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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.
| 1351. |
If A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)= |
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Answer» `[(1+2n,-4n),(n,1-2n)]` |
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| 1352. |
Find a sample space associated with the experiment of rolling a pair of dice (one is blue and other is red) once is Also, find the number of element of this sample space. |
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| 1354. |
Sum ton terms of the series 1+ (1+x)+ (1+ x+x^(2) ) + ( 1+ x+x^(2) + x^(3) ) + ….... |
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Answer» `(N)/( 1-X) -(x (1-x^(n) ))/( (1-x)^(2) )` |
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| 1355. |
The ratio in which the line segment joining the points A(-2,3,7), B(6,-1,2) is divided by the yz-plane is |
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Answer» " 1: 3 " |
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| 1356. |
Statewhetherthe Or'usedin the followingstatementsis exclusiveor"inclusiveGivereasonfor your answer. (i) Allintergersare positiveor negative (ii)Toapplyfor adrivinglicence , you shouldhave arationcardor apassport . |
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| 1357. |
Assertion (A): The ordinate of a point describing the circle x^(2) + y^(2) = 25 decreases at the rate of 1.5 cm/s. The rate of change of the abscissa of the point when ordinate equals 4 cm is 2 cm/s. Reason (R ) : x dx + y dy = 0 |
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Answer» Both A and B TRUE and R is the CORRECT EXPLATION of A |
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| 1358. |
How many four digit numbers are formed using the digit 2745 without repetition ? Out of them, how many are divisible by 3 ? Out of them how many are divisible by 9 ? |
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| 1359. |
Compute the following limits : Lt_(xto3)(x^(3)-6x-9)/(x^(4)-81) |
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| 1360. |
(sin^(2)3A)/(sin^(2)A)-(cos^(2) 3A)/(cos^(2)A)= |
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Answer» `COS2A` |
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| 1361. |
The value of 'c' in Lagrange's mean value theorem for f(x) = log xon [ 1,e] is |
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Answer» `e//2` |
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| 1362. |
Equation of a plane through the line (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and parallel to a coordinate axis is |
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Answer» `4Y - 3z + 1=0` |
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| 1363. |
If x = a cos^(4)t , y = b sin^(4)t then (dy)/(dx) at t = (3pi)/4 is |
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Answer» `(-B)/a` |
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| 1364. |
Prove that 1+cot^(2) theta = cosec^(2) theta |
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| 1365. |
The minimum value of a tan^(2)x + b cot^(2)x equals the maximum value of asin^(2) theta+b cos^(2) theta where a gt b gt 0. Then a/b is. |
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Answer» 2 |
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| 1366. |
Let f(x)=([a]^(2)-5[a]+4)x^(3)-(6{a}^(2)-5{a}+1)x-(tan x) xx sin xbe an even function for all x in R. Then the sum of all possible values of a is (where [.] and {.} denote gretest integer function and fractional part function, respectively ) |
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Answer» `(17)/(6)` |
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| 1367. |
Find the term independent of x in the expansion of (x^(2 +3/x)^(15) |
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| 1368. |
Solutions of the equations (2cosx-1)(3cosx+4)=0 is [0,2pi] is: |
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Answer» `pi/3` |
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| 1369. |
Range of the observations 2,3,5,9,8,7,6,5,7,4,3, is ……… |
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Answer» 11 |
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| 1370. |
The range of the function f(x)=(|x-4|)/(x-4) is |
| Answer» Answer :D | |
| 1371. |
A = {1, 2, 3, 4, 5}, S= {(x,y) : x in A, y in A}, then find the ordered which satisfy the conditions given below. x+y= 5 |
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| 1372. |
How many 4-digit number can be formed with thedigit 1, 2, 3, 4, 6 and 8 if repetition of digits is not allowed. |
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| 1373. |
If A, A_(1),A_(2),A_(3) are areas of excircles and incircle of a triangle, then (1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))= |
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Answer» `(2)/(sqrt(A))` |
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| 1375. |
A box contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, then probability that it is rusted, or is a bolt, is |
