28278 + Interview Questions in Maths in Class 12 Page 184 InterviewSolution

9151.	If x = 2 + 5i then value of the expression x^(3)-5x^(2)+33x-49 equals
Answer» `-20` 10 20 `-29` ANSWER :A

Discussion

9152.	A kite is flying at a height 151.5 m from horiozontal. The speed of the kite is 10 m/s. The distance of the kite from a boy who flies the kite is 250 m. Find the rate of change of thread of the kite.
Answer» ANSWER :8 m/s

Discussion

9153.	int "In" ( x + sqrt( 1+x^(4) )) dx.
Answer» ANSWER :`X "In" (x+ SQRT( 1+x^2) )- sqrt( 1+x^2) + C`.

Discussion

9154.	If A=[{:(1,1),(1,1):}]then A^(100) ………
Answer» 100 A `2^(99)A` `2^(100)A` 99 A Answer :B

Discussion

9155.	Statement I : Sum of the series 1^(3) - 2^(3) + 3^(3) - 4^(3) +…+ 11^(3) = 378 Statement II : For any off integer n ge 1, n^(3) - (n-1)^(3) +…+(-1)^(n-1) 1^(3) = (1)/(4)(2n-1) (n+1)^(2)
Answer» ANSWER :D

Discussion

9156.	A chord of length 8 units is at a distance of 4 uits from the centre of a circle then its radius is
Answer» `4sqrt(2)` `3sqrt(2)` `2sqrt(2)` `SQRT(2)` ANSWER :A

Discussion

9157.	Evaluation of definite integrals by subsitiution and properties of its : int_(-e)^(e)log((e^(5)-x^(5))/(e^(5)+x^(5)))dx=.............
Answer» E 5 0 `-e` ANSWER :C

Discussion

9158.	Find the values of the following integrals int(secx+tanx+(3)/(x)-4)dx
Answer» ANSWER :`log\|secx+tanx\|+log\|secx\|+3log\|x\|-4x+c`

Discussion

9159.	Let (1+ x + x^2)^n = a_0 + a_1x + a_2x^2 + …….+a_(2n)x^(2n) Then match the items of List - I with those of List-II The correct match is
Answer» `A to (IV) , B to (I), C to (III)` `A to (IV) , B to (III), C to (I)` `A to (III) , B to (I) , C to (II)` `A to (III) , B to (IV), C to (II)` ANSWER :D

Discussion

9160.	Prove that three lines drawn from origin with direction cosines proportional to (1,-1,1),(2,-3,0),(1,0,3) lie on one plane .
Answer» SOLUTION :Let `OVERSETTOA=i+j+koversettob=2i-3joversettoci+3k` The lines are co-planar if `oversettoa.(oversettobxxoversettoc)=0` Now `oversettoa.(oversettobxxoversettoc)=\|(1,-1,1),(2,-3,0),(1,0,3):\|=1(-9)+1(6)+1(3)=0`

Discussion

9161.	If f(x)=3x^(2)+4x+5, what must the value of k equal so that the graph of f(x-k) will be symmetric to the y-axis?
Answer» `-4` `-(4)/(3)` `-(2)/(3)` `(2)/(3)` Solution :Graph `y=3x^(2)+4x+5` in the standard window, and observe that the graph MUST be moved SLIGHTLY to the right to be symmetric to the y-axis. Therefore, k must be positive. Use CALC/minimum to find the vertex of the PARABOLA and observe that its x-coordinate is -0.66666. . ..if the function entered into `Y_(1)`, set `Y_(2)=Y_(1)(x-(2)/(3))` and graph `Y_(2)` to verify this answer.

