `implies""2beta=4, -2impliesbeta=2, -1` Sum of 2 and -1 is 1. |
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| 8294. |
Integrate the rational functions (2x)/(x^(2)+3x+2) |
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| 8295. |
If the lines 3x- 4y = 12 and 3x + 4y = 12meets on a hyperbolaS = 0then find the eccentricityof the hyperbola S = 0 |
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| 8296. |
The vapour pressure of CS_(2) at 50^(@)C is 854 torr and a solution of 2.0 gm sulphur in 100 gm of CS_(2) has vapour pressure 848.9 torr. If the formula of sulphur molecule is S_(n) , then calculate the value of "n" (approx) (At mass of S = 32):- (fill nearest integer value) [Assume very dilute solution]. |
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Answer» `(mol. Wt)_("solute") = 254.5` mol. Wt of `S_(n) = 32 xx n` `32 xx n = 254.5` `n = 7.95` `= 8`. |
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| 8297. |
If the line L: (x-1)/(4)=(y+3)/(-2)=(z+5)/(1) lies in the plane 2x+ly+mz=16 then l^(2)+m^(2) is equal to: |
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Answer» 16 |
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| 8298. |
Area enclosedby curvesy^2-5xy+6x^2+3x-y=0and y^2-5xy+6x^2+2x-y=0 is lambda sq units , then the value of lambda is |
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| 8299. |
Find the number of 4 - letter words that can be formed using the letters of the word RAMANA. |
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| 8300. |
Let E_(1), E_(2), E_(3), ....,E_(n) be independent events with respective probabilities p_(1), p_(2), p_(3), ....,p_(n). The probability that none of them occurs is ………. |
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Answer» `(1- p_(1))(1-p_(2))(1-p_(3))... (1-p_(N))` |
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