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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.
| 5101. |
This section contains 2 questions. Each question contains STATEMENT-I (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Statement-1: The equation sin^(2) x + cos^(2) y=2 sec^(2) z is only solvable ifsin x =1, cosy=1 and sec z=1 where x, y, z in R because Statement - 2 : Maximum value of sinx and cosy is 1 and minimum value of secz is 1. |
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Answer» Statement -1 is TRUE, Statement-2 is True, Statement -2 is a correct explanation for Statement-2 |
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| 5102. |
bara,barb,barc are mutually perpendicular unit vectors and bard is a unit vector equally inclined to each ofbara,barb and barc " at an angle of "60^(@). " Find the value of" abs(bara+barb+barc+bard)^(2). |
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| 5103. |
The minimum value of 27 secx + 64 cosecx for x in (0,pi/2) is……. And is obtained at ……. |
| Answer» ANSWER :B | |
| 5104. |
Write the first five termsif n^(th) terms is a_(n)=(2n-3)/(6) |
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| 5105. |
theta is acute angle between the lines x^(2)-xy-6y^(2)=0, then (2costheta+3sintheta)/(4sintheta+5costheta) is |
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Answer» 1 |
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| 5106. |
Two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60^(@). If the area of the quadrilateral is 43 then remaining two sides are |
| Answer» ANSWER :AB | |
| 5107. |
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the words start with P . |
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| 5108. |
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the words begin with I and end in P? |
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| 5109. |
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do the vowels never occur together |
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| 5110. |
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, do all the vowels always occur together |
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| 5111. |
sin(270^(@)-theta).sin(90^(@)-theta)-cos(270^(@)-theta).cos(90^(@)+theta)= |
| Answer» ANSWER :A | |
| 5112. |
If a,b in [0,2pi] and the equation x^(2)+4+3sin(ax+b)-2x=0 has at least one solution, then the value of (a+b) can be |
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Answer» `(7pi)/2` |
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| 5113. |
The value of k such that the lines 2x-3y+k=0, 3x-4y-13=0 and 8x-11y-33=0 are concurrent, is |
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Answer» 20 |
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| 5115. |
100 students appeared for two examinations .60 passed the first , 50 passed the second and 30 passed both . Find the probability that a student selected at random has failed in both examinations . |
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| 5116. |
The minimum and maximum values of sin^(4) x + cos^(4) x are |
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Answer» `1/2, 3/2` |
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| 5117. |
A tree stands vertically on a hill side which makes an angle of 15^(@) with the horizontal. From a point on the ground 35m. Down the hill from the base of the tree, the angle of elevation of the top of the tree is 60^(@). Find the height of the tree. |
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| 5119. |
Define f(x)={{:(x",",0lexle1),(2-x,,1lexle2):} then Rolles theorem is not applicable to f(x) because |
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Answer» f(X) is not DEFINED EVERY where on [0,2] |
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| 5120. |
Line through the points (-2,6) and (4,8) is perpendicular to the line through the points (8,12) and (x,24). Find the value of x. |
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| 5121. |
If (a+ b+ c) (b+ c-a)= kbcthen |
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Answer» ` k gt 0 ` |
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| 5122. |
x = t cos t , y = t + sint. Then (d^2x)/(dy^2) at t = pi/2 |
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Answer» `(PI + 4)/2` |
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| 5123. |
Find the cofficient x^(9) in the expansion of (ax^(2) - b/(cx))^(12) |
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| 5125. |
Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +........ |
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| 5127. |
Which of the following are sets ? Justify your answer. The collection of ten most talented writers of India. |
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| 5130. |
For the following,calculate mean deviation and coefficient of mean deviation. 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 |
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| 5132. |
If P_(1),P_(2),P_(3) are the altitudes of the DeltaABCthen , show that (1)/(P_(1)^(2))+(1)/(P_(2)^(2))+(1)/(P_(3)^(2))=(cotA+cotB+cotC)/(Delta) |
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Answer» `(2AB cos^(2)C//2)/(DELTA(a+b+c))` |
