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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.
| 5251. |
One cards is drawn from a pack of 52 cards , each of the 52 cards beingequally like to be drawn . Find the probability that the card drawn is red |
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| 5252. |
A =(2,3,-1), B(1,-1,2), C is a point on y-axis such that angleABC=pi//2then C = |
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Answer» `(0,3/2,0)` |
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| 5254. |
One cards is drawn from a pack of 52 cards , each of the 52 cards beingequally like to be drawn . Find the probability that the card drawn is an ace |
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| 5255. |
Expand (1+x)^4,(1-x)^3 and (1-x)^2 |
| Answer» SOLUTION :`(1+x)4=1-4x+6x^2-4x^3+x^4(1-x)63=1-3x+3x^2-x^2,(1-x)^2=1-2x+x^2` | |
| 5256. |
Evaluate the following limits : Lim_(h to 0) (sin (x+h) -sin x)/h |
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| 5257. |
Evaluate : (i) 2 xx 6! - 3 xx 5! (ii) (8!)/(4!) (iii) (20!)/(18!(20 - 18)!) |
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| 5258. |
For the series, 2 + 3+ 6 + 11+ 18+…….find its 50^(th) term (a_(50)) |
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| 5259. |
Write the equation of the lines for which tan theta = (1)/(2), where theta is the (ii) x intercept is =4. |
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| 5260. |
Given vec alpha + 3 hati + hatj + 2 hatk and vecbeta = hati - 2 hatj - 4 hatk are the position vectors of the points A and B. Then the distance of the point -hati + hatj + hatkfrom the plane passing through B and perpendicular to AB is |
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Answer» 5 |
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| 5261. |
Sin12^(@).Sin24^(@).Sin48^(@)Sin84^(@)= |
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Answer» 1/16 |
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| 5262. |
The sum of first three terms of a G.P. is (39)/(10) and their product is 1. Find the common ratio and the terms. |
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| 5263. |
Determine real values of x and y for which each statement is true (x+y)/(i)+ x- y+ 4=0 |
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| 5264. |
Find the equation of a parabola with vertex at the origin, focus at (4,0) and directrix x=-4 |
| Answer» SOLUTION :`y^2=16x] | |
| 5265. |
Let P =0 be the equation of a plane passing through the line of intersection of the planes 2x - y =0 and 3z - y=0 and perpendicular to the plane 4x + 5y - 3z =8. Then the points which lie on the planc P =0 is /are |
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Answer» `(0,9,17)` |
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| 5266. |
Statement-1: The funciton f: N to N given by f(n)=n-(-1)^(n) for all n in N is invertible. Statement-2: The successor and prodecessor of an even natural number are odd natural numbers and that of an odd natural number are even natural number. |
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Answer» 1 |
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| 5268. |
Find the root(3)(126) approximately to two decimal places. |
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| 5269. |
Range of sin^(-1)x-cos^(-1)x is |
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Answer» `[(-3PI)/2, pi/2]` |
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| 5270. |
Prove that (n!)^(2)le n^(n).(n!)lt (2n)!for all positive integers n. |
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| 5271. |
The value of x where x gt0 and tan("sec"^(-1)1/x)=sin(tan^(-1)2) is |
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Answer» `sqrt(5)` |
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| 5272. |
bara^(1)xxbarb^(1)+barb^(1)xxbarc^(1)+barc^(1)xxbara^(1)= |
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Answer» `(bara+barb+barc)/([BARABARBBARC])` |
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| 5273. |
If two sides of triangle are given by x^2-xy-6y^2=0 " and the centroid is " (11/3,-1) then equationthird side is |
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Answer» x+y=8 |
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| 5274. |
The vertices of a trianvle are A(-1,-7),B(5,1) and C(1,4). The equation of the bisector of /_ABC is |
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Answer» `x-7y+2=0` |
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| 5275. |
If f(x)=|log_e(x||, then f'(x)equals. |
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Answer» `1/(|X|)`, where `x != 0` |
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| 5276. |
