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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.
| 8102. |
If P,Q are two point on the line 3x+4y+15=0 such that OP=OQ=9, then the area of DeltaOPQ is |
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Answer» `6sqrt2` |
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| 8103. |
Find the mean deviation for the mean for the following data: |
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| 8105. |
Evaluate the following limits in lim_(xrarr2)(3x^(2)-x-10)/(x^(2)-4) |
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| 8107. |
There exists a positive real number x satisfying cos(tan^(-1)x)=x. Then the value of cos^(-1)(x^(2)/2) is |
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Answer» `pi/10` |
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| 8108. |
P(A)=0.5,P(B)=0.4. Find P(AcapB) if P(AcupB)=0.8. Give reason if it not valid. |
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Answer» <P> |
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| 8109. |
For alpha = pi//7 which of the following hold(s) good ? |
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Answer» `TAN ALPHA tan 2 alpha tan 3 alpha = tan 3 alpha - tan 2 alpha - tan alpha` |
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| 8110. |
If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ D |
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| 8111. |
If Sin^(-1)(x//5)+Cosec^(-1)(5//4)=pi//2 then a value of x is |
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Answer» 1 |
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| 8112. |
Eccentricity of the ellipse4x ^(3) + y 6(2) -8x+ 4x +4y -8=0 is |
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Answer» `(sqrt3)/(2)` |
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| 8113. |
Evaluate cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)=2 |
| Answer» SOLUTION :`(sqrt2-1)/2SQRT2` | |
| 8114. |
Solve the general value. tan ^(2) theta - (1 + sqrt3) tan theta + sqrt3 =0 |
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| 8115. |
If two of the sides of a parallelogram are represented by ax^2+2hxy+by^2=0" and "pq+qy=1 is one of its diagonals, prove that the other diagonal is y(bp-hq)=x(aq-hp). |
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| 8116. |
Letf(x)= (1)/(2)[f( xy ) + f((x)/(y)) ]AA x, y in R ^(+)such thatf(1)= 0, f^(1)(1) =2Now answer the following f(e) = |
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Answer» 2 |
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| 8117. |
Find the value of 'a' so that Iff(x) = (1 - tanx)/(4x -pi) , x ne (pi)/(4), is continuous on(0, (pi)/(2)), " findf " ((pi)/(4)) . |
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| 8119. |
Use quantifiers to convert each of the following open sentences defined on N, into a true statement: (i) x+5=8 (ii) x^(2)gt0 (iii) x+2lt4 |
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Answer» Solution :(i) `EXISTS x in N" such that "x+5=8" is a TRUE statement, since "x= 3 in N" satisfies "x+5=8,` (ii) `x^(2)gt 0 AA x in N` is a true statement, since the square of EVERY natural number is positive. (iii)`exists x in N" such that "x+2lt4" is a true statement, since "x=1 in N" satisfies "x+2lt4.` |
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| 8120. |
If the planes 2x + 3y + 4z + 7 = 0 and 4x + ky + 8z + 1 = 0 are parallel then k = |
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Answer» 2 |
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| 8121. |
If f(x+y) = f(x)f(y) and f(5)=32 then f(7)= |
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Answer» 35 |
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| 8122. |
If the equation of pair of bisectors of the angle between the pair of lines 3x^(2)+xy+by^(2)=0 is x^(2)-14xy-y^(2)=0 then b= |
| Answer» ANSWER :B | |
| 8123. |
If the pair of lines 8x^(2)+2xy-3y^(2)=0 forms a parallelogram with parallel pair which is passing through (-2,5) then its area is |
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Answer» `63//10` |
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| 8124. |
If the coefficient of r^(th) and (r+4)^(th) terms are equal in the expansion of (1+x)^(20), then the value of r will be |
| Answer» Answer :C | |
| 8125. |
If f: R rarrR defined by f(x)=2x+|x| then f(3x)-f(-x)-4x= |
| Answer» ANSWER :D | |
| 8126. |
If t=(2sqrt2-(1+sqrt3))/(sqrt3-1) and f(x)=(2x)/(1-x^2),g(x)=(3x-x^3)/(1-3x^2) then d/(dt) {f(g(t))} = |
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Answer» 1 |
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| 8127. |
A and B are two variable points on x, y axes respectively such that OA+OB=c. The locus of the foot of the perpendicular from origin on this line overset(" "harr)("AB") is |
