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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.
| 27101. |
Find the slope of the normal to the curve x=a cos^(3) theta,y=a sin^(3) theta at theta=(pi)/(4) . |
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| 27102. |
The values of a for which the matrix A = ((a,a^(2)-1,-3),(a+1,2,a^(2)+4),(-3,4a,-1)) is symmetric are |
| Answer» Answer :D | |
| 27103. |
One focus of a hyperbola is located at the point (1, -3) and the corresponding directrixis the line y = 2. Find the equation of the hyperbolaif its eccentricity is (3)/(2) |
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| 27104. |
Let l,m,n are the coefficients of x^5 in (1+2x+3x^2+…..)^(-3//2), (1+x+x^2 +x^3+….)^2, (1+x)^5 Respectively then : |
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Answer» `L LT m lt N ` |
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| 27105. |
Check the co planarity oflines vecr=(-3hati+hatj+5hatk)+lambda(-3hati+hatj+5hatk).vecr=(-hati+2hatj+5hatk)+mu(-hati+2hatj+5hatk) |
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| 27106. |
A hospital dietician wishes to find the cheapest combination of two foods, A and B that contains at least 0.5 milligram of thiamin and at least 600 calories. Each unit of A contains 0.12 milligram of thiamin and 100 calories, while each unit of B contains 0.10 milligram of thiamin and 150 calories. If each food costs Rs. 10 per unit, how many units of each should be combined at a minimum cost? |
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| 27107. |
A gentlemeninvitesa party of 10gueststo adinnerand places6 ofthemat onetableand theremaining4 atanotherthe tablebeinground. Thenumberof waysinwhichhe canarrange theguestsis |
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Answer» 152100 |
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| 27108. |
If hat(i)+hat(j), hat(j)+hat(k), hat(i)+hat(k) are the position vectors of the vertices of a Delta ABC taken in order, then angleA is equal to |
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Answer» `pi/2` `OA = HATI +hatj , OB = hatj + hatk` and `OC = hati + hatk` Now, `AB = - hati+ hatk` and `AC = hatk -hati` `:.costheta = ((AB).(AC))/(|AB||AC|) = ((-hati + hatk).(hatk -hatj))/(SQRT(1^(2) + 1^(2))sqrt(1^(2) +1^(2))) = (1)/(sqrt(2)sqrt(2)) = 1/2` `rArr theta= (pi)/(3)` |
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| 27109. |
The vectors a=2hati+hatj-2hatk, b=hati+hatj. If c is a vector such that a.c=|c| and |c-a|=2sqrt2, angle between axxb and c is 45^(@), then |(axxb)xxc| is |
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Answer» 3 `therefore |C-a|^(2) =|c|^(2) +|a|^(2) -2C*a=8` `=|c|^(2)+9-2|c| =8 RARR |c| = 1` Now , ` a xx b = | (hati , hatj , hatk ) , ( 2, 1 , -2), (1, 1 , 0)|=2 hati - 2 hatj+ hatk ` ` rArr | a xx b| = sqrt( 2^(2) +(-2)^(2)+1^(2))=3` `therefore|(a xx b) xx c|=|a xx b||c|sin 45^(@) = 3(1) ((1)/(sqrt(2)))=(3sqrt(2))/(2)` |
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| 27110. |
In a acute triangle ABC, altitudes from the vertices A, B and C meet the oppositesides at the points D, E and F respectively. If the radisu of the circumcircle ofDelta AFE,DeltaBFD, DeltaCED, DeltaABC be respectively R_(1), R_(2),R_(3) and R. Then the maximum value of R_(1)+R_(2)+R_(3) is : |
| Answer» Answer :D | |
| 27111. |
If int (4 sec^(2)" x tan x")/(sec^(2) " x + tan"^(2) x)" dx = log " |1 + f(x) | + Cthenf(x) = |
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Answer» 2 `sin^(2) ` x |
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| 27112. |
I : If G is the centroid of the Delta ABC, G' is the centroid of the Delta A'B'C' then bar(A A')+bar(BB')+bar(C C') = 3 bar(GG') II : If S is the circumcentre, 'O' is the orthocentre of Delta ABC then bar(SA) + bar(SB) + bar(SC) = bar(SO) |
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Answer» only I is TRUE |
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| 27113. |
