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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.
| 3301. |
State with reason, " All college teachers who are citizens of India " is set or not ? |
| Answer» SOLUTION :It is a SET, as it is WELL DEFINED. | |
| 3302. |
Let f(x) =x^(@) cos (1/x), when x ne 0 and f(x)=0, when x=0. Then f(x) will be differentiable at x=0, if |
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Answer» <P>`p gt 0` |
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| 3303. |
Evalute the following integrals int (xe^(x))/((1 + x)^(2))dx |
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Answer» |
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| 3305. |
Show that z = e ^(x) (x cos y - y sin y) is tarmonic function. |
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| 3306. |
Ifoverset(to)(u) , overset(to)(v) , overset(to)(w) are threenon- coplanarunitvectorsandalpha , beta , gammatheanglesbetweenoverset(to)(u) " and" overset(to)(v) , overset(to)(v) " and " overset(to)(w), overset(to)(w)"and" overset(to)(u) respectivelyand overset(to)(x) , overset(to)(y) , overset(to)(z)are unitvectorsalongthe bisectorsof theanglesalpha , beta, gamma respectively. Provethat [overset(to)(x) xx overset(to)(y) overset(to)(y) xx overset(to)(z) overset(to)(z) xx overset(to)(x)] = (1)/(16) [ overset(to)(u) overset(to)(v) overset(to)(w) ]^(2)" sec"^(2) . (alpha)/(2) " sec"^(2) .(beta)/(2) " sec"^(2) . (gamma)/(2) |
Answer»  SINCE `[vec(x) xx vec(y) vec(y) xx vec(z) vec(z) xx vec(x)] =[vec(x) vec(y) vec(z)]^(2)` [from EQ .(i)] `=(1)/(64) sec^(2) .(a)/(2) . Sec^(2) . (beta)/(2) sec^(2) . (gamma)/(2) [vec(u)+vec(v)vec(v)+vec(w)vec(w)+vec(u)]^(2)……(i)` and `[ve(u)+vec(v)vec(v)+vec(w)vec(w)+vec(u)]=2[vec(u)vec(v)vec(w)].....(iii)` `:. [vec(x) xx vec(y) vec(y) xx vec(z) vec(z) xx vec(x)]` `=(1)/(64) sec^(2) . (a)/(2). sec^(2) .(beta)/(2) . sec^(2).(gamma)/(2).4 [vec(u)vec(v)vec(w)]^(2)` `=(1)/(16). [vec(u)vec(v)vec(w)]^(2)sec^(2).(a)/(2).sec^(2).(beta)/(2).sec^(2).(gamma)/(2)` |
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| 3307. |
The quadrilateral formed by the lines x+8y+37=0, 7x-6y+11=0, x+8y-87=0, 7x-6y-51=0 is |
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Answer» PARALLELOGRAM |
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| 3308. |
A five digited number without repetetion is formed by the digits 1,2,3,4,5,6,7,8. The probability that the number has even digits at both ends is |
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Answer» `(3)/(14)` |
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| 3309. |
Evaluate the following define integrals as limit of sums : lim_( n rarr oo) [ (n!)/(n^(n))]^(1/n) |
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Answer» |
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| 3310. |
The probabilities that the events A and B occur are 0.3 and 0.4 respectively. The probability that both A and B occur simultaneously is 0.15. What is the probability that neither A nor B occurs? |
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| 3311. |
A car A is moving with constant velocity and at shown moment, stationary observer 'O' observers its regurlar velocity 0.5 rad/sec . Then at the same instant what angular velocity (rad/s) will observer 'B' in car-B observe ? |
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| 3312. |
Find the variance and standard deviation of the following data : (i) 6,7,10,12,13,4,8,12 (ii) 5,12,3,18,6,8,2,10 (iii) 350,361, 370, 373, 376, 379, 385, 387, 394, 395 |
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Answer» (II) Variance = 24.25, S.D = 4.95 (iii) `sigma^(2) = 183.2, sigma = sqrt(183.2)` |
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| 3313. |
If a function is not differentiable at x=c , then the function- |
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Answer» MAY ATTAIN a LOCAL MAXIMUM |
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| 3314. |
Find the vertex, focus, equation of directrix and axis, of parabolas x^(2) -2x+4y-3=0 |
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| 3316. |
The value of sum_(k=0)^(n)(i^(k)+i^(k+1)), where i^(2)= -1, is equal to |
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Answer» `i- i^(N)` |
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| 3317. |
sqrt(-8 - 6i) is equal to |
| Answer» Answer :A | |
| 3318. |
A and Bare two points on the Argand plane such that the segment AB is bisected at the point (0, 0). If the point A, which is in the third quadrant has principal amplitude theta, then the principal amplitude of the point B is |
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Answer» `-THETA` |
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| 3319. |
Integrate the following inte^xsece^xtane^xdx e^x=z |
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Answer» SOLUTION :`inte^x CDOT sece^x cdot tane^x DX` [PUT `e^x=z` then `e^xdx=dz`] `intseczcdottanzdz` `secz+C=sece^x+C` |
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| 3320. |
Two balls are drawn at random withreplacement from a box containing 10 black and 8 red balls.Find the probability that a. Both the balls are red. b. One of them is black and the other is red |
