28278 + Interview Questions in Maths in Class 12 Page 555 InterviewSolution

27701.	Solve : 2x^3-3x^2-14x+5=0 given that 2-3i is a root
Answer» ANSWER :`2+3i,2-3i,(-1)/2`

Discussion

27702.	Ifalpha , beta , gammaare therootsoftheequationx^3 +px^2 + qx +r=0then thecoefficientof x incubicequation whoserootsarealpha( beta+ gamma ), beta( gamma+ alpha)andgamma ( alpha+ beta) is
Answer» 2q `Q^(2) + PR` `p^(2) - qr` `r(pq - r)` ANSWER :2

Discussion

27703.	If A and B are two events such that P(A) ne 0 and P(B) ne 0, then P(A' \| B')= ……….
Answer» <P>`1- P(A\|B)` `1- P(A'\|B)` `(1- P(A CUP B))/(P(B'))` `(P(A'))/(P(B'))` Answer :C

Discussion

27704.	If (a_(1),1,1),(1,a_(2),1) and (1,1,a_(3)) are coplaner (where a_(i)ge1,i=1,2,3) then underset(i=1)overset(3)sum(1)/(1-a_(i)) = …………..
Answer» 0 `-1` 1 `3-underset(i=1)OVERSET(3)SUM a_(i)` Answer :C

Discussion

27705.	Evaluate int (1)/(x l (x ) l^(2) (x ) ....l^(n) (x)) dx where l^(n) (x) = log_(e) log_(e) ....... Log_(e)(x ) (n times)
Answer» ANSWER :`L^((n+1)) ` (X) + C

Discussion

27706.	If int(x+5)/(x^(2) + 4x+5)dx = a log(x^(2) + 4x+5) + b tan^(-1)(x+k) + constant then (a,b,c)=
Answer» `(1/2, 3,2)` `(1/2,1,2)` `(1/2,3,1)` (1,3,2) ANSWER :A

Discussion

27707.	Let V denote the root mean square speed of the molecules in an ideal diatomic gas at absolute temperature T. The mass of a molecule is m. Neglecting vibrational energy terms, which is True?
Answer» a MOLECULE can have a speed greater than `sqrt(2)v` v is proportional to `sqrt(T) ` the average ROTATIONAL kinetic energy of a molecule is `(mv^(2))/(4)` the average kinetic energy of a molecule is `(5mv^(2))/(6)` Solution :AVG.`K.E.=(5)/(2)KT=(5)/(6)mv^(2)""[:.(1)/(2)mv^(2)=(3)/(2)KT]`

Discussion

27708.	If H_(1), H_(2) are two harmonic means between two positive numbers a and b, (a != b), A and G are the arithmetic and geometric means between a and b, then (H_(2) + H_(1))/(H_(2) H_(1)) is
Answer» `A/G` `(2A)/G` `A/(2G^(2))` `(2A)/G^(2)` ANSWER :D

Discussion

27709.	The value of (b times c)(a times d)+(c times a)(b times d)+(a times b)*(c times d) is
Answer» [a, B, C] - [b, c, d] [a, b, c] + [b, c, d] 0 none of these Answer :C

Discussion

27710.	Let f(x)=((e^(xln(2^(x)-1)-(2^(x)-1)^(x)sinx))/(e^(xlnx)))^(1//x). Then right hand limit of f(x) at x = 0
Answer» is EQUAL to ln 2 is equal to `(ln2)/€` is equal to `e(ln2)` does not exist Answer :B

Discussion

27711.	Area lying in the first quadrant and bounded by the circle x^(2) + y^(2) = 4 and the lines x = 0 and x = 2 is
Answer» `PI` `pi/2` `pi/3` `pi/4` ANSWER :A

Discussion

27712.	The product of the lengths of the perpendiculars drawn from the point (-1,5) to the pair of lines 2x^(2) - xy - 3y^(2) + 6x + y + 4 = 0 is
Answer» `(68)/(SQRT2)` `(68)/(sqrt26)` `(65)/(sqrt2)` `(65)/(sqrt26)` ANSWER :D

