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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.
| 7051. |
Let bara =bari+2barj+bark, barb=bari-barj+bark, barc=bari+barj-bark. A vector coplanar to bara and barb " has a projection along " barc " of magnitude " 1/sqrt3, then the vector is |
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Answer» `4bari-barj+4bark, 2bari+barj+2bark` |
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| 7052. |
Write down the negation of following compound statements. All prime integers are either even or odd. |
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| 7053. |
int e^(-4x) cos x dxis |
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Answer» `(e^(-4X))/17 [ 4 cos X + sin x] + c` |
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| 7054. |
Let f(x)=(x-2)(x^(4)-4x^(3)+6x^(2)-4x+1)then value of local minimum of f is |
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Answer» `-2//3` |
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| 7055. |
The value of (1-tan^(2)15^(@))/(1+tan^(2)15^(@)) is |
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Answer» `(m-1)/(m^(2)+1)` |
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| 7056. |
Using sybols sub" and " cancelsub fill in the following blanks : a…………..{a, b, c} |
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| 7057. |
Using sybols sub" and " cancelsub fill in the following blanks : {a}………….{a, b, c} |
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| 7058. |
The valueof vec(AB)+vec(BC)+vec(DA)+vec(CD)is |
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Answer» `vec(AD)` |
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| 7059. |
Evaluate the following limits in Exercises lim_(xto3)(x^(4)-81)/(2x^(2)-5x-3) |
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| 7060. |
Determine whether the following functions are even or (odd). (i) f(x) = x((e^(x)-1)/(e^(x)+1)) (ii) f(x) = log(x+sqrt(x^(2)+1)), (iii) f(x) = a^(x) + a^(-x) + cos x (iv) f(x) = |x| + 1/2, where x cancel(in) Z |
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| 7061. |
Find the coefficient of x^7 in ( ax^(2) + (1)/( bx) )^(11) and the coefficient of x^(-7) in (ax + (1)/(bx^(2) ))^(11). If these coefficients are equal, find the relation between a and b. |
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| 7062. |
bari, barj, bark is a right handed orthonormal system of vectors and bara is a vector of magnitude 2 units satisyfing baraxxbari =barj then bara. bari = |
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Answer» `pmsqrt3` |
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| 7063. |
The position vectors A, B are bar(a), bar(b) respectively. The position vector of C is (5bar(a))/3-bar(b). Then |
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Answer» C is outside the `DeltaOAB` but INSIDE the ANGLE OBA |
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| 7064. |
If two points are A(x_(1),y_(1)) and B(x_(2),y_(2)), then the co-ordinates of the point P, which divides the line segment in the ratio m_(1) : m_(2) (internally), are given by : x=(m_(1)x_(2)+m_(2)x_(1))/(m_(1)+m_(2)), y=(m_(1)y_(2)+m_(2)y_(1))/(m_(1)+m_(2)) Find the co-ordinates of the point P, which divides (i) internally (ii) externally the line joining (1,-3) and (-3,9) in the ratio 1 : 3. |
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Answer» `(II) (3,-9)` |
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| 7065. |
The point (x,y) lie on line 2x+3y=6. The smallest value of the quantitly sqrt(x^2+y^2 " is m. The the value of" sqrt13m is _______ |
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| 7066. |
Two sides of a rhombus are along the lines, x-y+1 and 7x-y-5=0. If its diagonals interset at (-1,-2) then which one of the following is a vertex of this rhombus? |
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Answer» (-3,-8) |
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| 7067. |
Consider the circle x^2+y^2-4x-6y-3 = 0 If this circle touches the y axis, find its equation |
| Answer» SOLUTION :`x^2+y^2-4x-6y+9 = 0` | |
| 7068. |
If the equation x^(2) + 12 + 3 sin (a + bx) + 6x = 0has at least one real solution, when a, b in [0, 2 pi] , then the value of a = 3b is (n in Z) |
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Answer» `2 N pi` |
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| 7071. |
If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1. |
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| 7072. |
Find theperiod of (i) sin^(2)x+ 2cos^(2) x (ii)| sin x| |
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| 7073. |
Find the value of lamda if the lines 2x+3y+lamda=0, 3x-4y-13=0 and 8x-11y-33=0 are concurrent. |
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| 7074. |
Check whether the statement is true or not : 3 -: 4 i is a complex number. |
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| 7077. |
IF x^2+y^2=1 and P=(3x-4x^3)^2+(3y-4y^3)^2 then find 'P'. |
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Answer» 1 |
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| 7079. |
If barb, barc are like unit vectors and baraxx (barbxx barc) = bar0 then |
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Answer» `bara.barc=barb.barc` |
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| 7080. |
