InterviewSolution
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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.
| 6101. |
Lte p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : Shruti can type but she does not take shorthand. |
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Answer» <P> |
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| 6102. |
Differentiate the following functions: 7x^(6) + 8x^(5) - 3x^(4) + 11x^(2) + 6x+7 |
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| 6103. |
On her vacations Veena visits four cities(A, B, C and D) inrandom order. What is the probability that she visits (i) A before B? (ii) A before B and B before C? (iii) A fist and B last? (iv) A either first or second? (v) A just before B? |
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| 6104. |
If2 sin ((6)/(5) x) = 0 and cos ((x)/(5)) =then |
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Answer» `x = (n - 5) pi` |
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| 6105. |
U= {1, 2, 3, 4} and relation R = {(x,y): y gt x, x, y in U} then range of R is ……. |
| Answer» Answer :B | |
| 6106. |
Find the condition for the lines joining the origin to the points of intersection of the circle x^2+y^2=a^2 and the line lx+my=1 to coincide. |
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| 6107. |
If 0ltxlt1 then tan^(-1)(sqrt(1-x^(2))/(1+x))is equal to |
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Answer» `1/2cos^(-1)X` |
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| 6108. |
The locus of a point for which the sum of the squares of the distances from the coordinate planes is 5 unit is |
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Answer» `X^(2)+y^(2)+Z^(2)=8` |
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| 6109. |
Find all the points of discontinuity of the greatest interger function defined by f(x)= [x], where [x] denote the greatest integer less than or equal to x. |
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Answer» `(1)/(X-[x])` |
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| 6110. |
Draw the graph of the solution set of the inequation 2x + y ge 2, x-y le 1, x+ 2y le 8, x ge 0 and y ge 0 |
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Answer» Solution : First, we draw the graph of `2x + y ge 2` CONSIDER the line, 2x + y = 2. Now ` 2x + y =2 rArr x/1+ y /2 =1` This line meets the axes at A(l, 0) and B(O, 2). Clearly, the line AB represents 2x + y = 2. Now (0,0) does not satisfy` 2x+ y ge 2 ` Thus, the line AB and part of the plane separated by AB and not containing 0(0, 0), represent the solution set of `2x + y ge 2 ` (ii)Next we draw the graph of `x - y le 1` Consider the line, x-y = 1. `x-y = 1 rArr x/1 + y/((-1))=1` This line meets at the axes at A(1, 0) and C(0, -1). Clearly, the line AC represents x-y = 1. ALSO (0,0) SATISFIES `x - y le 1` Thus the line AC and part of the plane separated by AC and part of the plane separated by AC and containing O(0,0) represent the solution set of `x-y le 1 ` (iii) Now, we draw the graph of `x + 2y le 8` Consider the line, x + 2y = 8. Now `x+2y =8 rArr x/8+y/4=1` This line meets the axes at D(8, 0) and E(0, 4). So, the line DE represents x + 2y = 8. Also, (0, 0) satisfies the inequation, ` x+ 2yle 8` Thus the line DE and part of the plane containing O(0,0) represent the solution set of `x+2 le 8`. (iv) `x ge 0 ` is represented by the y-axies and the plane on its right (v) ` y ge 0 ` is represented by the x-axies and the plane above the x- axis. The intersection of all these planes is the REQUIRED shaded part , representing the solution of the gives system . 
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| 6111. |
Without using tables, give the value of each of the following : "cosec "675^(@) |
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| 6112. |
Differentiate (x ^(2) - 5x + 8) (x ^(3) + 7x + ) by i) using product rule ii) obtaining single polynomial expanding the product iii) logarithermic differentiation. Do they all give same answer |
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| 6113. |
If (a+1)x+(a^(2)-a-2)y+a=0 line is parallel to X - axis then a = ........... |
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| 6114. |
Statement - I : When the axes are rotated through an angle alpha the transformed equation of x cos alpha + y sin alpha = pis X = p Statement - II : A = (2,3), B= (3,5), C = (-1,4) are the vertices of a triangle and the origin is shifted to the point (1,1) then the centroid of the triangle is ((4)/(3),4) Which of the above statement is correct : |
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Answer» Only I |
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| 6115. |
(bara+2barb-barc).(bara-barb)xx(bara-barb-barc)= |
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Answer» `-[bara barb BARC]` |
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| 6116. |
Find all the values ofthetasatisfying the equationsin theta + sin 5 theta = sin3 theta, such that0 le theta le pi. |
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| 6117. |
I : The points (-2,3,5 ), (1,,2,3 ),(7,0,-1 ) are collinear. II: The points (2 ,-1,1 ) (1-3-5 ), (3,-4,-4 ) form an equilateral triangle. |
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Answer» collinear |
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| 6118. |
In the following, state whether A = B or not: A = { a, b, c, d } B={ d, c, b, a } |
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| 6119. |
The diagonal of a square is 8x- 15y =0 and one vertex of the square is (1, 2). The equations to the sides of the square passing through this vertex are |
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Answer» `23x+7y=9,7x+23y=53` |
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| 6120. |
Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3x + 2y - 12 = 0 ,(ii) 4x - 3y = 6, "" (iii) 3y + 2 = 0 . |
