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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.
| 13101. |
Let the palanes, P _(1) : 2x - y + z =2 and P _(2) : x + 2y -z =3 are given, On the bases of the above information, Answer the following questions The equation of the acute angle bisector of planes P _(1) and P _(2) is |
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Answer» `X - 3y + 2z +1=0` |
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| 13102. |
Let the palanes, P _(1) : 2x - y + z =2 and P _(2) : x + 2y -z =3 are given, On the bases of the above information, Answer the following questions Equation of the plane which passes through the point (-1,3,2) and is perpendicular too each of the planes P _(1) and P _(2) is |
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Answer» `X + 3y - 5z + 2=0` |
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| 13103. |
Compute price index for the following data by applying weighted average of price relative method. |
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| 13104. |
Show that the equation sinθ=x+1/x is not possible if x is real. |
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| 13105. |
Given f(x) = 4- ((1)/(2) - x)^(2//3) , g(x) = {:{((tan[x])/(x),","x cancel(=)0),(1,","x=0):}" "h(x)={x}, k (x) = 5^(log_(2)(x+3)) Then in [0,1], Lagrange's mean valuetheorem is not applicable to (where [.] and {.} represents the greatest integer functions and fractions part functions, respectively ) |
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Answer» f |
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| 13106. |
IF cos theta ne 0, and sec theta-1=(sqrt2-1) tan theta then theta= |
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Answer» `theta = {(2 N PI)/(3), n in Z}cup{2 n pi + (pi)/(2), n in Z}` |
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| 13107. |
A matrix is chosen at random from a set of all matrices of order 2 , with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non-zero will be : |
| Answer» Answer :C | |
| 13108. |
A ballon is in the shape of an inverted cone surmounted by a hemisphere. The height of the cone is equal to the diameter of the sphere. If h is the total of the ballon, how does the volume of the ballon changes with h? What is the rate in volume when h=9 units? |
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| 13109. |
The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2,4,10,12 and 14, then find the remaining two observations. |
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| 13110. |
If x = a{costheta + log tan((theta)/(2))} andy = a sin theta, then (dy)/(dx) is equal to |
| Answer» Answer :B | |
| 13111. |
(sin(70^(@))+cos(40^(@)))/(cos(70^(@))+sin(40^(@)))= .......... |
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Answer» 1 |
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| 13112. |
If A^(-1)=1/3[(1,4,-2),(-2,-5,4),(1,-2,1)] and |A|=3 the Adj A = |
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Answer» `3[(1,4,-2),(-2,-5,4),(1,-2,1)]` |
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| 13113. |
Evaluate lim_(xrarr0)f(x)," where "f(x)={{:((|x|)/(x)",",x ne0),(0",",x=0):} |
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| 13114. |
Write the following interval in set builder form. (1, 18) |
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| 13115. |
How many three digit numbers can be formed without using the digits0,2,3,4,5 and 6? |
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| 13116. |
State whether each of the following statement is true or false. Justify your answer. { 2, 3, 4, 5 } and { 3, 6} are disjoint sets. |
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| 13117. |
Write the converse of each of the following statements If an integer is even, then its square is divisible by 4. |
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| 13119. |
The set of values of lambda for which x^(2)-lambdax+sin^(-1)(sin4) gt 0" for all "x in R, is |
| Answer» ANSWER :A | |
| 13120. |
Differentiate the following functions w.r.t. x. (x^3 + sin x)^5 |
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| 13121. |
How many 7-digit number can be formed using the digits 1,2,0,2,4,2 and 4? |
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| 13122. |
Let A = sin^(8) + cos^(14) theta , then for all real theta |
| Answer» Answer :A | |
| 13123. |
If log_(2)sinx-log_(2)cosx-log_(2)(1-tan^(2)x)=-1 then x = |
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Answer» `pi//4` |
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| 13124. |
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even? |
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| 13125. |
If "cosec" theta + cot theta = (13)/5 then cot^(2) theta - "cosec"^(2) theta = (25)/12 |
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| 13126. |
Find the domain and the range of the functions f(x) = x^3 |
| Answer» SOLUTION :DOMAIN =R ,RANGE = R] | |
| 13127. |
Find the maximum area of an isosceles triangle inscribed in the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 with its vertex at one end of the major axis. |
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| 13128. |
Check whether the following probabilities P(A) and P(B) are consistently defined (i) P(A)=0.5,P(B)=0.7,P(AnnB)=0.6 (ii) P(A)=0.5,P(B)=0.4,P(AuuB)=0.8 |
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| 13130. |
Find the equation of the line which passes through the point (4, -5) and is perpendicular to the line 3x+4y+5=0 |
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| 13131. |
3 sin^(2) x -4 cos^(2) x in |
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Answer» `[0,3]` |
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| 13132. |
If |bar(a)|=2, |bar(b)|=3, (bar(a), bar(b))= pi//6, then find (bar(a) xx bar(b))^(2) |
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| 13133. |
If the equation (a-3)x^2+9y^2=4 represents the rectangular hyperbola then a = ........... . |
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| 13134. |
A ball is drawn at random from a box cpntaining 6 white , 8 red and 10 green balls . Determine the probability , that the ball drawn is (i)white (ii) , red , (iii)green , (iv)not red, (v)red or green. |
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| 13135. |
Consider the lines x = y = z andthe line 2x + y + z-1 = 0 = 3 x + y + 2z-2 is |
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Answer» The sortest DISTANCE between the TWO LINES is `(1)/(sqrt2)` |
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| 13136. |
First term a and common ratio r = 1 then sum of n terms on G.P. is S_(n) = na . |
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| 13137. |
Let f(x)=cospix+10x+3x^(2)+x^(3),-2lexle3. The absolute minimum value of f(x) is |
| Answer» Answer :B | |
| 13138. |
Consider the function f(x) satisfying the identityf(x) + f((x-1)/( x))= 1+ x AA x in R - {0,1}, and g(x)=2f ( x)- x+1 The domain of y = sqrt( g(x) )is |
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Answer» `(-oo, (1-sqrt(5))/(2)]UU[1, (1+sqrt(5))/(2)]` |
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| 13140. |
If cot^3alpha +cot ^2 alpha + cot alpha =1 then |
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Answer» `COS 2 alpha.tan alpha = -1` |
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| 13142. |
Identify the type of Or used in the following statements and check whether the statements are true or false: sqrt(2) is a rational number or an irrational number. |
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| 13143. |
A variable line drawn throgh the point of intersection of the lines x/a+y/b=1,x/b+y/a=1 meets the coordinate axes in A and B. Then the locus of midpoint of AB is |
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Answer» `2XY(a+b)=AB(x+y)` |
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| 13144. |
Identify the type of Or used in the following statements and check whether the statements are true or false: A rectangle isa quadrilateral or a 5-sided polygon. |
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| 13145. |
Identify the type of Or used in the following statements and check whether the statements are true or false: To enter into a public library children need an identity card from the school or a letter from the school authorities. |
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| 13147. |
State whether each of the following set is finite or infinite: The set of animals living on the earth |
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| 13148. |
If baru, barv and barw are three non - coplanar vectors then (baru+barv-barw).(baru-barv)xx(barv-barw) |
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Answer» `BARU.(barvxxbarw)` |
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| 13149. |
Number of positive integers in the domains of the functions f(x)= sqrt(log_(0.5) log _e((x^(2) + x)/( x+4)) ) is |
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| 13150. |
Equation of the plane through the mid-point of the join of A (4,5,-10) and B (-1,2,1) and perpendicular to AB is |
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Answer» `5x + 3Y - 11 z + (135)/(2) =0` |
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