InterviewSolution
Saved Bookmarks
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.
| 13151. |
Find the coefficient of a^(4)in the product (1+2a)^(4)(2-a)^(5) using binomial theorem . |
|
Answer» |
|
| 13153. |
The value of (1-tan^(2)(15^(@)))/(1+tan^(2)(15^(@))) is ……….. |
|
Answer» |
|
| 13154. |
If cot x = - sqrt(5) and x in second quadrant then sin x = .......... |
|
Answer» |
|
| 13155. |
Following are the marks obtained by 9 students in a mathematics test : 50, 69 , 20, 33, 53, 39, 40, 65 and 59The mean deviationfrom the median is ………… |
|
Answer» 9 |
|
| 13157. |
Two sides of a triangle is given . If the area of a triangle is maximum, then the angle between the two sides is |
|
Answer» `45^(@)` |
|
| 13158. |
The value of 4 sin 27^(0)= |
|
Answer» `SQRT(5 + sqrt(5)) + sqrt(3-sqrt(5))` |
|
| 13159. |
If a lt c lt b, and if 1-k_(1)lt ln ((b)/(a)) lt k_(2)-1 , then ( k _(1) , k_(2)) is |
|
Answer» `((a)/(B), (b)/(a))` |
|
| 13160. |
If the lines mx+ ( 2m + 3)y+ m + 6=0 and (2m+1) x + (m-1) y+m-9=0 intersects on Y-axis then m=….... |
|
Answer» `-1` OR `21` |
|
| 13162. |
If the equation of the locus of a point equi-distant from the points (a_(1), b_(1)) and (a_(2),b_(2)) is (a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0 then the value of c is |
|
Answer» `SQRT(a_(1)^(2)+b_(1)^(2)-a_(2)^(2)-b_(2)^(2))` |
|
| 13163. |
1 + (x)/( a_1) + ( x( x+a_1) )/( a_1 a_2 ) + .... + ( x ( x+a_1) (x+ a_2)... ( x+a_(n-1) ) )/( a_1 a_2 ..... a_n)= |
|
Answer» `(x+a_1) (x+a_2) ….. (x+a_n))/( a_1 a_2… a_n)` |
|
| 13164. |
Find the co-ordinates of vertices, length of major and minor axis, eccentricity, co-ordinates of foci, length of latus rectum, co-ordinates of the ends of latus rectum and equation of directrices of each of following ellipse. (i) (x^(2))/(16)+(y^(2))/(9)=1 , (ii) (x^(2))/(9)+(y^(2))/(16)=1 (iii) 16x^(2)+y^(2)=16 , (iv) x^(2)+4y^(2)=4 |
|
Answer» Vertices `=(0,pm4)`, major axis = 8, minor axis = 6, `e=(sqrt(7))/(4)`, co-ordinates of foci `=(0,pmsqrt(7))`, length of latus rectum `=(9)/(2)`, co-ordinates of the ends of latus `=(=m(9)/(4),pmsqrt(7))`, equation of directrices `y=pm(16)/(sqrt(7))` (iii) Vertex `(0,pm4)`, major axis =8 minor axis = 2, `e=(sqrt(15))/(4)`, co-ordinates of foci `=(0,pmsqrt(15))`, length of latus rectum `=(1)/(2)`, co-ordinates of the ends of latus rectum `=(pm(1)/(4),pmsqrt(15))`, equation of directrices `y=pm(16)/(sqrt(15))` (IV) Vertices `=(pm2,0)`, major axis =4 , minor axis = 2, e=(sqrt(3))/(2)`, co-ordinates of foci `=(pmsqrt(3),0)`, equation of directrices `x=pm(4)/(sqrt(3))` |
|
| 13165. |
If f((2tanx)/(1+tan^2x))=((cos2x+1)(sec^2x+2tanx))/(2) then f(4) = |
|
Answer» 1 |
|
| 13166. |
If M(alpha , beta , gamma ) is the mid point of the line segment joining the points A(x_(1),y_(1),z_(1)) and B then find B. |
|
Answer» |
|
| 13167. |
The vertex of the parabola y^(2) =(a-b) (x-a) is : |
|
Answer» (b, a) `RARR Y^(2) =(a-b) X, " where " Y= y & X = x-a "" :."Vertex"=(0,0)` `rArr X =0, Y=0 rArr x-a =0, y=0 rArr x=a, y =0` Co-ordinates of vertex are (a,0) |
|
| 13168. |
If vec(a), vec(b) and vec(c) are vectors with magnitudes 3,4 and 5 respectively and vec(a) + vec(b) + vec(c) = vec(0), then find the value of vec(a).vec(b) + vec(b).vec(c) + vec(c).vec(a). |
|
Answer» |
|
| 13169. |
If the vectors vec(a), vec(b), vec(c ) are represents the sides vec(BC), vec(CA) and vec(AB) respectivley of triangle ABC, then |
|
Answer» `vec(a).vec(B) = vec(b).vec(c )= vec(c ).vec(a)= 0` |
|
| 13170. |
A bag contains 5 red balls, 3 black balls and 4white balls. 3 balls are drawn at random . Theprobability that they are not of same colour is |
| Answer» Answer :D | |
| 13171. |
The stationary value of f(x) = (log x )/xis |
|
Answer» 0 |
|
| 13172. |