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| 5134. |
A straight line passes through (4,5) and makes an angle 60^(@) with x-axis in the positive directio . Its equation in te parametric form |
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Answer» `x=sqrt(3)lamda+4,y=lamda+5` |
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| 5135. |
Consider the system of equations sin x cos 2 y = (a ^(2) - 1)^(2) + 1, cos x sin 2 y = a = 1 The number of values of x in [0, 2 pi] , when the system has solution for permissible valuesof a, is/ are |
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Answer» 1 |
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| 5136. |
Assertion (A) : 3x^(2)+4xy+y^(2)=0 and 7x^(2)+12xy+y^(2)=0 are equally inclined to each other. Reasom (R): The pair of lines ax^(2)+2hxy+by^(2)=0 and px^(2)+2qxy+ry^(2)=0 are equally inclined to each other. |
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Answer» A is true, R is true and R `rArr A` |
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| 5137. |
A ={x| x is the letter of the word FELLOW} B ={x| is the letter of the word FLOW} then both sets are connected with ……. operation . |
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| 5138. |
If [x] stands for the greatest integer function , then [1/2 + (1)/(1000)] + [1/2 + (2)/(1000)]+.....+[1/2+ (999)/(1000)]= |
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Answer» 498 |
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| 5140. |
ABC is an isosceles triangle inscribed in a circle of unit radius. AB = AC and h is the altitude from A to BC. If P is the perimeter and Delta is the area of the triangle, then find the value of Lim_(hto0)(Delta)/p^(3)= |
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| 5141. |
Findthe value of (i) sin 18^(@) " " (ii) cos 18^(@) (iii) cos 36^(@)" " (iv) sin36^(@)(v) sin 72^(@)" " (vi) cos 72^(@) (vii) sin54^(@)" " (viii) cos54^(@) |
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Answer» Solution :(i) Let `theta =18^(@) ` Then `theta =18^(@)rArr 5theta =90^(@)` `rArr2theta =(90^(@) -3theta)` `rArr sin 2theta = sin (90^(@) -3theta) =cos 3 theta` `rArr2sinthetacos theta= 4 cos^(3) theta -3cos theta` `hArr 2 sin thetacos theta- 4 cos^(3) theta+ 3cos theta=0` `hArrcos theta (2 sin theta -4cos^(2) theta+ 3) =0` `hArr 2 sintheta- 4 cos^(2) theta+ 3=0[ :'cos theta= cos18^(@)ne 0]` `HARR2 sintheta- 4 (1 - sin^(2) theta) + 3 =0` `hArrsin theta= (-2 +- sqrt(4+6))/(8) =((-1 +-sqrt(5))/(4)` `hArr sin theta =((sqrt(5)-1)/(4))` `:.sin 18^(@)= ((sqrt(5)-1)/(4))` (ii) `cos^(2)18^(@) = (1- sin^(2)18^(@))` `={1-((sqrt(5)-1)^(2))/(16)} ={1-((6 -2sqrt(5))/(16)} =(10 +2sqrt(5))/(16)` `hArrcos 18^(@)=(sqrt(10 + 2sqrt(5)))/(4 )[ :'cos 18^(@) gt 0]` (iii)cos `36^(@)= (1-2 sin^(2)18^(@))` ` ={1-2 ((sqrt(5)-1)^(2)/(16)}={1-((6-2sqrt(5)))/(8)}` `=(sqrt(5)+1)/(4)` (iv) sin `36^(@)=sqrt(1- cos^(2) 36^(@))= {1 -((sqrt(5)+1)^(2))/(16)}^(1/2)` `={(10-2sqrt(5))/(16)}^(1/2) =(sqrt(10-2sqrt(5))/(4)` `(v)sin 72^(@)= sin (90^(@) -18^(@)) = cos 18^(@)= (sqrt(10+2sqrt(5)))/(4)` (vi)cos `72^(@)= cos (90^(@) -18^(@)) = sin 18^(@) = ((sqrt(5)-1))/(4)` `(vii) sin 54^(@) = sin (90^(@) -36^(@))= cos36^(@)=((sqrt(5)+1))/(4)` (VIII) ` cos 54^(@)= cos(90^(@)-36^(@))= sin36^(@) = (sqrt(10 -2sqrt(5)))/(4)` |
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| 5142. |
If theta is the parameter, then the family of lines represented by (2cos theta+3 sin theta)x+(3 cos theta-5sin theta)y-(5cos theta-7sin theta)=0are concurrent at the point |
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Answer» `(-1,1)` |
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| 5143. |
A jet of an enemy is flying along the curve y=x^2+2. A soldier is placed at the point (3,2). What is the nearest distanced between the soldier and the jet |
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| 5144. |
If one card is taken from 17 cards, numbered 1, 2, 3, …., 17 , then probability that number on it is divisible by 3 or 7 is |
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Answer» `5/17` |
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| 5145. |
Find the 20^(th)term of the series 2 xx 4 + 4 xx 6 + 6 xx 8 + ... + nterms. |
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| 5146. |
(1)/(2 xx 5) + (1)/(5 xx 8) + (1)/(8 xx 11)+ …..100 terms= …… |
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Answer» `(25)/(100)` |
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| 5147. |
Differentiate from first principles: 10. (1)/( x^((3)/(2)) ) |
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| 5148. |
If cos^(2) x - (c - 1) cosx + 2c ge 6 for every x in R, then the true set of values of c is |
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Answer» `[2, OO)` |
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| 5149. |
Find the derivative of f (x ) = Tan ^(-1) ((2x )/( 1 - x ^(2))) w.r.t g (x) =Sin ^(-1) ((2x )/( 1 + x ^(2))). |
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| 5150. |
If the line 3x+4y=8 is denoted by L, then the points (3, -5), (-5, 2) |
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Answer» lie on L |
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