A tower MPQ surmounted by a spiral QR stands on a harzontal plane. At the extremity 'A' ofa horizontal line AM it is found that MP and QR subtend equal angle. If MP = 3m,PQ = 28 m and QR = 5 m then MA = |
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Answer» `SQRT(36xx93)` |
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| 5277. |
2+7+14+…..+ (n^(2) + 2n-1)= |
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Answer» `N(2N^(2) + 9n+1))/( 6) ` |
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| 5278. |
From the following data, using mean, calculate mean deviation and the coefficient of mean deviation. 10, 70, 50, 53, 20, 95, 42, 60, 48, 80 |
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| 5279. |
2x^(2)-5xy+2y^(2)=0represents two sides of a triangle whose centroid is (2, 3) then area of triangle is |
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Answer» 7X + 2Y - 12 = 0 |
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| 5281. |
y=e^(sin^(-1)x) find y' at x=0: |
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Answer» e |
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| 5282. |
5,7 are the intercepts of a plane on the Y-axis Z -axisrespectively, if the plane is parallel to the X-axis then the equation of that plane is |
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Answer» `5y + 7z = 35` |
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| 5283. |
If each side of length 'a' of an equilateral triangle subteds an angle of 60^(@) at the top of a tower h metrs eigh situated at the centre of the triangle , then |
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Answer» `3A^(2) = 2H^(2)` |
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| 5284. |
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder. |
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| 5285. |
Find all values of x in (-pi,pi) satisfying the equation 8^(1+cosx+cos^(2)x+...)=4^(3). |
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Answer» `(PI)/(3),(2PI)/(3)` |
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| 5286. |
Complex number with magnitude 2 and argument (2pi)/3 is = .......... . |
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| 5287. |
If R= {(x,y): x, y in W, x^(2)+ y^(2)= 25}, then find the domain and range of R. |
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Answer» RANGE of R: Set of second element of ordered pairs in R = {5, 4, 3,0} |
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| 5288. |
A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha " where " oltalphaltpi/4 with the positive direction of x-axis, the equation of its diagonal not passing through the origin is |
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Answer» `(cosalpha+sinalpha)+X(cosalpha-sinalpha)=a` |
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| 5289. |
Find the coefficient of x^5 in the expansion of 1+(1+x)+ (1+x)^2 + … + (1+ x)^(10). |
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| 5290. |
Let alpha and betabe any two positive values of x for which2 cos x, |cos x| ,and 1 -3 cos ^(2) xare in G.P. The minimum value of |alpha - beta | is |
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Answer» `(PI)/( 3)` |
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| 5291. |
How many three digit numbers are there multiple of 5 ? (without repetition) |
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| 5294. |
underset(h to 0)(Lt)[(sqrt(3)sin((pi)/(6)+h)-cos((pi)/(6)+h))/(sqrt(3).h(sqrt(3)cosh-sin h))]= |
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Answer» `(-2)/(SQRT(3))` |
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| 5295. |
1/(1!) + 1/(3!) + 1/(5!) + … is. |
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Answer» `e^(-1)/2` |
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| 5296. |
For all real values of a and b, line(2a+b)x+(a+3b)y+(b-3a)=0 and mx+2y +6=0 " are concurrent. The " absm is equal to |
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| 5297. |
Let ABC be a triangle with incenter I and inradius r. Let D, E, and F be the feet of the perpendiculars from I to the sides BC, CA, and AB, respectively. If r_(1),r_(2) and r_(3), are the radii of circles inscribed in the quadrilaterals AFIE, BDIF, and CEID, respectively, Then (r_(1))/(r-r_(1))+(r_(2))/(r-r_(2))+(r_(3))/(r-r_(3))= |
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Answer» `(r_(1)r_(2)r_(3))/((R-r_(1))(r-r_(2))(r-r_(3)))` |
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| 5299. |
Find the slope of a line perpendicular to the line whose slope is0 |
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| 5300. |
Express the following expression in the form of a+ib: ((4i-1)/(2i+1))^(2) |
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