14949 + Interview Questions in Maths in Class 11 Page 186 InterviewSolution

9251.	if f(x) =x/sqrt(1-x^(2)), then (fofof)(x)=
Answer» `(X)/(SQRT(1+3x^(2)))` `(x)/(sqrt(1-x^(2)))` `(2X)/(sqrt(1+2x^(2)))` `(x)/(sqrt(1+x^(2)))` ANSWER :A

Discussion

9252.	If sin beta=sin(2alpha+beta), then tan(alpha+beta)-2tan alpha is
Answer» INDEPENDENT of `ALPHA` independent of `beta` dependent of both `alpha` and `beta` independent of both `alpha` and `beta` ANSWER :A::B::D

Discussion

9253.	Solve -8 le 5x-3 lt 7.
Answer» Answer :We have `-8 le 5X -3 lt7` or `-5 le 5x LT 10` or `-1 le x lt 2`

Discussion

9254.	Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1,3,4):}]
Answer» ANSWER :`:.A^(-1)-("ADJ A")/("det A")-[(7,-3,-3),(-1,1,0),(-1,0,1)]`

Discussion

9255.	Find the mean deviation about the mean of the distributon .
Answer» Solution : Now`M_(e)=(20+1/(2)) th item =(21/2)=10.5 th item` `thereforeM_(e)=12 ` `thereforeMD=(Sigmaf_(i)d_(i))/(SIGMA f_(i))=(25)/(20)=1.25`

Discussion

9256.	Find the mean deviation about the mean of the distributon .
Answer» Solution : NOW,`BARX=(Sigmaf_(i)x_(i))/(SIGMA f_(i))=(433)/(20)=21.65` `MD=(Sigma f_(i)\|x_(i)-barx\|)/(Sigma f_(i))=(25)/(20)=1.25 `

Discussion

9257.	Sum up 3+5+11 +29 + .... To n terms .
Answer» ANSWER :`(3n-1)/(2)+2N`

Discussion

9258.	Find the mean deviation about the mean for the data in {:("x"_(i),10,30,50,70,90),("f"_(i),4,24,28,16,8):}
Answer» ANSWER :16

Discussion

9259.	Evaluate the following limits in Exercises lim_(xto0)(sin (ax))/(()bx)
Answer» ANSWER :`(a)/(B)`

Discussion

9260.	The point (4, 1) undergoes the following two successive transformations : (i) Reflection about the line y = x (ii) Translation through a distance 2 units along the positive X -axis Then the final coordinates of the point are
Answer» `(4,3)` `(3,4)` `(1,4)` `((7)/(2) , (7)/(2))` ANSWER :B

Discussion

9261.	Write the first five terms of the sequences in obtain the corresponding series: a_(1)= 2, a_(n)= a_(n-1) + 3, AA n ge 2
Answer» ANSWER :2,5,8,11,14 SERIES: `2+5+ 8+ 11+ 14+`……

Discussion

9262.	If sin x+sin^(2)x+sin^(3)x=1 then cos^(6)x-4cos^(4)x+8 cos^(2)x=
Answer» 1 2 3 4 Answer :D

Discussion

9263.	For what values (s) of a will the two points (1,a,1) and (-3,0,a) lie on opposite sides of the plane 3x + 4y - 12z + 13=0 ?
Answer» `a LT -1 or a GT 1//3` `a =0` only `0 lt a lt 1` ` -1 lt a lt 1` ANSWER :A

Discussion

9264.	Calculate the length of the perpendicular from (7, 0) to the straight line 5x+12y-9=0 and show that it is twice the length of the perpendicular from (2, 1).
Answer» ANSWER :2 UNITS

Discussion

9265.	underset (x to (pi)/(4))(Lt) (1-cot^(3)x)/(2-cotx-cot^(3)x)=
Answer» `(11)/(4)` `(3)/(4)` `(1)/(2)` 0 Answer :B

Discussion

9266.	Equation of parabola with focus (-3, 0) and directrix x + 5 = 0 is …….
Answer» `X^(2) = 4(y + 4)` `x^(2) = 4 (y - 4)` `y^(2) = 4(x + 4)` `y^(2) = 4(x-4)` ANSWER :C

Discussion

9267.	Examine whether or not there is any term containing x^(9) in the expansion of (2x^(2) - (1)/(x))^(20)
Answer» ANSWER :No such TERM EXISTS.