Discussion

9162.	y=-x^(2)+120x-2,000 the equation above gives the profit in dollars, y, a coat manufacturer earns day where x is the number of coats sold. What is the maximum profit he earns in dollars?
Answer» ANSWER :`$1,600`

Discussion

9163.	What is the perimeter of quadrilateral STUR if it has vertices with (x,y) coordinates S(0,0), T(2,-4),U(6,-6) , R(4,-2) ?
Answer» `2sqrt20` `2sqrt5+2sqrt20` `8sqrt5` 80 Answer :C

Discussion

9164.	If A, B, C are any three events in an experiment then show that (i) P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B)) "if P"(B^(C)) gt 0 (ii) A sube B rArr P(A//C) le P(B//C) "if P(C)" gt 0 (iii) If A, B are mutually exclusive, then P(A//B^(C)) = (P(A))/(1-P(B)) "if P(B)" ne 1 (iv) If A, B are mutually exclusive and P(A uu B) ne 0 "then" P(A//A uu B) = (P(A))/(P(A) + P(B))
Answer» <P> ANSWER :(i) `P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B))` (ii) `RARR P(A//C) le P(B//C)` (iii) `P(A//B^(C)) = (P(A nn B^(C)))/(P(B^(C)))=(P(A))/(1-P(B))` (IV) `P(A nn B) = 0`

Discussion

9165.	The value of definite integral int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx is
Answer» 1 `-1` 0 2 Answer :A

Discussion

9166.	If a and b are unit vectors, then the greatest value of \|a+b\|+\|a-b\| is
Answer» 2 4 `2sqrt2` `sqrt2` Solution :LET `theta` be an ANGLE between UNIT vectors a and b. Then, `a.b =COS theta` Now, `\|a+b\|^(2)=\|a\|^(2)+\|b\|^(2)+2a.b` `=1+1+2xx1xx1xxcos theta` `=2+2 cos theta=4 "cos"^(2) theta/2` `implies \|a+b\|=2 "cos" theta/2` and `\|a-b\|^(2)=\|a\|^(2)+\|b\|^(2)-2a.b` `=2-2 cos theta=2 (2 "SIN"^(2) theta/2)` `\|a-b\|=2"sin" theta/2` `:. \|a+b\|+\|a-b\|=2 ("cos" theta/2 +"sin"theta/2) le 2 sqrt(2)`

Discussion

9167.	There are 5 letters and 5 addressed envelopes. If the letters are placed at random in the envelopes. Find the chance that exactly 3 letters go into correct envelopes.
Answer» ANSWER :`(1)/(12)`

Discussion

9168.	There are 5 letters and 5 addressed envelopes. If the letters are placed at random in the envelopes. Find the chance that all letters go into correct envelopes.
Answer» ANSWER :`(1)/(120)`

Discussion

9169.	A bag contains six balls. Two balls are drawn and found them to be red. The probability that 5 balls in the bag are red is
Answer» `5//6` `2//5` `1//3` `1//7` ANSWER :D

Discussion

9170.	Find the value of cos 1^@, cos 2^@ ….. Cos 100^@
Answer» SOLUTION :`cos 1^@ cos 2^@ …… cos 100^@ = 0` as `cos 90^@` is there which is ZERO.

Discussion

9171.	Find the shortest distacne between the lines vecr=hati+2hatj+3hatk+mu(2hati+3hatj+4hatk) and vecr=(2hati+4hatj+5hatk)+lambda(3hati+4hatj+5hatk)
Answer» ANSWER :x-2y+2z=0and x-2y+2z=6

Discussion

9172.	Statement-1 f(x) = \|{:((1+x)^(11),(1+x)^(12),(1+x)^(13)),((1+x)^(21),(1+x)^(22),(1+x)^(23)),((1+x)^(31),(1+x)^(32),(1+x)^(33)):}\| the cofferent of x in f(x)=0 Statement -2 If P(x)=a_(0)+a_(1)x+a_(2)x^(2)+a_(2)x_(3) +cdots+a_(n)s^(n) then a_(1)=P'(0), where dash denotes the differential coefficient.
Answer» ANSWER :A

Discussion

9173.	If the area of the triangle on the complex plane formed the points z , iz and z + iz is 50 square units, then \|z\| is
Answer» 5 10 15 none Answer :B

Discussion

9174.	A particle moves along the curve y=x^((3)/(2)) in the first quadrant in such a way that its distance from the origin increases at the rate of 11 units/sec. The value of (dx)/(dt) when x = 3 is …………
Answer» 4 `(9)/(2)` `(3sqrt(3))/(2)` NONE of these ANSWER :A

