14949 + Interview Questions in Maths in Class 11 Page 272 InterviewSolution

13551.	If A=[(1,2),(3,4)],B=[(3,8),(7,2)] and 2X+A=B then find X.
Answer» ANSWER :`[(1,3),(2,-1)]`

Discussion

13552.	Assertion (A): tantheta+2tan2theta+4tan4theta+8tan8theta+16cot16theta=cottheta Reason (R ): cottheta-tantheta=2 cot2theta
Answer» A is true, R is true and R is CORRECT explanation of A A is true, R is true and R is not correct explanation of A A is true, R is FALSE A is false, R is true Answer :A

Discussion

13553.	Translate the following statements into symbolic form: x and y are even integers.
Answer» ANSWER :`p^^q:X` and y are EVEN INTEGERS.

Discussion

13554.	Find the modulus and the arguments of the following complex numbers : (1+2i)/(1-3i)
Answer» Answer :Modulus `=(1)/(SQRT(2))` Argument `=(3PI)/(4)`

Discussion

13555.	If alpha and beta are the roots of the equation 2x^(2)-3x+1=0, form the equation whose roots are (alpha)/(2beta+3) and (beta)/(2alpha+3).
Answer» ANSWER :`40X^(2)-14+1=0`.

Discussion

13556.	Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 - 24 i.
Answer» ANSWER :x=3, y`=-3`

Discussion

13557.	There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C_(1), 50 to chemical C_(2), and 30 to both the chemicals C_(1) and C_(2). Find the number of individuals exposed to (i) Chemical C_(1) but not chemical C_(2) (ii) Chemical C_(2) but not chemical C_(1) (iii) Chemical C_(1) or chemical C_(2)
Answer» ANSWER :90, 20, 140

Discussion

13558.	Let f : R to R satisfy f (x) (2) =4, then f ((1)/(2))=
Answer» 0 `1/4` `1/2` 1` ANSWER :B

Discussion

13559.	If (x-a) cos theta + y sin theta = (x - a) cos phi + y sin phi = a and tan (theta/2)-tan(phi/2) = 2b then
Answer» `y^(2) = 2ax - (1-b^(2))X^(2)` `"TAN" (THETA)/(2) = (1)/(x) (y + bx)` `y^(2) = 2bx - (1 - a^(2))x^(2)` `"tan" (PHI)/(2) = (1)/(x) (y - bx)` Answer :A::B::D

Discussion

13560.	Evaluate the following limits: Lim_( x to pi/2 ) (cos x)/(pi/2-x)
Answer» ANSWER :1

Discussion

13561.	Find equation of line whose sum and product of intercepts on axis are 7 and 12 respectively.
Answer» ANSWER :`3X + 4y = 12, 4x + 3Y = 12`

Discussion

13562.	If DeltaABC, if "cos"(A)/(2)= sqrt((b+c)/(2c)) then
Answer» area of triangle is `(1)/(2)ab` circumradius is EQUAL to `(1)/(2)c` area of triangle is `(1)/(2)BC` circumradius is equal to `(1)/(2)a` ANSWER :A::B

Discussion

13563.	Construct truth tables for the following : (p implies q)^^(qimpliesp)
Answer» <P> Answer :`(##SCH_OPM_ISC_MAT_XI_C27_E06_017_A01##)` [RECALL that p => q is false only when p is TRUE and q is false ]

Discussion

13564.	Find dy/dx ify^(2)= 4ax.
Answer» ANSWER :`dy/dx = 2a/y`

Discussion

13565.	Using slopes determine which of the following sets of three points are collinear.(i) (5, -2), (7, 6), (0, -2)(ii)(-2, 3), (8, -5), (5 4)
Answer» (5, -2), (7, 6), (0, -2) (-2, 3), (8, -5), (5 4) (6, -1), (5, 0), (2, 3)