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Answer» (III) `y = - 2/3 `, INTERCEPT with y- AXIS ` = - 2/3` and no intercept with x- axis. |
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| 6121. |
Evaluate the following limits : Lim_( xto 0) (sin 2x + sin 6x )/(sin 5x - sin 3x) |
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| 6122. |
Differentiate the following with respect to x.y = (4x^(2)+1)e^(2x) |
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| 6123. |
Find the square roots of the following : 1-i |
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| 6124. |
Expand the following Sin(A + B+C) |
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| 6125. |
For what value of k will the line 4x + 3y + k = 0 touch the circle 2x^(2) + 2y^(2) = 5x |
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| 6127. |
Find the probability of getting almost two tails or at least two heads in a toss of three coins. |
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| 6128. |
((cosA+sinA)/(cosA-sinA))-((cosA-sinA)/(cosA+sinA))= |
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Answer» `2 cot 2A` |
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| 6129. |
Write out the expansions of the following: (f) ((2)/(x) - (x)/(2) )^(5) , x ne 0 |
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| 6130. |
Use the function f(x)=x^((1)/(x))(xgt0) to ascertain whether p^(e) or e^(p) is greater . |
| Answer» Answer :A | |
| 6132. |
Explain the concept of inertia. |
| Answer» Solution :The INABILITY of OBJECTS to MOVE on its own or change its state of motion is CALLED INERTIA. Inertia means resistance to change its state | |
| 6133. |
Write the component statements of the following compound statements and check whether they are true of false. (i) a multiple of 9 and 12 is 18. (ii)all sides of equilateral triangle are equal and each angle is 60^@. (iii) All angles and all sides of a rectangle are equal. (iv) 0 is smaller than 1 and greater than -1. |
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Answer» <P> SOLUTION :(i) p: a multiple of 9 is 18.q : a multiple of 12 is 18. p is true and q is false. (ii) p:all sides of an equilateral triangle are EQUAL. q: each angle of an equilateral triangle is `60^@`. both statements are true. (III) p: all angles of a rectangle are equal. q: all sides of a rectangle are equal. p is true and q is false. (iv) p : 0 is smaller than 1. q : 0 is greater than `-1`. both statements are true. |
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| 6134. |
Let f(x, y) be a periodic function, satisfying the condition f(x, y) = f(2x+2y, 2y-2x) AA x , y in R and let g(x) be a function defined as g(x)=f(2^(x), 0) Prove that g(x) is a periodic function and find its period |
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Answer» 12 |
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| 6136. |
If sintheta+sin3theta+sin5theta=0,0lethetale(pi)/(2) then theta = |
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Answer» `0,(PI)/(3)` |
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| 6137. |
Twostudents Anil and Ashima appeared in an examination . The probability thatAnil will quanlify the examination is 0.05 and thatAshima will qualify the examination is 0.10 . The probability hat both will qualify the examination is 0.02 . Find the Probabiity that both Anil and Ashima will not qualify the examination ? |
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| 6138. |
A unit vector normal to the plane through the points vec(i), 2vec(j)and 3vec(k) is |
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Answer» `(6 vec(i)-3vec(J) 2vec(K))/(7)` |
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| 6139. |
Radius of a sphere is 2 cm and error in it is 1/10 cm then arrange the approximate values of the following in decending order A) Error in diameter B) Error in Circumference C) Error in area D) Relative error in radius |
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Answer» A, B, C, D |
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| 6140. |
If A and B are mutually exclusive events with P(A)=(1)/(2)P(B)andAuuB=S, the sample space .find P(A). |
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| 6141. |
{:("Column-I", "Column-II"), ("a) "cos^(-1)(4x^(3)-3x)=3cos^(-1)x", then x can takes values", "p) "[1//2,1]), ("b) "sin^(-1)(3x-4x^(3))=3sin^(-1)x", then x can takes values", "q) "[-1//2,0]), ("c) "cos^(-1)(4x^(3)-3x)=3sin^(-1)x", then x can take values", "r) "[0,sqrt(3)//2]), ("d) "sin^(-1)(3x-4x^(3))=3cos^(-1)x", then x can takes values", "s) "[0, 1//2]):} |
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| 6142. |
Are the following pari of sets equal? Give reasons A= {x : x is a letter in the word LOYAL} B= { y : y is a letter in the word ALLOY}. |
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| 6143. |
A bag contains six white marbles and five red marbles. Can be drawn from the bag, if (i) thay can be of any colour. (ii) two must be white and two red. (iii) thay must all be of the same colour. |
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| 6145. |
A straight line L through the point (3,-2) is inclined at an angle60^@ " to the line " sqrt3x+y=1. If L also intersects the x-axis, then the equation of L is |
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Answer» `y+sqrt3x+2-3sqrt3=0` |
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| 6146. |
Find the derivative of the w.r.t.x sqrt ((1+ x ^(2))/(1 - x ^(2))) |
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| 6147. |
A wheel makes 360 revolutions in one minute. Through how many radian does it turn in one second? |
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| 6148. |
Show that sqrt([-1sqrt({-1-sqrt(-1+ ..."to"oo)})]) = omega, or omega^(2) |
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| 6150. |
If there are 1%,2%,3%,4% errors in r,r_(1),r_(2),r_(3) then the % error in area of triangle |
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Answer» 10 |
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