Discussion

27713.	If f:R to R is defined by f(x) = {(x-1, ",","for"x le 1),(2-x^(2), ",", "for"1 lt x le 3 ),(x-10, ",", "for"3 lt x lt 5 ),(2x, ",", "for"x ge 5 ):} then the set of points of discontinuity of f is
Answer» `R -{1,3,5}` `{1,3,5}` `R -{1,5}` `{1/5}` ANSWER :D

Discussion

27714.	x^(x^(2)-3)+(x-3)^(x^2)," for "x gt 3.
Answer» ANSWER :`X^(x^2-3)[(x^2-3)/(x)+2xlogx]+(x-3)^(x^2)[(x^2)/(x-3)+2X LOG(x-3)]`

Discussion

27715.	If x,y, z and w are non-zero real numbers andx^(2) + 5y^(2) + 5z^2+4w^(2) - 4xy - 4yz - 4zw = 0, then x, y, z,w are in
Answer» A.P. A.G.P H.P. G.P. Answer :4

Discussion

27716.	Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
Answer» ANSWER :8,8

Discussion

27717.	A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs. 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs. 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag ?
Answer» Answer :Minimum COST is Rs. 1950. The number of BAGS of cattle feed of brand P = 3 The number of bags of cattle FEE of brand Q = 6

Discussion

27718.	If theta is the angle between any two vectors vecaandvecb, then \|veca*vecb\|=\|vecaxxvecb\| when thetais equal to
Answer» 0 `(pi)/(4)` `(pi)/(2)` `pi` ANSWER :B

Discussion

27719.	Write the value x for which d/dxsin(sin^-1x)=1
Answer» SOLUTION :`d/dxsin(sin^-1x)=1` for `X in (-1,1)`

Discussion

27720.	A die is thrown 6 times If 'getting an odd number' is a success, what is the probability of i. 5 successes?ii. atleast 5, successes?iii. atmost 5 successes?
Answer» ANSWER :(i) `(3)/(32)` (ii) `(7)/(64)` (III) `(63)/(64)`

Discussion

27721.	The value of int_(0)^(pi//2) sin^(4)x cos^(6)x dx, is
Answer» `(3pi)/(216)` `(3pi)/(512)` `(pi)/(512)` none of these Solution :Using Gamma Function, we have `underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(Gamma(5//2)Gamma(7//2))/(2Gamma(4+6+2)/(2))=(Gamma(5//2)Gamma(7//2))/(2Gamma6)` `rArr `underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(((3)/(2)XX(1)/(2)xxGamma(1)/(2))((5)/(2)xx(3)/(2)xx(1)/(2)xxGamma(1)/(2)))/(2xx5!)=(3pi)/(512)`

Discussion

27722.	AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. IF EF = 17. then what is radius of the circle?
Answer» 10 12 13 15 Answer :C

Discussion

27723.	Consider f: R to R given by f (x) = 4x = 4x + 3.Show that f is invertible. Find the inverse of f.
Answer» ANSWER :`F ^(-1) ` is given by `f ^(-1) (y ) = (y -3)/(4)`

Discussion

27724.	If the circles of same radius 'a' and centres at (2, 3) and (5, 6) cut orthogonally, then a =
Answer» 3 4 6 10 Answer :B

Discussion

27725.	If the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 represents a pair of straight lines , then the square of the distance of their point of intersection from the origin is
Answer» `(C (a + b) - af^(2) - bg^(2))/(AB - H^(2))` `(c (a+ b) + f^(2) + g^(2))/( ab - h^(2))` `( c (a + b) - f^(2) - g^(2))/(ab - h^(2))` `(c (a + b) - f^(2) - g^(2))/((ab - h^(2))^(2))` Answer :C

