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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.
| 5151. |
Minimum value of 9 sec^(2) theta + 4 cosec^(2) theta + 7 is |
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Answer» 32 |
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| 5152. |
In the interval [0,1] the function x^(25)(1-x)^(75) takes a maximum value at |
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Answer» `x=0` |
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| 5153. |
If x lt 1, then 1/(x + 1) + (2x)/(1 +x^2) + (4x^3)/(1 + x^4) + ….oo = |
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Answer» `X` |
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| 5155. |
Evaluate : 8! |
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| 5157. |
Show that |(z-2)/(z-3)|=2 represents a circle. Find the centre of radius. |
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| 5158. |
Let f be function defined for every x , such that f^(11) = -f ,f(0) = 0 , f^(1)(0)=1 then f(x) is equal to |
| Answer» Answer :C | |
| 5159. |
A ladder AB of 10 mts long moves with its ends o the axes. When the end A is 6 mts form the origin. It moves away from it at 2mts/minute. Therate of increase of the area of the DeltaOAB is |
| Answer» Answer :D | |
| 5161. |
..........is the solution set for inequality 3x + 8 gt 2 ,x is real number. |
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| 5162. |
Two cards are drawn from awell shuffled pack of cards without replacement . Findthe probability that neither a Jack nor a card of spades is drawn . |
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| 5164. |
If sin (x + 20^(@)) = 2 sin x cos 40^(@),where x in (0.pi //2), then which of the following hold (s) good? |
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Answer» `COS 2X =1//2` |
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| 5166. |
Examine whether the following system of equations are consistent or inconsistent and if consistent find the complete solution. x+y+z=4," "2x+5y-2z=3," "x+7y-7z=5 |
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| 5167. |
If (1+ tan alpha)(1+ tan 4alpha)=2, alpha in (0, pi//16), then alpha is equal to: |
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Answer» `pi/20` |
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| 5169. |
A square whose side is 2 cm has its corners cut away so as to form a regular octagon then area of octagon is lambda(sqrt(2)-1) then lambda |
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Answer» 1 |
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| 5170. |
If A =Ø and B=Ø then does A and B are mutually exclusive. Give reason of your dedication. |
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| 5171. |
Write the negative of the followingstatement : "Some students are 25 (years) or older" |
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| 5172. |
Find the number of quadrant angles in the range of sin^(-1)x+cos^(-1)x+4cot^(-1)x |
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Answer» 3 |
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| 5173. |
Inverse of (3+4i)/(4-5i) |
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Answer» `-(8)/(25)+(31)/(25)i` |
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| 5175. |
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms. |
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| 5176. |
findthe generalsolutionforsec ^2 2x=1 - tan 2x |
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| 5178. |
If the transformed equation of a curve is 17x^(2) - 16xy + 17y^(2)=225 when the axes are rotated through an angle 45^(@), then the original equation of the curve is |
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| 5179. |
A ray of light travelling along the line x+y = 1 line incident on the x-axis and after rrefraction it enters the other side of the x-axis by turing pi//6 away from the x-axis. The equation of the line along which the refracted ray travels is |
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Answer» `X+(2-sqrt3)y=1` |
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| 5180. |
A tetrahedron has vertices O(0, 0,0), A(1,2,1), C(2,1,3), D (-1, 1,2). Show that the angle between the faces OAB and ABC is cos^(-1) ((19)/(35)). |
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| 5181. |
Find the maximum and minimum values of 13 cos x + 3sqrt(3) sinx-4. |
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Answer» `[-18,10]` |
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| 5182. |
Find the absolute maximum and absolute minimum of f(x) =8x^(3) + 81x^(2) - 42x - 8 on [-8, 2] |
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| 5183. |
If (1)/(6) sin x, cos x, tan x are in G.P. then x is equal to |
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Answer» `2NPI` |
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| 5184. |
Let f, g and h be the lengths of the perpendiculars from the circumcentre of DABC on the sides a, b andc , respectively, and a/f + b/g + c/h = 1/lambda (abc)/(fgh) , then lambda is |
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Answer» 4 |
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| 5185. |
f(x) = x - [3 - log ((sinx)/(x))]-2 to be continuous at x = 0 , then f (0) = |
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Answer» 0 |
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| 5186. |
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A pmsqrt((A+G )(A−G )). |
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| 5187. |
Let f(x)={[sqrt(n^(2)+1)]-[sqrt(n^(2)+x)]}^(1//2),where [.] is the greatest inger function and n in N then the value of x for which f(x) is defined |
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Answer» `SQRT(K)`, where `k=0, 1, 2........n` |
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| 5188. |
Find the middle term in expansion of : (2x+3y)^(9) |
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| 5189. |
Calculate the mean and variance after the following data: |
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| 5190. |
If A=[(1,-2,3),(2,3,-1),(-3,1,2)] and B=[(1,0,2),(0,1,2),(1,2,0)] then examine whether A and B commute with respect to multiplication of matrices. |
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| 5191. |
sinx+i cos 2x and cosx-isin2x are conjugate to each other for |
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Answer» `X= n PI, n in Z` |
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| 5192. |
Find the number of points ehre the function f (x) = max { sgn (x), - sqrt( 9-x ^(2)), x^(3)} is continuous but not differentiable. |
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| 5193. |
Find two number whose arithmetic mean is 5 and the geometric mean is 4. |
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| 5194. |
The vector equation of the line passing through the point vec(i)-2vec(j) + vec(k) and perpendicular to the vectors 2vec(i)-3vec(j)-vec(k), vec(i) + 4vec(j)-2vec(k) is |
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Answer» `VEC(R )= (vec(i) -2vec(J) + vec(K)) + t(10vec(i) + 3vec(j) + 11vec(k))` |
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| 5195. |
The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show thata:b =(m+sqrt(m^2-n^2)):(m-sqrt(m^(2)-n^2)) . |
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| 5196. |
If theta lies in the second quadrant and tan theta=(-5)/(12), find the value of (2cos theta)/(1-sin theta). |
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| 5197. |
Assertion (A) : cos20^(@) - sin20^(@) gt 0 Reason (R) : If theta in R, cos theta - sin theta gt 0 choose the correct answer |
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Answer» A is TRUE, R is true and R is correct explanation of A |
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| 5198. |
Show that Delta = ((a^(2) -b^(2)) sin A sin B)/( 2 sin ( A-B) ) |
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| 5199. |
If the line y-sqrt(3)x+3=0 cuts the curve y^(2)=x+2 at A and B and point on the line P is (sqrt(3), 0) then PA. PB = |
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Answer» `(4(SQRT(3)+2))/(3)` |
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| 5200. |
Point (2, k) is the exterior point of the circles x^(2) + y^(2) + x - 2y - 14 = 0 and x^(2) + y^(2) = 13, then k lies in ……… interval. ' |
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Answer» `(-3, - 2) CUP (3, 4)` |
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