Discussion

9175.	Let f be a function defined on [-pi/2, pi/2] by f(x) = 3cos^(4)x - 6 cos^(3)x -3 Then the range of f(x) is
Answer» `[-12,-3]` `[-6,-3]` `[-6,3)` `(-12,3]` ANSWER :A

Discussion

9176.	Differentiate sin^(-1) ((1)/(sqrt(x + 1)))
Answer» ANSWER :`(-1)/(2 SQRTX (1 + X))`

Discussion

9177.	Ifa ray of light incident along the line 3x+ (5-4 sqrt2 ) y= 15gets reflected from the hyperbola (x^(2))/( 16)-(y^(2))/( 9)=1 then reflected ray goes along the line
Answer» `xsqrt 2- y +5=0 ` ` sqrt2y -x+5=0 ` ` sqrt2y -x-5=0` ` 3X- (4sqrt2+5)y +15=0 ` ANSWER :D

Discussion

9178.	The solution of the differential equation (dy)/(dx) = sin (x +y) tan (x + y) -1 is
Answer» `COSEC (x + y) + tan (x + y) = x +C` `x + cosec (x + y) = c` `x + tan (x +y) =c` `x + sec (x +y) =c` ANSWER :B

Discussion

9179.	Form a quadratic equation with rational coefficients if one of its root is cot^(2)18^(@).
Answer» ANSWER :`X^(2)-10x+5=0`

Discussion

9180.	A noraml to the parabola at a point A on the parabola whose equation is y^(2)=2013x cuts the axis of x at N. AN is produced to the point B such that NB=1/2AN. If the normals through any point of the parabola y^(2)=2013x, cut the line 2x - 2013 = 0, in points whose ordinates are in AP, then the slopes of these normals are in
Answer» AP GP HP none of these Answer :B

Discussion

9181.	A normal to the parabola at a point A on the parabola whose equation is y^(2)=2013x cuts the axis of x at N. AN is produced to the point B such that NB=1/2AN. If C is a point on the parabola y^(2)=2013x such that OCN=pi/2 (O being origin), then projection of CN on x-axis is equal to
Answer» 2013 `2013/2` 4026 none of these Answer :A

Discussion

9182.	A noraml to the parabola at a point A on the parabola whose equation is y^(2)=2013x cuts the axis of x at N. AN is produced to the point B such that NB=1/2AN. If two more normals to the parabola y^(2)=2013x pass through B, then they are
Answer» coincident INCLINED at `pi/4` inclined at `pi/6` inclined at `pi/2` ANSWER :D

Discussion

9183.	Prove that the function f given by f(x) = log \| cos x\|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi).
Answer» Solution :f(x) = log cos x ` rArrf'(x) = (-SIN x)/(cos x) =- tan x` (a) For STRICTLY decreasing FUNCTION `f'(x) LT 0` ` rArr-tan x lt 0` ` rArrtan xgt 0` ` rArr x in ]0,PI/2[` (b) Forstrictly decreasing function ` f'(x) gt 0` ` rArr- tan x gt 0` ` rArrtan x lt 0` ` rArrx in ]pi/2, pi [`

Discussion

9184.	Find all possible values of (i) sqrt(\|x\|-2) (ii) sqrt(3-\|x-1\|) (iii) Sqrt(4-sqrt^2))
Answer» Solution :`sqrt(\|x\|-2)` we know that SQUARE roots are defined for non- negative values only . It implies that we must have `\|x\|-2 LE 0` Thus `sqrt(\|x\|-2) ge 0 ` (ii) `sqrt(3-\|x-1\|)` is defined when `3-\|x-1\| le 0 ` But the maximum value of 3-\|x-1\| is 3 , when \|x-1\| is 0 HENCE for `sqrt(3-\|x-1\|)` to get defined , `0 le 3- \|x-1\| le 3 ` Thus , `sqrt(3-\|x-1\|)in [0,sqrt(3)]` Alternatively , `\|x-1\| ge 0` `rArr-\|x-1\| le 0 ` `rArr3-\|x-1\|le3` But for `sqrt(3-\|x-1\|)` to get defined ,we must have `0 le 3 -\|x-1\| le 3 ` `rArr0 le sqrt(3-\|x-1\| le sqrt(3)` (iii) `sqrt(4-sqrt(x^2))=sqrt(4-\|x\|)` `\|x\| ge 0 ` `rArr- \|x\| le 0 ` `rArr4-\|x\| le 4 ` But for `sqrt(4-\|x\| )` to get defined `0 le 4 - \|x\| le 4 ` `therefore0 le sqrt(4-\|x\|) le 2 `