Discussion

9268.	Using binomial theorem ,Evaluateeach of the following (101)^(4)
Answer» ANSWER :`104060401`

Discussion

9269.	Four cards are drawn from a full pack of cards . Find the probability thatthere are two spades and two hearts,
Answer» ANSWER :`=(468)/(20825)`.

Discussion

9270.	Find the n^(th) term and 12^(th) term of the sequence 6, 18, 54 ……
Answer» ANSWER :`2(3)^(12); (-1)^(n) 6(3)^(n-1)`

Discussion

9271.	(a ) /( b^(2) - c^(2)) + ( c)/( b^(2) - a^(2)) = 0then B =
Answer» ` (pi )/(2) ` ` (pi )/(4)` ` ( 2pi )/( 3) ` ` (pi )/(3) ` ANSWER :D

Discussion

9272.	Find the component statements of the following compound statements: The number 100 is divisible by 3,11 and 5.
Answer» ANSWER :DIVISIBLE 3,11,5

Discussion

9273.	If f(x)= {(ax^(2)-b,-1
Answer» `a=1/2, b=-3/2` `a=-1/2, b=3/2` `a=-1/2, b=-3/2` `a=1/2, b=3/2` ANSWER :C

Discussion

9274.	A and B are two mutually exclusive events of an experiment: If P(not A) = 0.65, P(A cup B) = 0.65and P(B) = p, then the value of p is
Answer» ANSWER :p=0.30

Discussion

9275.	If two sides of a triangle are 3 feet and 12 feet and included angle is 150^(@) then the area of the triangle in square feet is a
Answer» 36 24 72 9 Answer :D

Discussion

9276.	Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (i) x-sqrt(3) y+8=0
Answer» Answer :`(i)X cos 120^(@) + y sin 120^(@) = 4, 4 , 120^(@) (ii) x cos 90^(@) + y sin 90^(@) = 2,2, 90^(@) ; ` (III) ` x cos 315^(@) + y sin 315^(@) = 2 sqrt2 , 2 sqrt2 , 315^(@)`.

Discussion

9277.	Differentiate from first principles: 8. x+ (1)/( x)
Answer» ANSWER :`1- (1)/( x^2)`

Discussion

9278.	Find the maximum value of 1+sin(pi/4+theta) + 2cos(pi/4-theta).
Answer» 1 2 3 4 Solution :We have , `1+sin(pi/4+theta)+2cos(pi/4-theta)` `=1+1/sqrt(2)(costheta+sintheta) + sqrt(2)(costheta+sintheta) = 1+1/sqrt(2(+sqrt(2))(costheta+sintheta)` `=1+(1/sqrt(2)+sqrt(2)).sqrtcos(theta-pi/4)` `therefore` maximum VALUE`=1+(1/sqrt(2)+sqrt(2)).sqrt(2)=4`

Discussion

9279.	Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0. When roots are x_(1),x_(2) and x_(3). Number of values of theta in [0,2pi] for which at least two roots are equal
Answer» 3 4 5 6 Answer :C

Discussion

9280.	Find Lt_(xto0)(tanax-tanbx)/x.
Answer» ANSWER :a-b

Discussion

9281.	(cos A - cos 3A)/(cos A) + (sin A + sin 3A)/(sin A)=
Answer» 1 2 3 4 Answer :D

Discussion

9282.	If 15ltxlt30then f(x)=\|x-15\|+\|x-30\| is
Answer» Increasing Decreasing Constant cannot be estimated Answer :C

Discussion

9283.	If sqrt(2)cos A = cos B + cos^(3)B, and sqrt(2)sin A = sin B- sin^(3)B then sin(A-B)=
Answer» `+- 1` `+- (1)/(2)` `+- (1)/(3)` `+- (1)/(4)` ANSWER :C

Discussion

9284.	If G is the centroid of DeltaABC then bar(GA)+bar(GB)+bar(GC)=
Answer» `BAR(0)` `bar(OG)` `2BAR(OG)` `3bar(OG)` Answer :A