Discussion

27726.	How many integers are there from 17 to 765, inclusive?
Answer» ANSWER :752

Discussion

27727.	Iftanalpha = b/a, a gt b gt 0 andif0 ltalpha lt (pi)/(4), thensqrt((a+b)/(a-b))- sqrt((a-b)/(a+b)) isequalto
Answer» `(2 SIN alpha)/( sqrt(cos2 alpha ))` `(2 cosalpha)/( sqrt(cos 2 alpha))` `(2 sin alpha)/( sqrt(sin 2 alpha))` `(2 cosalpha)/( sqrt( sin 2 alpha))` ANSWER :A

Discussion

27728.	If int (x^(2) tan^(-1) x)/(1 + x^(2))dx = xtan^(-1) x - (1)/(2) "log " (1 + x^(2)) + f(x) + cthen f(x) =
Answer» `- (TAN^(-1)x)/(2)` `- (1)/(2) (tan^(-1) x)^(2)` `(tan^(-1)x)/(2)` `((tan^(-1)x)^(2))/(2) ` Answer :B

Discussion

27729.	Whch of the following is correct?
Answer» `COS 1^(@) gt cos1^(@)` `cos 1^(@) lt cos1^(@)` `cos1^(@)=sin 1^(@)` `SIN1^(@) = 1/(180^(@)) sin1^(@)` ANSWER :A

Discussion

27730.	Solve the equationx^4 +x^3 -25 x^2 +41x+ 66=0giventhat3 + I sqrt(2)is a root
Answer» ANSWER :`-6 ,-1,3 +- I SQRT(2)`

Discussion

27731.	Differentiate w.r.t.x the function. (logx)^(log x), x gt 1.
Answer» Answer :`(LOGX)^(LOG x)[(1)/(x)+(log(log x))/(x)], x gt 1`

Discussion

27732.	lim_(xto0)(sqrt(x^(2)+100)-10)/(x^(2))=
Answer» 0 `0.1` `0.05` `-0.05` ANSWER :C

Discussion

27733.	If lim_(xtoa) {(f(x))/(g(x))} exists, then
Answer» 0 2 4 `oo` Solution :If `F(x)=SIN((1)/(x))" and "g(x)=(1)/(x)," then both "underset(xto0)limf(x)" and "underset(xto0)limg(x)" do nto EXIST, but "underset(xto0)LIM(f(x))/(g(x))=0" EXISTS"`

Discussion

27734.	If vec(a), vec(b)" and "vec(c) are three unit vectors such that vec(a)+vec(b)+vec(c)=vec(O), find the value of vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a).
Answer» ANSWER :`-3//2`

Discussion

27735.	Solve: x^2dy+(xy+y^2)dx=0, given x=1 and y = 1.
Answer» ANSWER :`y + 2X = 3X^(2) y`

Discussion

27736.	The orthocentre of the triangle formed by (2, -1//2), (1//2, -1//2) and (2, (sqrt(3)-1)//2) is
Answer» `((3)/(2), (SQRT(3)-3)/(6))` `(2, -(1)/(2))` `((5)/(4), (sqrt(3)-2)/(4))` `((1)/(2), -(1)/(2))` ANSWER :B

Discussion

27737.	Evalute the following integrals int (sin^(3//2) x + cos^(3//2)x)/(sqrt(sin^(3) x.cos^(3) x.sin(x + theta))) dx
Answer» Answer :`(2)/( COS THETA) SQRT(cos theta TAN x + sin theta ) + c `

Discussion

27738.	Ifthe sumofthedistancesofa pointPfrom two perpendicular linesina planesis1,thenthelocusofP isa
Answer» RHOMBUS circle straightline pairofstraightlines ANSWER :A

Discussion

27739.	If 5x -2y + k =0 is a tangent to the parabola y^(2) = 6x, then their point of contact is
Answer» `((6)/(5), (6)/(5))` `((6)/(5), (6)/(25))` `((6)/(25), (6)/(5))` `((6)/(25), (6)/(25))` ANSWER :C