Discussion

9185.	Using the proprties of determinants in Exercise 7 to 9, prove that \|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}\|=(a-1)^3
Answer» ANSWER :`(a-1)^3`

Discussion

9186.	((2007)!)/((2007))is an integer & n in N, then find maximum value of n.
Answer» ANSWER :9

Discussion

9187.	Find the area (in sq. unit) bounded by the curves : y = e^(x), y = e^(-x) and the straight line x =1.
Answer» ANSWER :`(E + (1)/(e) - 2)` sq. UNIT

Discussion

9188.	S=sum_(r=1)^(4)tan^(2)(2r-1)(pi)/(16) is an integer divisible by
Answer» 2 3 5 7 Answer :A::D

Discussion

9189.	Find the quadrants of the coordinate planes such that for each point (x,y) on these quadrants ( wherex ne 0 , y ne 0) , the equation,(sin^(4) theta )/x + ( cos^4 theta)/( y)=(1)/(x+y)is soluble fortheta.
Answer» ANSWER :`rArr` X and y must be same SIGN, which is TRUE in ist and 3rd QUADRANT only.

Discussion

9190.	Statement-1 : if P and D be the ends of conjugate diameters then the locus of mid-point of PD is a circle. and STATEMENT-2 : if P and D be the ends of conjugate diameter, then the locus of intersection of tangents at P and D is an ellipse.
Answer» Statement-1 is TRUE, statement-2 is true, Statement -2 is a CORRECT explanation for Statement -1 Statement -1 is true, Statement-2 is true , Statement-2 is NOT a correct explanation for statement-1 Statement-1 is true, Statement-2 is FALSE Statement-1 is False, Statement-2 is true Answer :D

Discussion

9191.	Which of the following numbers is NOT prime? (Hind : avoid actually computing these numbers.)
Answer» `6!-1` `6!-1` `6!-41` `7!-1` ANSWER :B

Discussion

9192.	Write tan^(-1)(sqrt((1-cosx)/(1+cosx))), 0 lt x lt pi in the simplest form.
Answer» ANSWER :`(X)/(2)`

Discussion

9193.	Express the following differential equations in the form (dy)/(dx) = F((y)/(x)). (i) xdy - ydx = sqrt(x^(2) + y^(2))dx (ii) [x - y Tan^(-1)((y)/(x))] dx + x Tan^(-1)((y)/(x)) dy = 0 (iii) xdy = y(log y - log x+1)dx
Answer» Answer :(i) `(dy)/(dx) = (y)/(X) + SQRT((1+((y)/(x))^(2)))` `(dy)/(dx) = ((y)/(x) Tan^(-1)((y)/(x))-1)/(Tan^(-1)((y)/(x)))` (III) `(dy)/(dx) = (y)/(x)[log((y)/(x))+1]`

Discussion

9194.	Each of five questions on a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. If the random variable X is the number of questions answered correctly, the probability that the student will get at most three answers correct is
Answer» `45/512` `63/64` `781/1024` `979/1024` ANSWER :B