If U= {1,2,3,4,5,6,7,8,9,}, A={1,2,3,4,}, B={2,4,6,8) and C = {3,4,5,6}.Find : (i) A^(c) (ii)B^(c) (iii) A(uuC)^(c) (iv) (AuuB)^(c) (v) (A^(c))^(c) (vi) (B-C)^(c). |
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Answer» (II) ={1,3,57,9}. (III) ={7,8,9}. (IV) ={1,2,3,4,6,8}. (V)={1,2,3,4}. (i) ={1,3,4,5,6,7,9}. |
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| 7081. |
Determine also, for which values of nepsilonZ, (sqrt3-i)^n is real |
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| 7082. |
Let the algebraic sum of the perpendicular distances from the points (2,0) (0,2) and (1,1) to a variable straight line be zero, then the line passe through a fixed point whose coordinate are (a,b), then a+b is |
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| 7083. |
A farm house uses atleast 800 kg of special food daily. The special food is a mixture of corn and soyabean with the following compositions The dietary requirements of the special food stipulate atleast 30% protein and at most 5% fibre. Determine the daily minimum cost of the food mix. |
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| 7084. |
If |__.__| denotes the greatest integer less than or equal to the real number under consideration and -1lt=xlt0,0lt=ylt1,1lt=zlt2, then the value of the determinant |(|__x__|+1,|__y__|,|__z__|),(|__x__|,|__y__|+1,|__z__|),(|__x__|,|__y__|,|__z__|+1)| is |
| Answer» ANSWER :C | |
| 7085. |
Complete the following table |
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| 7086. |
Find the sum of x(x+y) + x^(2) (x^(2) + y^(2)) + x^(3) (x^(3) + y^(3))+……..to n terms |
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| 7087. |
The position vector of a point lying on the line joining the points whose position vectors are bar(i)+bar(j)-bar(k) and bar(i)-bar(j)+bar(k) is |
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Answer» `BAR(j)` |
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| 7088. |
Compute the standard deviation for the following distribution. |
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| 7089. |
d/(dx)(Tan^(-1)""(x)/(sqrt(a^2-x^2))= |
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Answer» `1/(SQRT(a^2+X^2))` |
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| 7090. |
A die is thrown. Describe the following events: (i) A: anumber less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3 (iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3 Also find A uu B, A nn B, B uu C, E nn E, D nn E, A - C, D - E, E nn F',F' |
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| 7091. |
Use p : I like this school , q : I like Mr. Sexena. Express each of the following statements in words . ~p |
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| 7092. |
If D, E and F are respectively the mid-points of AB, AC and BC in DeltaABC then bar(BE)+bar(AF)= |
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Answer» `BAR(DC)` |
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| 7093. |
A function 'f' from a set X toY is called onto if very yinY , EE x in Xsuch that f(x) =y . Unless the contrary is specified a real function is onto if it takes all real values ,Othervise ,it is called o into function , Thus , if X and Y are finite sets , then 'f' can not be onto if Y contains more elements then 'x' Now answer the following Which of the following is not true |
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Answer» A one-one function from theset {a, B, C} to `{ alpha, beta, gamma}` is onto also |
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| 7095. |
cos ^(3) x sin 2x = sum _(x =0) ^(n) ar sin (rx) AA x in R, then |
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Answer» `N = 5, a _(1) = 1//2` |
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| 7096. |
A function 'f' from a set X toY is called onto if very yinY , EE x in Xsuch that f(x) =y . Unless the contrary is specified a real function is onto if it takes all real values ,Othervise ,it is called o into function , Thus , if X and Y are finite sets , then 'f' can not be onto if Y contains more elements then 'x' Now answer the following The polynomial functionf(x)= a_0 x^(n) +a_1 x^(n-1)+a_2x^(n-2)+.......+a_nwherea_0 ne 0is onto for |
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Answer» `0 lt x lt 2` |
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| 7097. |
If the portion of a line intercepted between the coordinate axes is divided by the point (2,-10 in the ratio 3:2. then the equation of that line is |
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Answer» `5x-2y-20=0` |
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| 7098. |
Write contrapositive and converse of the following statements: If it rains then roads are wet. |
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Answer» CONVERSE: If roads are wet, it has rained. |
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| 7099. |
If absbara = 3, absbarb =4 and (bara,barb)=(2pi)/3 , " then the value of " (3bara-2barb).(bara+2barb) is |
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Answer» 61 |
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| 7100. |
If the Internal bisector of angleAOB where 0=(0,0,0), A =(3,4,12), B=(1,2,2) intersects AB at C then y-coordinate of C is |
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Answer» `11/8` |
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