Discussion

27740.	Match the following {:(I.,(1-i)(1+2i)(1-3i)=,"a)"6-8i),(II.,(1-i)^6+(1-i)^3=,"b)"-2i),(III.,((1+i)/(1-i))^3-((1+i)/(1+i))^3=,"c)"-2-10i),(IV.,sqrt(-5+12i)=,"d)"2+3i):}
Answer» a,c,B,d b,d,c,a d,b,a,c c,a,b,d Answer :A

Discussion

27741.	Letz_1, z_2 , z_3in Csuchthat\|z_1 \|= \|z_2\| =\|z_3\| =\|z_1+z_2+ z _3\|=4 . If\|z_1 - z _2 \|= \| z _1+z _ 3 \|andz_2nez_3, thenvaluesof\|z_1+z_2 \|* \|z_1+z _ 3\|is_____.
Answer» Solution :Since , `\|z_(1)\| = \|z_(2)\| = \|z_(3)\| = 4`, oringin is circumcentre of triangleformed by `A(z_(1)),B(z_(2)) and C(z_(3))` . So,orhtocentre of trinagle is `z_(1)+z_(2)+z_(3)\|=4` Given that `\|z_(1)-z_(2)\|=\|z_(1)-z_(3)\|` `rArr AB = AC ` `therefore angle BAC = 90^(@)` (orthocentre is at vertex A) Thus, `\|z_(1)+z_(2)\|.\|z_(1)+z_(3)\| = \|z_(4) -z_(3)\|\|z_(4)-z_(2)\| ` `= (AC)(AB)= (4sqrt(2))(4sqrt(2)) = 32`

Discussion

27742.	Let a, b, c in R, agt0, and the function f: R to R be defined by f(x)=ax^(2)+bx+c. Statement -1 b^(2)lt4ac rArr f(s) gt 0 for evergy value of x. Statement - 2 : f is strictly decreasing in the interval (-oo,-b//2a) and strictly increasing in the interval (-b//2a,oo).
Answer» ANSWER :A

Discussion

27743.	If 0 lt alpha lt pi/2 is a fixed andgle .If P=(cos theta sin theta) and Q ={cos (alpha- theta),sin (alpha - theta) then Q is obtained from P by
Answer» <P>coleckwise rotaion around ORIGIN through an angle `alpha` anti -clockwise rotation around origin through an angle `alpha` reflection in the line through reflection in the line trough originwith slope tan `alpha/2` Solution :In the ARGAND plane P is represented by `E^(i0)` and Q is represented by `e^i(alpha - theta)` Now rotation about a line with angle `alpha` is given by `e^(theta) rarr e^(alpha- theta)`.ThereforeQ is obtained fromP by reflection in the line MAKING an anlgle `alpha //2`

Discussion

27744.	The production of item A is x and the production of item B is y. If the corner points of the bounded feasible region are (1, 0), (2, 0), (0, 2) and (0, 1) then the maximum profit z = 2000x + 5000y is ……..
Answer» 20000 5000 4000 10000 Answer :D

Discussion

27745.	The maximum value of f(x)=5cos x + 12 sin x is ………..
Answer» 13 12 5 17 Answer :A

Discussion

27746.	Evaluate the following integrals (iii) int_(-1)^(1)\|x\|dx
Answer» ANSWER :1

Discussion

27747.	(-veca).vecbxx(-vecc)) =
Answer» `vecaxxvecb.vecc` `-VECA.(VECBXXVECC)` `vecaxxvecc.vecb` `veca.(veccxxvecb)` ANSWER :B

Discussion

27748.	Evaluate the following inegrals intsqrt(x^(2) + 4)dx
Answer» ANSWER :`(X)/(2)sqrt(x^(2)+4)+2sinh^(-1)((x)/(2))+C`

Discussion

27749.	Estimate the value of int_(0)^(0.5) x^(2)dx using the Riemann sums corresponding to 5 subintervals of equals witdh and applying (i) left-end rule (ii) right-end rule (iii) the mid-point rule.
Answer» ANSWER :`int_(0)^(0.5)X^(2)` DX is approximately 0.04125