Discussion

13566.	If a function f(x)=(ax+b)/(cx+d) is such that (f@f)(x)=x, then
Answer» `d=-a` `d=a` `a=b=1` `a=b=c=d=1` ANSWER :A

Discussion

13567.	Draw the graphs of the following : y = x -[x] in[ 0,3]
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_022_A01##)`

Discussion

13568.	P(n) : 2n + 1, for n = …………it is not a prime number.
Answer» 1 2 3 4 Answer :D

Discussion

13569.	Let g(x) = {{:((x^2 + x "tan" x - x "tan" 2x)/(ax + tan x - tan 3x"),x != 0),(0,x = 0):}. If g'(0) exists and is equal to nonzero value b, then 52 b/a is equal to ………
Answer»

Discussion

13570.	If y= log((x)/(a + bx))^(x) then x^3 (d^2y)/(dx^3) =
Answer» `(X(DY)/(DX) - y)^2` `(x (dx)/(dy) - x)^2` `(x (dy)/(dx) + y)^2` `(x(dx)/(dy) - y)^2` ANSWER :A

Discussion

13571.	In what ratio, the line joining (-1, 1) and (5,7) is divided by the line x+y=4 ?
Answer» ANSWER :`1 : 2`

Discussion

13572.	The value of (tan3x)/(tanx) do not lie between …………
Answer» `-(1)/(3)and0` `(1)/(3)AND3` `-(1)/(3)and(1)/(3)` `-3and3` ANSWER :B

Discussion

13573.	Find the product of lengths of perpendiculars drawn from (2, 1) upon the lines 12x^(2)+25xy+12y^(2)+10x+11y+2=0
Answer» ANSWER :`(2)/(5)`

Discussion

13574.	Find the vertex, focus and directix of the parabola (x-h)^(2)+4a(y-k)=0.
Answer» ANSWER :`(H,K),(h,k-a),y=a+k`

Discussion

13575.	Solve the following equations sqrt(3) Sin theta - Cos theta = sqrt(2)
Answer» ANSWER :`2NPI+(PI)/(3),NINZ`

Discussion

13576.	If the standard deviation of variable x is 4 and y = (3x + 7)/(4) then the standard deviation of variable y is
Answer» ANSWER :3

Discussion

13577.	The remainder left out when 8^(2n) -( 62)^( 2n+1) is divided by 9 is
Answer» 2 7 8 0 Answer :A

Discussion

13578.	Find sqrt(x^(4)+4)-sqrt(x^(2)-4) when x is large.
Answer» ANSWER :`4/x`

Discussion

13579.	In DeltaABC , " find " b cos ^(2).(C)/(2)+c cos^(2).(B)/(2)
Answer» ` s ` ` 2S` ` 3S` ` 4S ` ANSWER :A

Discussion

13580.	Assertion (A) : f(x) sinx is continuous on R . Reason (R): f(x) = sinx is defindAA x in R. The correct answer is
Answer» Both (A) and (R) are true and (R)is the correct EXPLANATION of (A) Both (A) and (R)are true and (R)is not the correct explanation of (A) (A) is true but (R) is FALSE (A) is false but (R) is ture ANSWER :A

Discussion

13581.	Find the derivative of x^(5)(3-6x^(-9))
Answer» ANSWER :`15X^(4)+(24)/(X^(5))`

Discussion

13582.	theta_(1),theta_(2)in[0,2pi]andtheta_(1) and theta_(2) satisfy the equation tantheta=1 then tan((theta_(1))/(2)).tan((theta_(2))/(2))= ………….
Answer» 0 `-1` 2 1 Answer :B

Discussion

13583.	If the line y=mx, meets the lines x+2y=1 and 2x-y+3=0 at one point only then m=?
Answer» `1` `-1` `-2` NONE of these Answer :B

Discussion

13584.	Find the angle between the pair of straight lines given by
Answer» ANSWER :`60^@`

Discussion

13585.	The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations
Answer» ANSWER :24, 12

Discussion

13586.	If a, b, c are the sides ofDeltaABC, inscribed in a given circle, then (deltaa)/(CosA)+(deltab)/(CosB)+(deltac)/(CosC)=
Answer» 0 1 `PI` `2PI` ANSWER :A