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Answer» |
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| 3321. |
Let f(1)= -2 and f'(x ) ge 4.2 for 1 le x le6 . The possible value of /(6) lies in the interval: |
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Answer» `[15,19]` |
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| 3322. |
If tanalpha=(1)/(2)and3cosx+4sinx=5, then x is equal to |
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Answer» `npi+alpha` |
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| 3323. |
Ratio of middle term in (px^3 +(q)/(x^2))^15 is |
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Answer» <P>`p:qx^2` |
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| 3324. |
If the s.d of-5, -4,-3, -2,-1, 0, 1, 2, 3, 4, 5 is sqrt(10) then find the standard deviation of 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 |
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Answer» |
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| 3325. |
s= 0 is a hyperbola , if s+ k =0(k is a real number )represents equation of the asymptotes thans+ 2k =0 represents |
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Answer» HYPERBOLA |
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| 3326. |
Consider curves S_(1): sqrt(|x|)+sqrt(|y|)=sqrt(a), S_(2): x^(2)+y^(2)=a^(2) and S_(3)": "|x|+|y|=a." If "alpha" is area bounded by "S_(1) and S_(2), beta" is area bounded by "S_(1) and S_(3) and gamma is the area bounded by S_(2) and S_(3), then |
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Answer» `alpha=a^(2)(pi-(2)/(3))` Consider `x,YGT0` `therefore""sqrt(x)+sqrt(y)=sqrt(a)` `therefore""y=(sqrt(a)-sqrt(x))^(2)` `y'=2(sqrt(a)-sqrt(x))(-(1)/(sqrt(x)))=2(-(sqrt(a))/(sqrt(x)))` `therefore""y''=(sqrt(a))/(x^(3//2))gt0` So, graph is concave upward. Area bounded by `S_(1)` and coordinate AXIS in first quadrant `=overset(a)underset(0)int(sqrt(a)-sqrt(x))^(2)DX` `=overset(a)underset(0)int[a+x-2sqrt(a)sqrt(x)]dx` `=[ax+(x^(2))/(2)-4sqrt(a)(x^(3//2))/(3)]_(0)^(a)` `=a^(2)+(a^(2))/(2)-(4a^(2))/(3)` `=(a^(2))/(6)` Area bounded by `S_(2)` and coordinate axis in first quadrant `=(pia^(2))/(4)` Area bounded by `S_(3)` and coordinate axis in first quadrant `=(a^(2))/(2)` `therefore"Area bounded by "S_(1) and S_(3), alpha=4((pia^(2))/(4)-(a^(2))/(6))` `=a^(2)(pi-(2)/(3))` `"Area bounded by "S_(1) and S_(3), beta=4((a^(2))/(2)-(a^(2))/(6))=(4a^(2))/(3)` `"Area bounded by "S_(2) and S_(3),gamma=4((pia^(2))/(4)-(a^(2))/(2))=a^(2)(pi-2)` `"Also, "(beta)/(gamma)=(4)/(3sqrt((pi-2)))` |
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| 3327. |
An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60^(@). If after 10 seconds, the elevation is observed to be 30^(@), then the uniform speed of the aeroplane per hour is |
| Answer» Answer :C | |
| 3328. |
Ajay enrolled himself in an online practice test portal provided by his school for better practice. Out of 5 questions in a set-I, he was able to solve 4 of them and got stuck in the one which is as shown below. If A and B are independent events, P(A) = 0.6 and P(B) = 0.8, then answer the following questions. P(A cap B) = |
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Answer» 0.2 |
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| 3329. |
Ajay enrolled himself in an online practice test portal provided by his school for better practice. Out of 5 questions in a set-I, he was able to solve 4 of them and got stuck in the one which is as shown below. If A and B are independent events, P(A) = 0.6 and P(B) = 0.8, then answer the folloqing questions. P(A cup B) = |
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Answer» 0.92 |
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| 3330. |
Ajay enrolled himself in an online practice test portal provided by his school for better practice. Out of 5 questions in a set-I, he was able to solve 4 of them and got stuck in the one which is as shown below. If A and B are independent events, P(A) = 0.6 and P(B) = 0.8, then answer the following questions. P(B|A) = |
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Answer» 0.14 |
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| 3331. |
Ajay enrolled himself in an online practice test portal provided by his school for better practice. Out of 5 questions in a set-I, he was able to solve 4 of them and got stuck in the one which is as shown below. If A and B are independent events, P(A) = 0.6 and P(B) = 0.8, then answer the following questions. P(A|B) = |
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Answer» 0.6 |
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| 3332. |
Ajay enrolled himself in an online practice test portal provided by his school for better practice. Out of 5 questions in a set-I, he was able to solve 4 of them and got stuck in the one which is as shown below. If A and B are independent events, P(A) = 0.6 and P(B) = 0.8, then answer the following questions. P (not A and not B) = |
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Answer» 0.01 |
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| 3333. |