Discussion

27750.	For a parabolay^(2)-2y-4x+9=0, the tangent at some point B is 3y = x + 10, where the normal at some other point K is 27y - 9x + 10 = 0. Letalpha, betaare the segments of the chord BK cut by the axes of the parabola. Find the number of integral values of 'a' for which the equation3x^(2)-(alpha+beta)x+(a^(2)-5a-(353)/(27))alphabeta=0has its roots real and distinct.
Answer» Solution :Clearly BK is a FOCAL chord so `alpha+beta+alphabeta RARR alpha beta=(100)/(9)` For real and distinct roots `D gt 0` `rArr""a^(2)gt 5a gt 14 lt0""rArr""gt 2 LT 7` NUMBER of intergral values of a are 8.

Discussion

Explore topic-wise InterviewSolutions in .

Solve : 2x^3-3x^2-14x+5=0 given that 2-3i is a root

Ifalpha , beta , gammaare therootsoftheequationx^3 +px^2 + qx +r=0then thecoefficientof x incubicequation whoserootsarealpha( beta+ gamma ), beta( gamma+ alpha)andgamma ( alpha+ beta) is

If A and B are two events such that P(A) ne 0 and P(B) ne 0, then P(A' | B')= ……….

If (a_(1),1,1),(1,a_(2),1) and (1,1,a_(3)) are coplaner (where a_(i)ge1,i=1,2,3) then underset(i=1)overset(3)sum(1)/(1-a_(i)) = …………..

Evaluate int (1)/(x l (x ) l^(2) (x ) ....l^(n) (x)) dx where l^(n) (x) = log_(e) log_(e) ....... Log_(e)(x ) (n times)

If int(x+5)/(x^(2) + 4x+5)dx = a log(x^(2) + 4x+5) + b tan^(-1)(x+k) + constant then (a,b,c)=

Let V denote the root mean square speed of the molecules in an ideal diatomic gas at absolute temperature T. The mass of a molecule is m. Neglecting vibrational energy terms, which is True?

If H_(1), H_(2) are two harmonic means between two positive numbers a and b, (a != b), A and G are the arithmetic and geometric means between a and b, then (H_(2) + H_(1))/(H_(2) H_(1)) is

The value of (b times c)*(a times d)+(c times a)*(b times d)+(a times b)*(c times d) is

Let f(x)=((e^(xln(2^(x)-1)-(2^(x)-1)^(x)sinx))/(e^(xlnx)))^(1//x). Then right hand limit of f(x) at x = 0

Area lying in the first quadrant and bounded by the circle x^(2) + y^(2) = 4 and the lines x = 0 and x = 2 is

The product of the lengths of the perpendiculars drawn from the point (-1,5) to the pair of lines 2x^(2) - xy - 3y^(2) + 6x + y + 4 = 0 is

If f:R to R is defined by f(x) = {(x-1, ",","for"x le 1),(2-x^(2), ",", "for"1 lt x le 3 ),(x-10, ",", "for"3 lt x lt 5 ),(2x, ",", "for"x ge 5 ):} then the set of points of discontinuity of f is

x^(x^(2)-3)+(x-3)^(x^2)," for "x gt 3.

If x,y, z and w are non-zero real numbers andx^(2) + 5y^(2) + 5z^2+4w^(2) - 4xy - 4yz - 4zw = 0, then x, y, z,w are in

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

If theta is the angle between any two vectors vecaandvecb, then |veca*vecb|=|vecaxxvecb| when thetais equal to

Write the value x for which d/dxsin(sin^-1x)=1

A die is thrown 6 times If 'getting an odd number' is a success, what is the probability of i. 5 successes?ii. atleast 5, successes?iii. atmost 5 successes?