Discussion

9195.	Use following sequence, A_n = 3 - 8n What is A_(11) - A_(9) ?
Answer» ANSWER :`-16`

Discussion

9196.	Let f(x)=x^(2)+3x-3, x ge0 if in points x_(1),x_(2),x_(3),...x_(n) are so chosed on the x-axis such that (i) (1)/(n) underset(i=1) overset(n)sumf^(-1)(x_(i))=f((1)/(n)underset(i=1) overset(n)sumx_(i)) (ii) underset(i=1) overset(n)sumf^(-1)(x_(i))=underset(i=1) overset(n)sumx_(i) wehre f^(-1) denots the inverser of f. then mean of x_(1),x_(2),x_(3),....x_(n) is :
Answer» 1 2 3 4 Answer :A

Discussion

9197.	Differentiate the functions sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))
Answer» ANSWER :`(DY)/(DX)= (1)/(2)`

Discussion

9198.	Sum to n terms the series 4 + 14 + 30 + 52+ 82+ 114+.........
Answer» ANSWER :`N (n+1) ^(2)`

Discussion

9199.	If a function f:CtoC is defined by f(x)=3x^(2)-1, where C is theset of complex numbers, then the pre-images of -28 are
Answer» 3,-3 3I,-3i 3i only `-3i` only Answer :B

Discussion

9200.	Let veca = hati + hatj + hatk, vecb = hati - ahtj + hatk and hati - hatj - hatkbe three vectors. A vector vecv in the plane of veca and vecb, whose projection on vecc is (1)/(sqrt3), is given by :
Answer» `4i-j+4k` `i+j-2k` `4i+j-4k` `3i+j-3k` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If x = 2 + 5i then value of the expression x^(3)-5x^(2)+33x-49 equals

A kite is flying at a height 151.5 m from horiozontal. The speed of the kite is 10 m/s. The distance of the kite from a boy who flies the kite is 250 m. Find the rate of change of thread of the kite.

int "In" ( x + sqrt( 1+x^(4) )) dx.

If A=[{:(1,1),(1,1):}]then A^(100) ………

Statement I : Sum of the series 1^(3) - 2^(3) + 3^(3) - 4^(3) +…+ 11^(3) = 378 Statement II : For any off integer n ge 1, n^(3) - (n-1)^(3) +…+(-1)^(n-1) 1^(3) = (1)/(4)(2n-1) (n+1)^(2)

A chord of length 8 units is at a distance of 4 uits from the centre of a circle then its radius is

Evaluation of definite integrals by subsitiution and properties of its : int_(-e)^(e)log((e^(5)-x^(5))/(e^(5)+x^(5)))dx=.............

Find the values of the following integrals int(secx+tanx+(3)/(x)-4)dx

Let (1+ x + x^2)^n = a_0 + a_1x + a_2x^2 + …….+a_(2n)x^(2n) Then match the items of List - I with those of List-II The correct match is

Prove that three lines drawn from origin with direction cosines proportional to (1,-1,1),(2,-3,0),(1,0,3) lie on one plane .

If f(x)=3x^(2)+4x+5, what must the value of k equal so that the graph of f(x-k) will be symmetric to the y-axis?

y=-x^(2)+120x-2,000 the equation above gives the profit in dollars, y, a coat manufacturer earns day where x is the number of coats sold. What is the maximum profit he earns in dollars?

What is the perimeter of quadrilateral STUR if it has vertices with (x,y) coordinates S(0,0), T(2,-4),U(6,-6) , R(4,-2) ?

The value of definite integral int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx is

If a and b are unit vectors, then the greatest value of |a+b|+|a-b| is

There are 5 letters and 5 addressed envelopes. If the letters are placed at random in the envelopes. Find the chance that exactly 3 letters go into correct envelopes.

There are 5 letters and 5 addressed envelopes. If the letters are placed at random in the envelopes. Find the chance that all letters go into correct envelopes.

A bag contains six balls. Two balls are drawn and found them to be red. The probability that 5 balls in the bag are red is

Find the value of cos 1^@, cos 2^@ ….. Cos 100^@

Find the shortest distacne between the lines vecr=hati+2hatj+3hatk+mu(2hati+3hatj+4hatk) and vecr=(2hati+4hatj+5hatk)+lambda(3hati+4hatj+5hatk)

Statement-1 f(x) = |{:((1+x)^(11),(1+x)^(12),(1+x)^(13)),((1+x)^(21),(1+x)^(22),(1+x)^(23)),((1+x)^(31),(1+x)^(32),(1+x)^(33)):}| the cofferent of x in f(x)=0 Statement -2 If P(x)=a_(0)+a_(1)x+a_(2)x^(2)+a_(2)x_(3) +cdots+a_(n)s^(n) then a_(1)=P'(0), where dash denotes the differential coefficient.