Discussion

13587.	Find the confficient of x^5 in the product (1+2x)^6 (1-x)^7 using binomial theoram.
Answer» ANSWER :171

Discussion

13588.	For any two sets A and B, prove that : (i) (A-B)=A Delta(A capB) (ii) Lambda cap(Lamda capB)'=phi (iii) A - (A-B)=A capB (iv) A cap (A' cup B) = A cap B.
Answer»

Discussion

13589.	Solve sin 3x + sin x + 2 cos x = sin 2x + 2 cos^(2)x
Answer» Answer :`(2n+1)(PI)/(2),NPI-(pi)/(4),2npi+(pi)/(2),2npi`

Discussion

13590.	Lim_(x to pi/2) (1-sin x)/((pi/2-x)^(2))
Answer» ANSWER :`1/8`

Discussion

13591.	Two thirds of students in a class are boys and rest girls.It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
Answer» ANSWER :`.75`

Discussion

13592.	Find the value of 'c' so that 2x - y + c=0 may touch the ellipse x ^(2) + y ^(2) = 2.
Answer» ANSWER :`C = PM 3`

Discussion

13593.	Number of solutions of equationn sin^(2)theta- 4/(sin^(3)theta-1)=1-4/(sin^(3)theta-1), theta in [0,6pi]
Answer» 2 4 6 8 Answer :C

Discussion

13594.	Evaluate the following limits : Lim_(x to oo) 2x(sqrt(x^(2)+1)-x)
Answer» ANSWER :1

Discussion

13595.	The constant c of Lagrange's mean value theorem for f(x) =2 sin x+ sin 2x "in" [0,pi] is
Answer» `(pi )/( 6)` `( pi )/( 2)` `(pi )/( 3)` `pi` ANSWER :C

Discussion

13596.	Which of the following are sets ? Justify your answer. The collection of all the months of a year beginning with the letter J.
Answer» ANSWER :it is a SET

Discussion

13597.	There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a women?
Answer» ANSWER :`3/5`

Discussion

13598.	Prove that cos. (pi)/(11). cos . (2 pi)/(11). cos . (3 pi)/(11) cos. (4 pi)/(11). cos . (5 pi)/(11)=(1)/(32)
Answer» `1/4` `1/8` `1/16` `1/32` ANSWER :D

Discussion

13599.	If r_(1)^(2)=r_1r_(2)+r_(2)r_(3)+r_(3)r_(1) then the triangle is
Answer» `60^(@)` `90^(@)` `30^(@)` `120^(@)` Answer :B

Discussion

13600.	Evaluate underset(xrarr0)lim((1-cosx)/(x)) ?
Answer» ANSWER :`UNDERSET(x->0)"LT" =0`

Discussion

Explore topic-wise InterviewSolutions in .

If A=[(1,2),(3,4)],B=[(3,8),(7,2)] and 2X+A=B then find X.

Assertion (A): tantheta+2tan2theta+4tan4theta+8tan8theta+16cot16theta=cottheta Reason (R ): cottheta-tantheta=2 cot2theta

Translate the following statements into symbolic form: x and y are even integers.

Find the modulus and the arguments of the following complex numbers : (1+2i)/(1-3i)

If alpha and beta are the roots of the equation 2x^(2)-3x+1=0, form the equation whose roots are (alpha)/(2beta+3) and (beta)/(2alpha+3).

Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 - 24 i.

Let f : R to R satisfy f (x) (2) =4, then f ((1)/(2))=

If (x-a) cos theta + y sin theta = (x - a) cos phi + y sin phi = a and tan (theta/2)-tan(phi/2) = 2b then

Evaluate the following limits: Lim_( x to pi/2 ) (cos x)/(pi/2-x)

Find equation of line whose sum and product of intercepts on axis are 7 and 12 respectively.

If DeltaABC, if "cos"(A)/(2)= sqrt((b+c)/(2c)) then

Construct truth tables for the following : (p implies q)^^(qimpliesp)

Find dy/dx ify^(2)= 4ax.