Show that the relation R defined in the set A of all triangles as R={(T _(1), T _(2))):T _(1) is similar to T _(2)} is equivalence relation. Consider three right angle triangles T_(1) with sides 3,4,5,T_(2) with sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles amongT_(1), T_(2) and T_(3) are related ? |
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| 27114. |
int_(1)^(2) (4x^(3) - 5x^(2) + 6x + 9)dx. |
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| 27115. |
Show that the function f(x)=1/x is decreasing in (0,oo). |
| Answer» Solution :`F(x)=1/xrArrf(x)=-1/x^2lt0` for `x in(0,OO)THEREFORE` f is decreasing in `(0,oo)`. | |
| 27116. |
Choose the correct answer intsqrt(x^(2)-8x+7) dx is equal to |
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Answer» `1/2(X-4)SQRT(x^(2)-8x+7)+9logabs(x-4+sqrt(x^(2)-8x+7))+C` |
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| 27118. |
The plane 2x - 3y + 6z + 9 =0 makes an angle with positive direciton of X -axis is ........ |
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Answer» `COS^(-1)""(3sqrt(5))/(7)` |
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| 27119. |
माना कि n अवयवों वाला कोई अतिरिक्त समुच्चय x है तो X पर कितने संबंध है? |
| Answer» ANSWER :A | |
| 27120. |
Which of the following equation is equal to 6y+6x=66? |
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Answer» `33=x+y` |
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| 27121. |
Ratio of the area of the triangle formed by points A(alpha), B(beta), C(gamma) to the area of the triangle formed by its tangents is (1)/(4)(alpha, beta, gamma epsi) (0,2 pi) then find the vlaue of |alpha- beta|+|beta-|gamma|+gamma-alpha| |
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| 27122. |
Findthe areaof theregionboundedby thecurvesy= (x-1), (x-2)and X - axis. |
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| 27123. |
Evaluate the definite integrals int_(0)^(1)(dx)/(sqrt(1+x)-sqrtx) |
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| 27124. |
Definite integration as the limit of a sum : lim_(ntooo)(1^(p)+2^(p)+3^(p)+.......+n^(p))/(n^(p+1))=........... |
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Answer» <P>1 |
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| 27126. |
What is the numberof possiblevaluesofK(5 gt k gt 0) suchthatg(x) = f(x) -k hasexactly one root ? |
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| 27127. |
Prove that there exist infinitely many natural numbers 'a' with the property that the number p = n^4 a isnot prime for any natural number n. |
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| 27128. |
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? |
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| 27129. |
Let f(x)=e^x sgn (x+[x]) , where sgn is the signum function and [x] is the greatest integer function . Then |
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Answer» `lim_(x to 0+)f(x)=0` |
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| 27130. |
The total number of neutrons present in 54 mL H_(2) O(l) are :- |
| Answer» Answer :A | |
| 27131. |
Find the equation of the circle passing through (0,0) and making intercepts 4,3 on X- axis and Y - axis respectively |
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| 27132. |
Find the area bounded by curves {(x, y) : y ge x^(2) "and" y = |x|}. |
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| 27133. |
Check the injectivty and surjectiveity of the following functions : (i)f : N to Ngiven by f (x) = x ^(2) (ii) f :Z to Z given by f (x) = x ^(2) (iii) f : R to R given by f (x) =x ^(2) (iv) f : N to N given by f (x) = x ^(3) (v)f : Z to Z given by f (x) = x ^(3) |
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Answer» (ii) Neither injective nor surjective (III) Neither injective nor surjective (iv) Injective but not surjective (V) Injective but not surjective |
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| 27135. |
By giving counter examples , show that "If measures of all the angles of a triangle are equal, then the triangle is an obtuse angled triangle" are not true: |
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Answer» SOLUTION :Let is `DELTAABC` `/_A =/_B =/_C =60^@` Clearly no ANGLE is obtuse. `:. The triangle is not obtuse angled. |
