Saved Bookmarks
This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 2. |
If possible , find BA and AB , whereA=[{:(2,1,2),(1,2,4):}],B=[{:(4,1),(2,3),(1,2):}] |
|
Answer» |
|
| 3. |
Evaluate: intsqrt(2-x-x^(2))/(x^(2))dx |
| Answer» Solution :`-sqrt(2-X-x^(2))/(x)+sqrt(2)/4"ln"|(4-x+2sqrt(2)sqrt(2-x-x^(2))/(x)-sin^(-1))|(2x+1)/(3)+K` | |
| 4. |
"Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(9)):}] and alpha, beta, gamma be non-zero real number such that alpha p^(6)+betap^(3)+gammal is the zero matrix. Then find the value fo (alpha^(2)+beta^(2)+gamma^(2))^(alpha-betaxxbeta-gammaxxgamma-alpha) |
|
Answer» |
|
| 5. |
The points (5, -5, 2), (4, -3, 1), (7, -6, 4) and (8, -7, 5) are the vertices of |
|
Answer» a rectangle |
|
| 6. |
A person takes 4 tests in succession. The probability of his passing the first test is p, that of his passing each succeeding test is p or p/2 depending on his passing or failing the preceding test, Find the probabilty of his passing just three tests. |
|
Answer» SOLUTION :Probability of passing just in 3 tests `=p^3(1-p)+(p^3(1-p))/2XX3` `=(p^3(2-2p+3-3p))/2` `=(p^3(5-5p))/2=5/2p^3(1-p)` |
|
| 7. |
For real numbers x and y, let M be the maximum value of expression x^4y + x^3y + x^2 y + x y + xy^2 + xy^3 + xy^4 , subject to x + y = 3. Find [M] where [.] = G.I.F. |
|
Answer» |
|
| 8. |
The values of a which the integral int|x-a|dx ge 1 is satisfied are |
| Answer» Answer :A,B,C | |
| 9. |
A straight line perpendicular to the 2x + y = 3 is passing through (1, 1). Its y-intercept is |
| Answer» ANSWER :D | |
| 10. |
Integrate the following functions sin^-1 ((2x)/(1+x^2)) |
|
Answer» SOLUTION :`int sin^-1((2x)/(1+X^2)) dx` =`int 2 tan^-1x dx = 2int 1 XX tan^-1 x dx` =`2[tan^-1x xx x-int 1/(1+x^2) dx]` `2[x tan^-1 x -1/2 int(2x)/(1+x^2) dx]` =`2 [x tan^-1x -1/2 log (1+x^2)]+c` =`2 x tan^-1x -log(11+x^2)+c` |
|
| 11. |
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing ? |
|
Answer» |
|
| 12. |
A is a set having 6 distinct elements. The number of distinct functions from A to A which are not bijections is |
|
Answer» 1)`6!-6` |
|
| 13. |
int_(-2)^(2) |[x]| dx= |
|
Answer» 1 |
|
| 14. |
Let a=hati+2hatj+hatk, b=hati-hatj+hatk and c=hati+hatj-hatk. A vector in the plane a and b whose projection on c is (1)/(sqrt3), is |
|
Answer» `HATI+hatj-2hatk` `thereforer = ( hati + 2 hatj + HATK ) + lambda(hati-hatj+hatk)` `=(1+lambda)hati + (2 -lambda)hatj + (1+lambda)hatk` PROJECTION of r on `c=(r*c)/(|c|)` `rArr ([(1+lambda)hati+(2-lambda)hatj+(1+lambda)hatk]*(hati+hatj-hatk))/(sqrt((1)^(2)+(1)^(2)+(-1)^(2)))=|(1)/(sqrt(3))|` `rArr (1+lambda + 2 -lambda - 1-lambda)/(sqrt(3))=|(1)/(sqrt(3))|` `rArr2-lambda = pm 1 rArr lambda 1,3 ` `thereforer = 2 hati +hatj + 2 hatk , 4 hati -hatj + 4 hatk` |
|
| 15. |
Inthe following two A.P. 's ow many terms are identical ? 2,5,8,11… to 60 terms and 3,5,7,…..50 terms |
|
Answer» |
|
| 16. |
For each of the exercises given below, verify that thegiven function (implicit orexplicit) is a solution of the correspondingdifferential equation. xy = ae^(x) + be^(-x) + x^(2) : x (d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy + x^(2) - 2 = 0 |
| Answer» | |
| 17. |
{n(n+1)(2n+1):n in 1} sub |
|
Answer» `{6K : K in I}` |
|
| 19. |
Let AB be the chord 4x-3y+5=0 with respect to the circle x^(2)+y^(2)-2x+4y-20=0 If C=(7,1) then the area of the triangle ABC is |
|
Answer» 15 SQ. units |
|
| 20. |
Let F_(1)(x_(1),0)and F_(2)(x_(2),0)" for "x_(1)lt0 and x_(2)gt0 the foci of the ellipse (x^(2))/(9)+(y^(2))/(8)=1. Suppose a parabola having vertex at the origin and focus at F_(2) intersects the ellipse at point M in the first quadrant and ata point N in the fourth quardant. The orthocentre of the triangle F_(1)MN, is |
|
Answer» `(-(9)/(10),0)` `therefore e-sqrt(1-(b^(2))/(a^(2)))-sqrt(1-(8)/(9))=(1)/(3)`. So, the coordinates of foci are `F_(1)(-1,0)` and `F_(2)(1, 0)`. Theequation of the PARABOLA having vertex at theorigin and focusat `F_(2)(1, 0) is y^(2)=4x`. Solving `(x^(2))/(9)+(y^(2))/(8)=1 and y^(2)=4x`, we find that the coordinates of M and N are `((3)/(2),sqrt6) and ((3)/(2),-sqrt6)` respectively. Clearly, ALTITUDE through `F_(1) " of " F_(1)MN` is a x-axis i.e. y = 0. the equation of the altitude through `M((3)/(2),sqrt6)`is `y-sqrt6=(5)/(2sqrt6)(x-(3)/(2))` Solving the equation with y = 0, we obtain `(-9//10, 0)` the orthocentre of `DeltaF_(1)MN`. |