Using slopes determine which of the following sets of three points are collinear.(i) (5, -2), (7, 6), (0, -2)(ii)(-2, 3), (8, -5), (5 4)

If a function f(x)=(ax+b)/(cx+d) is such that (f@f)(x)=x, then

Draw the graphs of the following : y = x -[x] in[ 0,3]

P(n) : 2n + 1, for n = …………it is not a prime number.

Let g(x) = {{:((x^2 + x "tan" x - x "tan" 2x)/(ax + tan x - tan 3x"),x != 0),(0,x = 0):}. If g'(0) exists and is equal to nonzero value b, then 52 b/a is equal to ………

If y= log((x)/(a + bx))^(x) then x^3 (d^2y)/(dx^3) =

In what ratio, the line joining (-1, 1) and (5,7) is divided by the line x+y=4 ?

The value of (tan3x)/(tanx) do not lie between …………

Find the product of lengths of perpendiculars drawn from (2, 1) upon the lines 12x^(2)+25xy+12y^(2)+10x+11y+2=0

Find the vertex, focus and directix of the parabola (x-h)^(2)+4a(y-k)=0.

Solve the following equations sqrt(3) Sin theta - Cos theta = sqrt(2)

If the standard deviation of variable x is 4 and y = (3x + 7)/(4) then the standard deviation of variable y is

The remainder left out when 8^(2n) -( 62)^( 2n+1) is divided by 9 is

Find sqrt(x^(4)+4)-sqrt(x^(2)-4) when x is large.

In DeltaABC , " find " b cos ^(2).(C)/(2)+c cos^(2).(B)/(2)

Assertion (A) : f(x) sinx is continuous on R . Reason (R): f(x) = sinx is defindAA x in R. The correct answer is

Find the derivative of x^(5)(3-6x^(-9))

theta_(1),theta_(2)in[0,2pi]andtheta_(1) and theta_(2) satisfy the equation tantheta=1 then tan((theta_(1))/(2)).tan((theta_(2))/(2))= ………….

If the line y=mx, meets the lines x+2y=1 and 2x-y+3=0 at one point only then m=?

Find the angle between the pair of straight lines given by

The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations

If a, b, c are the sides ofDeltaABC, inscribed in a given circle, then (deltaa)/(CosA)+(deltab)/(CosB)+(deltac)/(CosC)=

Find the confficient of x^5 in the product (1+2x)^6 (1-x)^7 using binomial theoram.

For any two sets A and B, prove that : (i) (A-B)=A Delta(A capB) (ii) Lambda cap(Lamda capB)'=phi (iii) A - (A-B)=A capB (iv) A cap (A' cup B) = A cap B.

Solve sin 3x + sin x + 2 cos x = sin 2x + 2 cos^(2)x

Lim_(x to pi/2) (1-sin x)/((pi/2-x)^(2))

Two thirds of students in a class are boys and rest girls.It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

Find the value of 'c' so that 2x - y + c=0 may touch the ellipse x ^(2) + y ^(2) = 2.

Number of solutions of equationn sin^(2)theta- 4/(sin^(3)theta-1)=1-4/(sin^(3)theta-1), theta in [0,6pi]

Evaluate the following limits : Lim_(x to oo) 2x(sqrt(x^(2)+1)-x)

The constant c of Lagrange's mean value theorem for f(x) =2 sin x+ sin 2x "in" [0,pi] is

Which of the following are sets ? Justify your answer. The collection of all the months of a year beginning with the letter J.

There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a women?

Prove that cos. (pi)/(11). cos . (2 pi)/(11). cos . (3 pi)/(11) cos. (4 pi)/(11). cos . (5 pi)/(11)=(1)/(32)

If r_(1)^(2)=r_1r_(2)+r_(2)r_(3)+r_(3)r_(1) then the triangle is

Evaluate underset(xrarr0)lim((1-cosx)/(x)) ?