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| 27136. |
As theta increases from (pi)/(4) to (5pi)/(4), the value of 4"cos"(1)/(2)theta |
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Answer» increases, and then decreases 
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| 27137. |
Evalute the following integrals int (4x + 1)/(sqrt(2x^(2) + x -3))dx |
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| 27138. |
Find the area of the smaller region enclosed by the circle x^(2)+y^(2)=4 and the line x+y=2 by the integration method. |
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Answer» `2 (PI - 2)` |
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| 27139. |
Two dice are thrown . Event A is " the sum of the two dice is ?" and Event B is " at least one die is 6. " Are A and Binependent ? |
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Answer» Solution :From Example` C, P(A) = (6)/(36)` . EventB incules (1 and 6) , (2 and 6) ,.., 96 and 6) , (6 and 1), (6 and 2),…,(6 and 5) , so ` P(B) = (11)/(36)` . Onlythe two throws (6 and 1) and (1 and 5 ) are in the event ` A|B, so P(A|B) = (2)/(36) , P(B)P(A) = ((1)/(36)) ((6)/(36)) = (11)/(216) ne (2)/(36) ` . so A and B are not INDEPENDENT. |
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| 27140. |
T_(m) denotes the number of triangles that can be formed with the vetices of a regular polygan of m sides. If T_(m+1)-T_(m)=15, then m is equal to |
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Answer» 3 |
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| 27141. |
Three cards are drawn from pack of 52 cards one after another without replacement. Find the probability of getting king in 1^(st) draw, queen in 2^(nd) draw and ace in 3^(rd) draw. |
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| 27142. |
If A={1, 2, 4}, B={2, 4, 5}, C={2,5} then (A-B)xx(B-C)= |
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Answer» `{(1,2),(1,5),(2,5)}` |
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| 27143. |
If the equation to the locus of points equidistant from the points (-2,3),(6,-5) is ax+by+c=0, where a>0, then the ascending order of a,b,c is |
| Answer» Answer :B | |
| 27144. |
If the complex number z is such that |z-1|le1sand|z-2|= find the maximum possible value|z|^(2) |
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| 27145. |
Each of m urns consisting 6 red and 8 black balls. The (m+1)^(th) urn consisting 7 red and 7 black balls. One of the (m+1) urns is selected randomly and two balls are drawn from it without replacement and found to be black. If the probability that (m+1)^(th) urn was selected to draw the ball is 1/17, then the value of m equal to |
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Answer» 16 |
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| 27146. |
Let log_(a)N=alpha + beta wherealphais integerandbeta =[0,1). Then , On the basis of above information , answer the following questions. If N_1 is number of integerswhen a=2 and alpha=2 and N_2 is number of integers whenalpha=1 and a=3 , then the minimum value of (N_1 sec^(2) theta +N_(2) "cosec"^2 theta ) |
| Answer» Answer :A | |
| 27147. |
If (x^(4))/((x - a)(x - b)(x - c)) = P(x) + (A)/(x - a) + (B)/(x - b) + (C )/(x - c), then P(0) + A(a - b)(a - c) = |
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Answer» `a^(4) + B^(4) + C^(4) + a` |
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| 27148. |
Box A contains 2 black and 3 red balls , while box B contains 3 black and 4 red balls . Out of these two boxes one is selected at random and the probability of choosing bos A is double that of box B . If a red ball is drawn from the selected box , then the probability that it has come from box B, is |
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Answer» `(21)/(41)` |
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| 27150. |
A triangle has its vertices on a rectangular hyperola. Prove that the orthocentre of the triangle also on the same Hyperola. |
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