|
| 22. |
Evaluate the following definite integrals as limit of sums : int_(0)^(2)(2x+3)dx |
|
Answer» |
|
| 23. |
Find the variance for the discrete data given below. 350, 361, 370, 373, 376, 379, 385, 387, 394, 395 |
|
Answer» |
|
| 24. |
Find x,y if (2x+y,1) = (x,2x+3y) |
|
Answer» Solution :`THEREFORE` 2X + y = x , 1 = 2x + 3Y `{x + y = 0} XX 2` 2x + 3y = 1 `therefore` -y = -1 or y = 1 `therefore` x= -1 |
|
| 25. |
Let R-(alpha, beta), be the range of (x +3)/((x -1) (x +2)). Then the sum of the intercepts of the line alphax + beta y + 1 =0 on the coordinate axis is |
| Answer» ANSWER :B | |
| 26. |
The mean deviation about the mean of data in the following frequency distribution: |
| Answer» Answer :B | |
| 27. |
Vertify mean value theorem for the following functions: f(x)= log_(e)x, x in [1, 2] |
|
Answer» |
|
| 28. |
If f(x)={{:((x^(2)log(cosx))/(log(1+x^(2))),x ne 0),(0,x = 0):}, then f is |
|
Answer» DISCONTINUOUS at zero |
|
| 29. |
Let S = {1, 2, 3, 4, 5}. The number of ordered pairs of subsets (A, B) of S such that A cap B ={3} and A cup B =S is………… |
|
Answer» |
|
| 30. |
{x in R :(sqrt(6 + x - x^(2)))/(2 x + 5)ge (sqrt(6 + x - x^(2)))/(x - 4)}= |
|
Answer» [-2,3] |
|
| 31. |
The mean height of 25 (male workers in a factory is 161 cms and the mean height of 35 female workers in the same factory is 158 cms. The combined mean height of 60 workers in the factory is |
| Answer» Answer :A | |
| 32. |
Classify the following as scalar and vector quantities. (i) time period (ii)distance (iii) force (iv) velocity (v) work done |
|
Answer» (ii)scalar (iii)VECTOR (IV)vector (V) scalar |
|
| 33. |
If f(x)={{:(Ax, 0 lt x lt 5), (A(10-x), 5 le x lt 10):} is a p.d.f of a continuous random variable X, then find its mean. |
|
Answer» |
|
| 34. |
Find int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx |
|
Answer» |
|
| 35. |
Choose the correctanswer. The planes 2x-y+4z=5 and 5x-2.5y+10z=6 area)perpendicularb)parallelc)intersect y-axisd)passes through (0, 0, 5/4) |
|
Answer» perpendicular `therefore` Th normals are parallel. Hence, the planes are parallel `threfore` The answer is (B) |
|
| 36. |
Number of identical ............... |
|
Answer» SEQUENCE `=5+(n-1)6=6n-1` `100^(th)` term of first sequence `=2+99xx3=299` `100^(th)` term of second sequence `=3+99xx2=201` `:. 6n-1 lt 201` `n lt 101/3` `n lt 33.6 implies n=33` |
|
| 37. |
The Number of ways in which five different books to be distributed among 3 persons so that each person gets at least one book, is equal to the number of ways in which? 5 persons are allotted 3 different residential flats so that each person is allotted at most one flat and no two persons are allotted the same flat |
|
Answer» Number of parallelograms (some of which may be overlapping) formed by one set of 6 parallel lines and other set of 5 parallel lines that goes in other direction |
|
| 38. |
If x= 9 is a chord of contact of the hyperbolax^(2) -y^(2) =9, then the equation of the tangents at one of the points of contact is |
|
Answer» `x+sqrt3 y+2=0` |
|
| 40. |
Evaluate the following integral inta^(x)cos2xdx |
|
Answer» |
|
| 41. |
Find the value of x (del z)/(delx) + y (del z)/( dely) if z = log ((x ^(3) - y ^(3))/(x ^(2) +y ^(2))). |
| Answer» | |
| 42. |
inte^(x)secx(1+tanx)dx equals |
|
Answer» `E^(X)cosx+C` |
|
| 44. |
Represent graphically a displacement of 40 km,30^@ east of north. |
| Answer» Solution :`oversetrarr(OP) `in the figure REPRESENTS the REQUIRED DISPLACEMENT. | |
| 45. |
A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and angleAEB and angleCDB have the same measure. What is the value of x ? |
|
Answer» |
|
| 46. |
Find the number of ways of arranging the letters of the word. COMBINATION |
|
Answer» |
|
| 47. |
If y=cos^(-1)((x-x^(-1))/(x+x^(-1))), then (dy)/(dx) is |
|
Answer» `{:{((2)/(1+x^(2))",",xgt0),(-(2)/(1+x^(2))",",XLT0):}` |
|
| 48. |
Solve the following equation for x , y and z : log_2 x + log_4 y + log_4 z = 2 log_3 y + log_9 z + log_9 x = 2 log_4 z + log_(16) x + log_(16) y =2 |
|
Answer» `x=2//3 , y = 27//8 , Z=32//3` |
|
| 49. |
S_(10) = cos'(pi)/(180) + cos'(3pi)/(180) + "….." cos '(19pi)/(180) |
|
Answer» `(SIN'pi/9cos'pi/18)/(sin'pi/90)` |
|