14949 + Interview Questions in Maths in Class 11 Page 129 InterviewSolution

6401.	Write the first six terms of the sequences given by(i)a_(1)=a_(2)=1, a_(n)=a_(n-1)+a_(n-2)(n ge 3)(ii)a_(1)=4, a_(n+1)=2na_(n)
Answer» ANSWER :(i) 1, 1, 2, 3, 5, 8 (ii) = 15360

Discussion

6402.	The possible values of a such that the equation x^(2)+2ax+a= sqrt(a^(2)+x -(1)/(16))-(1)/(16), x ge -a, has two distinct real root are given by
Answer» [01] `(-OO, 0]` `[0, oo)` `(3/4, oo)` ANSWER :D

Discussion

6403.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 5. . .A
Answer» ANSWER :`in`

Discussion

6404.	A cubic function of x has maximum 10 and minimum -5/2, when x = -3 and x = 2 respectively. Find the function.
Answer» Answer :`(1)/(5)x^(3) + (3)/(10)x^(2) - (18)/(5)x + (19)/(10)`

Discussion

6405.	If A={1,3,5,6}, the number of elements in P{P(A)} is
Answer» A. `2^(4)` B. `2^(16)` C. `4` `D. 16` ANSWER :B

Discussion

6406.	Value of 'K' so that equation 16x^2+24xy+ly^2+kx--12y-21=0. Represents a pair of parallel lines is
Answer» `PM3` `pm4` -16 `PM25` Answer :C

Discussion

6407.	Without using tables, give the valueof the following : "sec"(15pi)/(4)
Answer» ANSWER :`SQRT(2)`

Discussion

6408.	If A=580^(0) then -sqrt(1+sinA)-sqrt(1-sinA)=
Answer» `2"COS"(A)/(2)` `2"SIN"(A)/(2)` `-2 "cos"(A)/(2)` `-2 "sin"(A)/(2)` ANSWER :B

Discussion

6409.	The equation of the pair of perpendicular lines passing through origin and forming an isosceles triangle with the line 2x+3y=6, is
Answer» 2 `(36)/(13)` 3 `(36)/(sqrt(13))` ANSWER :B

Discussion

6410.	Leta gt 2be a constant . If there are just 18 positive integers satisfying the inequality (x- a) ( x-2a) (x-a^(2))lt 2then the value of a is …………
Answer» ANSWER :5

Discussion

6411.	Four digit numbers are formed from the digits = [4 = 24 2, 5,6, 7, 8 (without repetition of digits).Q How many of there are exactly divisible by 7.
Answer» ANSWER :24

Discussion

6412.	Four digit numbers are formed from the digits = [4 = 24 2, 5,6, 7, 8 (without repetition of digits).Q How many of there are odd.
Answer» ANSWER :48

Discussion

6413.	Consider the points A (1,-1,3), B(2,-4,5) and C(5,-13,11).Find AB, BC and AC
Answer» SOLUTION :`SQRT14, root(3)(14), root(4)(14)`

Discussion

6414.	The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and vec(d) are two vectors satisfying vec(b) xx vec(c )= vec(b) xx vec(d) and vec(a).vec(d)= 0. Then the vector vec(d) is equal to
Answer» `VEC(B)+ ((vec(b).vec(C ))/(vec(a).vec(b))) vec(c )` `vec(b) + ((vec(b).vec(c ))/(vec(a).vec(b))) vec(c )` `vec(b)- ((vec(b).vec(c ))/(vec(a).vec(b))) vec(c )` `vec(c )-((vec(a).vec(c ))/(vec(a).vec(b))) vec(b)` ANSWER :D

Discussion

6415.	If (x+iy)^(3) = u + iy, then show that u/x + v/y = 4(x^(2)-y^(2))
Answer» ANSWER :`4(X^(2)-y^(2))`

Discussion

6416.	If "tan" (x)/(2) cot h ((x)/(2)) = 1 then cos x cos hx =
Answer» 1 2 0 -1 Answer :A

Discussion

6417.	If Lt_(ntooo)a_(n)=l" where "a_(n+1)=sqrt(2+a_(n)),n = 1,2,3...., find the value of l.
Answer» ANSWER :2

Discussion

6418.	The numbers of bacteria increases at the rate of 4% every hour. If there were 40 beacteria present originally, then how many bacteria will be present at the end of 4^(th) hour ? How many bacteria will be there in 4^(th) hour?
Answer» ANSWER :170, 45

Discussion

6419.	Series (1)/(log_(2)^(2)) + (1)/(log_(4)^(4)) + (1)/(log_(8)^(4)) + …..+ (1)/(log_(2^(n))4)=……….
Answer» `(n(n+1))/(2)` `(n(n+1)(2n+1))/(12)` `(n(n+1))/(4)` NONE of these Answer :C

Discussion

6420.	If f(x) = cos (log_(e) x), then f(x)f(y) -1/2[f(x/y) + f(xy)] has value
Answer» -1 `1//2` -2 0 Answer :D

Discussion

6421.	Find equaiton of hyperbola satisfying given conditons Foci of hyperbola will be foci of eppipse (x^(2))/(25) + (y^(2))/(9) = 1 having eccentricity 2.
Answer» ANSWER :`(X^(2))/(4) - (y^(2))/(12) = 12`

Discussion

6422.	In Delta ABC, if cos^2 A+ cos^2 B+cos^2 C=1, then the triangle is
Answer» equilateral ISOCELES RIGHT ANGLED right angled ISOSCELES Answer :C