Discussion

9285.	Find the equation of pair of bisectors of the angles between the pair of lines. 3x^(2)+xy-2y^(2)=0
Answer» ANSWER :`X^(2)-10xy-y^(2)=0`

Discussion

9286.	If A is any event of sample space S then P(A)in[0,1].
Answer» ANSWER :TRUE STATEMENT

Discussion

9287.	Statement 1 : f(x)=cos(x^(2)-tan x) is a non-periodic function. Statements 2 : x^(2)-tan x is a non-periodic function .
Answer» STATEMENT 1 is true, statement 2 is true, statement 2 ISCORRECT EXPLANATION for statement 1. Statement 1 is true, statement 2 is true, statement 2 is notcorrect explanation for statement 1. Statement1 is false, but statement 2 is true Statement 1 is true, but statement 2 is false Answer :B

Discussion

9288.	Examine the continuity of the following : x + sinx
Answer» Answer :` F(x) = x + sin x ` is CONTINUOUS for all ` x in RR ` .

Discussion

9289.	What is the relationship of each resulting condition inverse , contatpositive , inverse to the original conditional (p)impliesq ?
Answer»

Discussion

9290.	For non null sets A and B if n(AcupB) = 36 ,n(A - B )= 15 and n(AcapB) = 16then n(B) = ….. .
Answer» ANSWER :21

Discussion

9291.	There are 60 students in a class . The following is the frequency distribution of the marks obtained by the student in a test.Where x is a positive integer. Determine the mean and standard deviation of the marks.
Answer» ANSWER :1.12

Discussion

9292.	Let f (x) be an odd function for continuous at x in R If f(x) is continuous at x = a, prove that it is continous at x=-a
Answer» ANSWER :`-a`

Discussion

9293.	Let (f(x+y)-f(x))/2 = (f(y)-a)/2+xy for all real x and y . If f(x) is differentiable and f'(0) exists for all real permissible values of a and is equal to sqrt(5a-1-a^2) then f(x) is
Answer» POSITIVE for all real X negative for all real x f(x) = 0 has real ROOTS cannot say ANYTHING about the sign of f(x) Answer :A

Discussion

9294.	Aspherical ballon is being inflated at the rate of 35cc/min. The rate of increases in the surface area ("in" cm^(2) "min") of the ballon when its diameter is 14 cm, is :
Answer» 10 `SQRT(10)` 100 `10sqrt(10)` ANSWER :A

Discussion

9295.	If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?
Answer» ANSWER :30

Discussion

9296.	If y=2+\|x\| -\|x\| -\|x-1\|-\|x+1\|, then y'(-1/2)+y'(3/2) +y'(5/2)=
Answer» 0 1 `-1` `-2` ANSWER :D

Discussion

9297.	If \|A\|!=0 and (A-2I) (A-3I) = 0 then A^(-1)=
Answer» `(A-5I)/(6)` `(5I-A)/(5)` `(5A-I)/(6)` `(5I-A)/(6)` ANSWER :D

Discussion

9298.	Derive the equation fo the locus of a point twice as far from (-2,3,4)as from (3, -1, -2).
Answer» Answer :`3X ^(2) + 3y ^(2) + 3Z ^(2)- 14 yy + 24 z + 27 =0`

Discussion

9299.	Solve the following equations: x^(2)+4ix-4=0
Answer» ANSWER :`-2I`

Discussion

9300.	Find the square roots of the following : 6 sqrt(2)i-7
Answer» ANSWER :`+-(SQRT(2)-3I)`

Discussion

Explore topic-wise InterviewSolutions in .

if f(x) =x/sqrt(1-x^(2)), then (fofof)(x)=

If sin beta=sin(2alpha+beta), then tan(alpha+beta)-2tan alpha is

Solve -8 le 5x-3 lt 7.

Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1,3,4):}]

Find the mean deviation about the mean of the distributon .

Find the mean deviation about the mean of the distributon .

Sum up 3+5+11 +29 + .... To n terms .