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Answer» `x^2+y^2=CXY` |
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| 8128. |
If AB=7 units, BC=8 units, AC=5 units, then the side PQ will be |
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Answer» `(SQRT(28))/(3)` units |
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| 8129. |
Let theta = (0,(pi)/(4)) and t_(0) = (tan theta)^(tan theta), t_(2) = (tan theta)^(cot theta), t_(3) = (cot theta)^(tan theta) .t_(4) = (cot theta)^(cot theta) then |
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Answer» `t_(1) gt t_(2) gt t_(3) gt t_(4)` |
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| 8130. |
Find k, if the equation 2x^(2) + kxy - 6y^(2) + 3x + y + 1 = 0 represents a pair of lines. Find the point of intersection of the lines and angle between the lines for this value of k. |
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| 8131. |
The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+ pi/6) for real-valued x is |
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Answer» [-1/4, 1/2] |
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| 8132. |
Two plant A and B of a factory show following results about the number of workers and the wages paid to them. In which plant, A or B isthere greater variability in individual wages ? |
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| 8133. |
If inDelta ABC,b-c = 3sqrt3 , A= 120 ^(@)andthe areaofDelta ABC = (9sqrt3)/( 2) sq.cm, then a= |
| Answer» ANSWER :C | |
| 8134. |
By the principle of mathematical induction, prove that, for nge11^(3) + 2^(3) + 3^(3) + . . .+ n^(3)=((n(n+1))/(2))^(2) |
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Answer» because p(K +1) ` is true ` because ` By the principle of mathematical INDUCTION,p(n) istrue for all value of n. |
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| 8135. |
Evaluate the following limits. Lt_(xto3)1/(x+1) |
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| 8138. |
Distance of pont P (vecp) from the plane vecr. vecn = 0 is |
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Answer» `|VECP. VECN|` |
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| 8139. |
If S_(n)=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+….. n terms, then |
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Answer» `S_(10)=TAN^(-1)""5/6` |
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| 8140. |
Let S_(1),S_(2),S_(3), ….Are squares such that for each nge1, The length of the side of S_(n) is equal to length of diagonal of S_(n+1). If the length of the side S_(1) is 10 cm then for what value of n, the area of S_(n) is less than 1 sq.cm. |
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Answer» 7 |
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| 8141. |
If log(5+sqrt(26))=sinh^(-1)(k) then k = |
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Answer» 2 |
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| 8142. |
If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k), then (vec(a) xx vec(b))/(|vec(a) xx vec(b)|) + (vec(b) xx vec(a))/(|vec(b) xx vec(a)|)= |
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Answer» `VEC(0)` |
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| 8143. |
f(x) ((sinx)/(sina))^((1)/(x-a) ) " if " x ne aand f(x) = k if x = a and f(x) is continuous at x= a then k = |
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Answer» ` E^(TANA)` |
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| 8144. |
Two dice are tossed. Find whether the following two events A and B are independent : A = {(x, y): x + y = 11} and B = {(x, y): x ne 5} where (x, y) denotes a typical sample point. |
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| 8145. |
If A and B are two square matrices of order n and A and B commute then for any real number k |
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Answer» `A-kI,B=kI` are not COMMUTE |
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| 8146. |
If f(x)=|x|^(|sinx|) then f^1(-pi/4) is equal to |
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Answer» `(PI/4)^(1//sqrt2)(SQRT(2)/2"In"4/pi-(2SQRT2)/pi)` |
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| 8147. |
A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number les than or equal to 3 will appear, (iii) A number les than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number les than 6 will appear. |
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| 8150. |
A card is drawn from a well shuffled pack of 52 cards . Findthe probability of an ace |
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