the mean and standard deviation of some data for the time taken to complete a test are calculated with the following results: Number of observations = 25, mean = 18.2 seconds , standard deviation = 3.25 seconds. Further , another set of 15 observations x_1,x_2,........,x_15, also in seconds , is now available and we have sum_(i=1)^15 x_i = 279 and sum_(i=1)^15 x_i^2 = 5524. Calculated the standard deviation based on all 40 observations. |
|
Answer» |
|
| 13173. |
bara,barb,barc and bard are the position vectors of four coplanar points such that (bara-bard).(barb-barc)=(barb-bard).(barc-bara)=0. Show that the point bard represents the orthocentre of the triangle with bara,barb and barc as its vertices. |
|
Answer» orthocentre |
|
| 13174. |
Describe the real valued function f(x) = a^(x). Also draw its graph, when 0 lt a lt 1. |
|
Answer» `(##VVA_ISC_MAT_XI_MTP_20_E01_026_A01##)` |
|
| 13175. |
ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of xy is |
|
Answer» `(2AB)/(a^(2)-B^(2))` |
|
| 13177. |
On which the following intervals in the function x^(100)+sinx-1decreasing ? |
| Answer» Answer :D | |
| 13178. |
If the point (sqrt(2), - sqrt(2))was transformed as (0, -2) by rotation of axes at an angle theta, then theta = |
|
Answer» `(PI)/(6)` |
|
| 13179. |
Under what conditions is 2x^(2)+kx+2 always positive ? |
|
Answer» |
|
| 13180. |
All the values of x satisfying sin2x+sin4x=2sin3x are |
|
Answer» `NPI//3` |
|
| 13182. |
The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted. |
|
Answer» |
|
| 13183. |
The range of value of p for which the equation sincos^(-1)(cos(tan^(-1)x))=p has a solution is |
|
Answer» `(-1/(SQRT(2)),1/(sqrt(2)))` |
|
| 13184. |
Let M be a 3xx3 matrix satisfying {:M[(0),(1),(0)]=[(1),(-1),(6)]=[(1),(1),(-1)]and","M=[(1),(1),(1)]=[(0),(0),(12)]:} Then the sum of the diagonal entries of M, is |
|
Answer» `{:M[(0),(1),(0)]=[(1),(-1),(6)]RARR [(b),(y),(m)]=[(-1),(2),(3)]rArr b=-1,y=2,m=3:}` `{:M[(1),(-1),(0)]=[(1),(1),(1)]rArr a-b=1,x-y=1,l-m=-1:}` `rArra=0,x=3,l=2` and, `{:M[(1),(1),(1)]=[(0),(0),(12)]rArra+b+c=0,x+y+z=0,l+m+n=12:}` `rArr c=1,z=-1,n=7` `:. " Sum of diagonal ELEMENTS of "M=a+y+n=0+2+7=9` |
|
| 13185. |
cos theta + sin theta - sin 2 theta = (1)/(2), 0 lt theta lt (pi)/(2) |
|
Answer» |
|
| 13187. |
Find the standard deviation of 8,11,14,17,20,23,26. |
Answer» Solution : Here `n=7` Arithmetic MEAN `BARX=(sumx_(i))/n=119/7=17` STANDARD deviation `sigma=SQRT((sum(x_(i)-barx)^(2))/n)` `=sqrt(252/7)=sqrt(36)=6`. |
|
| 13188. |
If cos(x+pi//3)+cosx=a has real solutions, then |
|
Answer» a NUMBER of integral values of a is 3 |
|
| 13189. |
If (-2, 6) is the image of the point (4, 2) with respect to the line L = 0, then L = |
|
Answer» `6x-4y-7=0` |
|
| 13190. |
Is the given relation a function? Give reason for your answer. t= {(x, 3)|x is a real number} |
|
Answer» |
|
| 13192. |
Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the altitude through B |
|
Answer» |
|
| 13193. |
Find the sum of n terms of each of the following (5^(4) -1^(4)) + (8^(4) -4^(4)) + (11^(4)-7^(4)) +…….. |
|
Answer» |
|
| 13194. |
A line with positive direction consines passes through the point P (2, 1,2) and marks equal angles with the coordinate axes. The line meets the plane 2x + y + z =9 at point Q. The length of the line segment PQ equals |
|
Answer» 1 |
|
| 13195. |
If X= {8^(n)-7n -1"/"n in N}" and "Y= {49n -49"/"n in N}. Then, |
|
Answer» `X SUB Y` |
|
| 13196. |
If cot(x//2) - cosec (x //2) = cot xthen x = |
|
Answer» `x = 4 n pi pm (2PI)/(3), n in Z` |
|
| 13197. |
A line with positive direction cosines passes through the point P(2,-1,2) and makes equal angles with the coordinate axes. If the line meets the plane 2x+y+z=9 at the point Q, then the length PQ equals. |
| Answer» Answer :C | |
| 13199. |
Find the numbers of ways in which 12 apples may be eqully divided among 3 childrens. |
|
Answer» |
|
| 13200. |
lim_(xrarra)(xf(a)-af(x))/(x-a)=f(a)-(a)f'(a). |
|
Answer» AF'(a) |
|