If the area of the triangle on the complex plane formed the points z , iz and z + iz is 50 square units, then |z| is

A particle moves along the curve y=x^((3)/(2)) in the first quadrant in such a way that its distance from the origin increases at the rate of 11 units/sec. The value of (dx)/(dt) when x = 3 is …………

Let f be a function defined on [-pi/2, pi/2] by f(x) = 3cos^(4)x - 6 cos^(3)x -3 Then the range of f(x) is

Differentiate sin^(-1) ((1)/(sqrt(x + 1)))

Ifa ray of light incident along the line 3x+ (5-4 sqrt2 ) y= 15gets reflected from the hyperbola (x^(2))/( 16)-(y^(2))/( 9)=1 then reflected ray goes along the line

The solution of the differential equation (dy)/(dx) = sin (x +y) tan (x + y) -1 is

Form a quadratic equation with rational coefficients if one of its root is cot^(2)18^(@).

A normal to the parabola at a point A on the parabola whose equation is y^(2)=2013x cuts the axis of x at N. AN is produced to the point B such that NB=1/2AN. If C is a point on the parabola y^(2)=2013x such that OCN=pi/2 (O being origin), then projection of CN on x-axis is equal to

A noraml to the parabola at a point A on the parabola whose equation is y^(2)=2013x cuts the axis of x at N. AN is produced to the point B such that NB=1/2AN. If two more normals to the parabola y^(2)=2013x pass through B, then they are

Prove that the function f given by f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi).

Find all possible values of (i) sqrt(|x|-2) (ii) sqrt(3-|x-1|) (iii) Sqrt(4-sqrt^2))

Using the proprties of determinants in Exercise 7 to 9, prove that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

((2007)!)/((2007))is an integer & n in N, then find maximum value of n.

Find the area (in sq. unit) bounded by the curves : y = e^(x), y = e^(-x) and the straight line x =1.

S=sum_(r=1)^(4)tan^(2)(2r-1)(pi)/(16) is an integer divisible by

Find the quadrants of the coordinate planes such that for each point (x,y) on these quadrants ( wherex ne 0 , y ne 0) , the equation,(sin^(4) theta )/x + ( cos^4 theta)/( y)=(1)/(x+y)is soluble fortheta.

Statement-1 : if P and D be the ends of conjugate diameters then the locus of mid-point of PD is a circle. and STATEMENT-2 : if P and D be the ends of conjugate diameter, then the locus of intersection of tangents at P and D is an ellipse.

Which of the following numbers is NOT prime? (Hind : avoid actually computing these numbers.)

Write tan^(-1)(sqrt((1-cosx)/(1+cosx))), 0 lt x lt pi in the simplest form.

Express the following differential equations in the form (dy)/(dx) = F((y)/(x)). (i) xdy - ydx = sqrt(x^(2) + y^(2))dx (ii) [x - y Tan^(-1)((y)/(x))] dx + x Tan^(-1)((y)/(x)) dy = 0 (iii) xdy = y(log y - log x+1)dx

Each of five questions on a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. If the random variable X is the number of questions answered correctly, the probability that the student will get at most three answers correct is

Use following sequence, A_n = 3 - 8n What is A_(11) - A_(9) ?

Differentiate the functions sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))

Sum to n terms the series 4 + 14 + 30 + 52+ 82+ 114+.........

If a function f:CtoC is defined by f(x)=3x^(2)-1, where C is theset of complex numbers, then the pre-images of -28 are

Let veca = hati + hatj + hatk, vecb = hati - ahtj + hatk and hati - hatj - hatkbe three vectors. A vector vecv in the plane of veca and vecb, whose projection on vecc is (1)/(sqrt3), is given by :