The value of int_(0)^(pi//2) sin^(4)x cos^(6)x dx, is

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. IF EF = 17. then what is radius of the circle?

Consider f: R to R given by f (x) = 4x = 4x + 3.Show that f is invertible. Find the inverse of f.

If the circles of same radius 'a' and centres at (2, 3) and (5, 6) cut orthogonally, then a =

If the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 represents a pair of straight lines , then the square of the distance of their point of intersection from the origin is

How many integers are there from 17 to 765, inclusive?

Iftanalpha = b/a, a gt b gt 0 andif0 ltalpha lt (pi)/(4), thensqrt((a+b)/(a-b))- sqrt((a-b)/(a+b)) isequalto

If int (x^(2) tan^(-1) x)/(1 + x^(2))dx = xtan^(-1) x - (1)/(2) "log " (1 + x^(2)) + f(x) + cthen f(x) =

Whch of the following is correct?

Solve the equationx^4 +x^3 -25 x^2 +41x+ 66=0giventhat3 + I sqrt(2)is a root

Differentiate w.r.t.x the function. (logx)^(log x), x gt 1.

lim_(xto0)(sqrt(x^(2)+100)-10)/(x^(2))=

If lim_(xtoa) {(f(x))/(g(x))} exists, then

If vec(a), vec(b)" and "vec(c) are three unit vectors such that vec(a)+vec(b)+vec(c)=vec(O), find the value of vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a).

Solve: x^2dy+(xy+y^2)dx=0, given x=1 and y = 1.

The orthocentre of the triangle formed by (2, -1//2), (1//2, -1//2) and (2, (sqrt(3)-1)//2) is

Evalute the following integrals int (sin^(3//2) x + cos^(3//2)x)/(sqrt(sin^(3) x.cos^(3) x.sin(x + theta))) dx

Ifthe sumofthedistancesofa pointPfrom two perpendicular linesina planesis1,thenthelocusofP isa

If 5x -2y + k =0 is a tangent to the parabola y^(2) = 6x, then their point of contact is

Match the following {:(I.,(1-i)(1+2i)(1-3i)=,"a)"6-8i),(II.,(1-i)^6+(1-i)^3=,"b)"-2i),(III.,((1+i)/(1-i))^3-((1+i)/(1+i))^3=,"c)"-2-10i),(IV.,sqrt(-5+12i)=,"d)"2+3i):}

Letz_1, z_2 , z_3in Csuchthat|z_1 |= |z_2| =|z_3| =|z_1+z_2+ z _3|=4 . If|z_1 - z _2 |= | z _1+z _ 3 |andz_2nez_3, thenvaluesof|z_1+z_2 |* |z_1+z _ 3|is_____.

Let a, b, c in R, agt0, and the function f: R to R be defined by f(x)=ax^(2)+bx+c. Statement -1 b^(2)lt4ac rArr f(s) gt 0 for evergy value of x. Statement - 2 : f is strictly decreasing in the interval (-oo,-b//2a) and strictly increasing in the interval (-b//2a,oo).

If 0 lt alpha lt pi/2 is a fixed andgle .If P=(cos theta sin theta) and Q ={cos (alpha- theta),sin (alpha - theta) then Q is obtained from P by

The production of item A is x and the production of item B is y. If the corner points of the bounded feasible region are (1, 0), (2, 0), (0, 2) and (0, 1) then the maximum profit z = 2000x + 5000y is ……..

The maximum value of f(x)=5cos x + 12 sin x is ………..

Evaluate the following integrals (iii) int_(-1)^(1)|x|dx

(-veca).vecbxx(-vecc)) =

Evaluate the following inegrals intsqrt(x^(2) + 4)dx

Estimate the value of int_(0)^(0.5) x^(2)dx using the Riemann sums corresponding to 5 subintervals of equals witdh and applying (i) left-end rule (ii) right-end rule (iii) the mid-point rule.

The value of (b times c)(a times d)+(c times a)(b times d)+(a times b)*(c times d) is