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Answer» `3/8` |
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| 1376. |
int(1+cos2x)/(sin^(2)2x)dx : |
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Answer» `(1)/(2)cotx+c` |
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| 1377. |
When axes rotated an angle of (pi)/(3) the transformed form of 7x^(2) + 2 sqrt(3) xy + 9y^(2) - 8 = 0 is |
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Answer» `3x^(2)-y^(2) + 2 sqrt(3) - 6 = 0` |
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| 1378. |
Consider the three points P, Q, R whose coordinates are respectively(2, 5, -4), (1, 4, -3), (4, 7, -6)then the ratio in which the point Q divides PR. |
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Answer» `1:3` |
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| 1379. |
If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z), prove that x, y , x are in A.P |
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Answer» A.P |
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| 1380. |
Coefficient of variation of two distributions are 60 and 70 their standard deviations are 21 and 16, respectively . What are their arithmetic means. |
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| 1382. |
Straight lines (x)/(a)+(y)/(b)=1, (x)/(b)+(y)/(a)=1,(x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 form a rhombus of area ( in squareunits) |
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Answer» `(ab)/(|a^(2)-B^(2)|)` `(x)/(a)+(y)/(b)=1""…(i)""(x)/(b)+(y)/(a)=1` `(x)/(a)+(y)/(b)=2""…(iii) ""(x)/(b)+(y)/(a)=2""…(iv)` CLEARLY , (i), (iii) and (ii), (iv) FORM two sets of parallel lines. So, the four lines form a parallelogram. Area of RHOMBUS`=|((2-1)(2-1))/({:((1)/(a),(1)/(b)),((1)/(b),(1)/(a)):})|=|(1)/((1)/(a^(2))-(1)/(b^(2)))|` `implies` Area of the rhombus `=(a^(2)b^(2))/(|b^(2)-a^(2)|)` |
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| 1383. |
Show that, whatever be the value of a, the lines x cos a + y sin ct = a and x sin ct - y cos a = a are tangents to the circle x^(2) + y^(2) =-a^(2). Hence obtain the locus of the points from which perpendicular tangents can be drawn to the circle x^(2) + y^(2) =a^(2 ) |
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| 1384. |
What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on Y-axis ? |
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Answer» `sqrt41` |
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| 1385. |
d/(dx) (sin^(-1)(2/(x^(-1) + x))) is euqal to |
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Answer» `2/(1 + x^2), 0lt |x| LT 1` |
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| 1386. |
The shortest distance between the z-axis and the line x+y+2z-3=0=2x+3y+4z-4, is : |
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| 1387. |
If there is an error 0.05 sq.cm in the surface area of a sphere then the error in its volume when the radius =20 cm is |
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Answer» 1 c.c |
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| 1389. |
If P_(1) "and" P_(2) are the lenghts of perpendiculars from origin to the lines x. sec a+y . Csc a=2a and x.cos alpha+y. sin alpha =a cos 2 alpha, |
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Answer» `4 sin^(2) 4 ALPHA` |
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| 1390. |
Moving along the x - axis there are two points with x = 10 + 6t, x =3 + t^(2), the speed with which they are rechingfrom eachother at the time of encounter is (x is the cm and t is in seconds) |
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Answer» 16 cm/sec |
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| 1391. |
If Lt_(x to 0)(1+ax+bx^(2))^(2//x)=e^(3), findan and b. |
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| 1394. |
If sec A tan B + sec B tan A = 91 then the value of (secA secB + tanA tan B)^(2) - 91^(2) is equal to |
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Answer» 1 |
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| 1395. |
Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4). |
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| 1396. |
If Tantheta=(Cosalpha-Sinalpha)/(Cosalpha+Sinalpha)andtheta is acute then theta + alpha = |
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Answer» `(PI)/(5)` |
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| 1397. |
n^(3)-n is divisible by 6, for each natural number n ge 2 |
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| 1398. |
Write the truth value of the following statement: Sum of measure of an angle of triangle is 180^(@) or 360^(@) |
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| 1399. |
The value of lim_(x to (pi)/(2)) (sinx-(sinx)^(sinx))/(1-sinx+logsinx) is |
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Answer» 1 |
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| 1400. |
Equation of the bisector of the angle between the planes x+2y+2z-9=0,4x-3y+12z+13=0 |
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Answer» `25x+17y+62z-78=0` |
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