a = hat I -hatj +hat k b=hat I -2hat j +hat k ,c =phat I +2 hat j +q hatk and d=phat I + q hat j +2 hat kare given vectors if the projection of c on a is 5sqrt(3) units and if a,b and c form a parallelopiped of volume 5 cubic unitsthen tan^(-1)(b,d)= |
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Answer» `(PI)/(2 )` |
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| 3334. |
int5/sqrt(1-x^2)+7/(1+x^2)dx |
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Answer» SOLUTION :`int5/sqrt(1-x^2)+7/(1+x^2)DX` =`5intdx/sqrt(1-x^2) +7intdx/(1+x^2)` =`5sin^-1x+7tan^-1x+C` |
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| 3335. |
Write the component statement "7 is an rational number or irrational number" compound statements and check whether the compound statement is true or false. |
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Answer» <P> SOLUTION :The component statement arep: 7 is a rational NUMBER Q : 7 is an irrational number |
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| 3336. |
int_(0)^(pi//2) (Cos^(3//2)x)/(Cos^(3//2) x+Sin^(3//2)x)dx= |
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Answer» `PI` |
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| 3338. |
(d)/(dx) F(x) = (e^(sin x))/(x) , x gt 0. If int_(1)^(4) (2e^(sin x^(2)))/(x) dx=F(K)-F(1), then one of the possible values of K is : |
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Answer» 4 |
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| 3339. |
The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is |
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Answer» `3((x^(2))/(a^(2))-(y^(2))/(b^(2)))=4` `(x sec theta)/(a) - y (tan theta)/(b) =1` (1) Equation of one of asymptote `RARR (x)/(a) +(y)/(b) =0` (2) `rArr` Coordinates of Q on the asymptote are `(a(sec theta -tan theta), (-b(sec theta -tan theta))` Let mid-point of PQ is `M(h,K)` `rArr h = (a sec theta+(a sec theta -a tan theta))/(2)` `rArr (h)/(a) = sec theta - (tan theta)/(2)` (3) SIMILARLY, `(k)/(b) = tan theta - (sec theta)/(2)` (4) `(3)+(4) rArr (h)/(a) + (k)/(b) = (sec theta + tan theta)/(2)` (5) `(3)-(4) rArr (h)/(a) - (k)/(b) = (3)/(2) [sec theta - tan theta]` (6) Now `(5) xx (6) rArr (h^(2))/(a^(2)) - (k^(2))/(b^(2)) = (3)/(4)` or, `4((x^(2))/(a^(2))-(y^(2))/(b^(2))) =3` |
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| 3340. |
For n observations x_1, x_2,……., x_n underset(i=1) overset( n) sum x_i^(2) = 500 and underset( i=1) overset( n) sum x_i = 100, then least possible value of n= _______________ |
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Answer» |
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| 3341. |
Assertion (A) : If a, b are two non collinear vectors, then the vector componentof b along the line perpendicular to a is(a xx(bxxa))/(|a|^(2))Reason (R) :a xx (b xxc) = (a . c) b - (a . B) cand vector component of b on c is(b *(c)/(|c|))(c)/(|c|) |
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Answer» Both (A) and (R) are TRUE and (R) is the CORRECT EXPLANATION of (A) |
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| 3342. |
Let 'c'be a positive real number such that area bounded by y = 0 , y = [tan^(-1)x] from x= 0 to x = c is equal to area bounded by y= 0, y = [cot^(-1)x],from x = 0 to x = c (where [***] represents greatest integer function), then |
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Answer» `C = tan1+cot1` |
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| 3343. |
Method of integration by parts : int cos^(-1)((1)/(x))dx..... |
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Answer» `X SEC^(-1)x+cos ^(-1)x+c` |
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| 3344. |
Let x_(1),x_(2), x_(3)be roots of equation x^3 + 3x + 5 = 0. What is the value of the expression (x_(1) + 1/x_(1))(x_(2)+1/x_(2)) (x_(3)+1/x_(3)) ? |
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Answer» |
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| 3345. |
If three dice are thrown , the probability that they show the numbers in A.P is |
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Answer» `1//36` |
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| 3346. |
The orthocentre of the triangle whose sides are given by equations x=1,y=0 and x+y-2=0, is |
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Answer» `(-1,0)` |
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| 3347. |
If A=[(i,0),(0,(i)/(2))] where(i=sqrt(-1)), then A^(-1)= |
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Answer» `[(i,0),(0,(i)/(2))]` |
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| 3348. |
Integrate the function in Exercise. e^(x)((1+sinx)/((1+cosx))) |
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| 3349. |
if f(x) =(2013) x^(2012) -(2012)x^(2011)-2014x+1007 thenshow thatfor x in [0,1007^(1//2011)], f(x) =0 has atleastone realroot. |
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| 3350. |
If A and B are matrices such thatA+B and BA are both defined , then : |
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Answer» A and B canbe any matrices |
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