Find the mean deviation about the mean for the data in {:("x"_(i),10,30,50,70,90),("f"_(i),4,24,28,16,8):}

Evaluate the following limits in Exercises lim_(xto0)(sin (ax))/(()bx)

The point (4, 1) undergoes the following two successive transformations : (i) Reflection about the line y = x (ii) Translation through a distance 2 units along the positive X -axis Then the final coordinates of the point are

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= 2, a_(n)= a_(n-1) + 3, AA n ge 2

If sin x+sin^(2)x+sin^(3)x=1 then cos^(6)x-4cos^(4)x+8 cos^(2)x=

For what values (s) of a will the two points (1,a,1) and (-3,0,a) lie on opposite sides of the plane 3x + 4y - 12z + 13=0 ?

Calculate the length of the perpendicular from (7, 0) to the straight line 5x+12y-9=0 and show that it is twice the length of the perpendicular from (2, 1).

underset (x to (pi)/(4))(Lt) (1-cot^(3)x)/(2-cotx-cot^(3)x)=

Equation of parabola with focus (-3, 0) and directrix x + 5 = 0 is …….

Examine whether or not there is any term containing x^(9) in the expansion of (2x^(2) - (1)/(x))^(20)

Using binomial theorem ,Evaluateeach of the following (101)^(4)

Four cards are drawn from a full pack of cards . Find the probability thatthere are two spades and two hearts,

Find the n^(th) term and 12^(th) term of the sequence 6, 18, 54 ……

(a ) /( b^(2) - c^(2)) + ( c)/( b^(2) - a^(2)) = 0then B =

Find the component statements of the following compound statements: The number 100 is divisible by 3,11 and 5.

If f(x)= {(ax^(2)-b,-1

A and B are two mutually exclusive events of an experiment: If P(not A) = 0.65, P(A cup B) = 0.65and P(B) = p, then the value of p is

If two sides of a triangle are 3 feet and 12 feet and included angle is 150^(@) then the area of the triangle in square feet is a

Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (i) x-sqrt(3) y+8=0

Differentiate from first principles: 8. x+ (1)/( x)

Find the maximum value of 1+sin(pi/4+theta) + 2cos(pi/4-theta).

Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0. When roots are x_(1),x_(2) and x_(3). Number of values of theta in [0,2pi] for which at least two roots are equal

Find Lt_(xto0)(tanax-tanbx)/x.

(cos A - cos 3A)/(cos A) + (sin A + sin 3A)/(sin A)=

If 15ltxlt30then f(x)=|x-15|+|x-30| is

If sqrt(2)cos A = cos B + cos^(3)B, and sqrt(2)sin A = sin B- sin^(3)B then sin(A-B)=

If G is the centroid of DeltaABC then bar(GA)+bar(GB)+bar(GC)=

Find the equation of pair of bisectors of the angles between the pair of lines. 3x^(2)+xy-2y^(2)=0

If A is any event of sample space S then P(A)in[0,1].

Statement 1 : f(x)=cos(x^(2)-tan x) is a non-periodic function. Statements 2 : x^(2)-tan x is a non-periodic function .

Examine the continuity of the following : x + sinx

What is the relationship of each resulting condition inverse , contatpositive , inverse to the original conditional (p)impliesq ?

For non null sets A and B if n(AcupB) = 36 ,n(A - B )= 15 and n(AcapB) = 16then n(B) = ….. .

There are 60 students in a class . The following is the frequency distribution of the marks obtained by the student in a test.Where x is a positive integer. Determine the mean and standard deviation of the marks.

Let f (x) be an odd function for continuous at x in R If f(x) is continuous at x = a, prove that it is continous at x=-a

Let (f(x+y)-f(x))/2 = (f(y)-a)/2+xy for all real x and y . If f(x) is differentiable and f'(0) exists for all real permissible values of a and is equal to sqrt(5a-1-a^2) then f(x) is

Aspherical ballon is being inflated at the rate of 35cc/min. The rate of increases in the surface area ("in" cm^(2) "min") of the ballon when its diameter is 14 cm, is :

If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

If y=2+|x| -|x| -|x-1|-|x+1|, then y'(-1/2)+y'(3/2) +y'(5/2)=

If |A|!=0 and (A-2I) (A-3I) = 0 then A^(-1)=

Derive the equation fo the locus of a point twice as far from (-2,3,4)as from (3, -1, -2).

Solve the following equations: x^(2)+4ix-4=0

Find the square roots of the following : 6 sqrt(2)i-7