Discussion

6423.	If cos x= tan y, cos y= tan z' cos z= tan x then
Answer» `SIN X= sin y= sin z= sin 18^(0)` `sin x= sin y= sin z= 2SIN 18^(0)` `sin x= sin y= sin z= sin 36^(0)` `sin x= sin y= sin z= 2sin 36^(0)` Answer :B

Discussion

6424.	Identify the quantifier in the following statements. There exists a capital city for every state of India.
Answer» ANSWER :There EXISTS

Discussion

6425.	IF in a Delta ABC, r_3=r_1+r_2+r, then angle A+ angle B=
Answer» `120^(@) ` ` 100 ^(@) ` ` 90 ^(@) ` ` 80 ^(@) ` Answer :C

Discussion

6426.	Write down all the subsets of the following sets {a,b}
Answer» ANSWER :`φ, { a }, { B }, { a, b }`

Discussion

6427.	Sameer throws , an ordinary die . What is the probability that he throws 2
Answer» ANSWER :`(1)/(6)`

Discussion

6428.	If f(x)=(25-x^(4))^(1//4) for 0 lt x lt sqrt5 then f(f((1)/(2)))=
Answer» `2^(-4)` `2^(-3)` `2^(-2)` `2^(-1)` ANSWER :D

Discussion

6429.	Find the mean deviation from the mean for the following data : (i)13,15,16,15,18,15,14,18,17,10 (ii)38,70,48,40,42,55,63,46,54,44 (iii)37,48,50,23,47,58,29,27,31,40
Answer» ANSWER :(i)1.7 , (II)8.4 , (III)9.6

Discussion

6430.	Thethird vertex of trianglewhose centroid is origin and two vertex are (0,-2,5) and (-2,-2,-1) is
Answer» (2,4,-4) (2,-4,-4) (-2,4,-4) (-2,-4,-4) ANSWER :A

Discussion

6431.	Find the coordinates of the vertices and the foci and the length of the latus rectum of the ellipse 9x^(2)+25y^(2)=225.
Answer» Answer :Vertices `(pm5, 0)`, FOCI `(PM4, 0)`. LENGTH of latus RECTUM `=18/5` UNITS

Discussion

6432.	If sin theta, cos theta, tan theta are in GP then cos^(9)theta + cos^(6) theta + 3 cos^(5) theta=
Answer» 1 -1 0 2 Answer :A

Discussion

6433.	Let the area of triangle ABC be ((sqrt(3)-1))/(2),b=2 and c=(sqrt(3)-1), and angleA the measure of the angle C is
Answer» `15^(@)` `30V` `60^(@)` `75^(@)` ANSWER :A

Discussion

6434.	Find the derivative of sin x at x = 0.
Answer» ANSWER :1

Discussion

6435.	If from the point P (f,g,h) perpendicular PL, PM be drawn to YZ and ZX planes then the equation of the plane OLM is
Answer» `x/f + y/g - z/h =0` `x/f + y/g + z/h =0` `x/f - y/g + z/h =0` `- x/f + y/g + z/h =0` ANSWER :A

Discussion

6436.	If bara is parallel to barbxxbarc then (baraxxbarb).(baraxxbarc))=
Answer» `BARA^(2)(BARB.BARC)` `barb^(2)(bara.barc)` `barc^(2)(bara.barb)` 0 Answer :A

Discussion

6437.	If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^(2), thenD=\|(x^(N_(1)),y^(N_(2))),(z^(N_(3)),w^(N_(4)))\|(N_(1),N_(2),N_(3),N_(4)inN)
Answer» has a maximum VALUE of 2 has a minimum value of 0 16 different D are POSSIBLE has a minimum value of -2 Answer :A::C::D

Discussion

6438.	Range of (\|x-4\|)/(x-4) is
Answer» `R-{4}` R `{-1, 1}` `R- {-1, 1}` ANSWER :C

Discussion

6439.	Expand (1)/((1+3x)^(2)) in powers of x. Find a condition on x for which the expansion is valid.
Answer» Answer :`=1-6x+27x^(2)-108X^(3)+405x^(4)-….,\|x\|gt (1)/(3)`.

Discussion

6440.	If the perimeter of a certain sectorof a circle is equal to the lengthof the arc of the semicircle having the same radius , find the angle of the sector in degrees .
Answer» ANSWER :`65^(@)27'16'`

Discussion

6441.	The straight lines represented by (y-mx)^2=a^2(1+m^2) and (y-nx)^2 =a^2(1+n^2) form a
Answer» rectangle rhombus trapezium Scalane `DELTA^("LE")` ANSWER :B

Discussion

6442.	The real value of theta for which the expression (1+I cos theta)/(1-2i cos theta)is a real number is
Answer» `npi+(PI)/(4), n inZ` `npi+(-1)(pi)/(4), n inZ` `2NPI +-(pi)/(4), n inZ` None of these Answer :C

Discussion

6443.	If U_(n) = sin n theta.sec^(n)theta, V_(n)=cosnthetasec^(n)theta for n=0,1,2,……. Then V_(n)-V_(n-1) + U_(n-1) tan theta = ?
Answer» 0 1 `SIN THETA` `COS theta` ANSWER :A

Discussion

6444.	sin (- (11pi)/(3))
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

6445.	The value of (sin 55^(@) - cos 55^(@))/(sin 10^(@)) is
Answer» `(1)/(SQRT2)` 2 1 `sqrt2` ANSWER :D

Discussion

6446.	The range of y = sin^(-1)((x^(2))/(1+x^(2))) is
Answer» `(0, pi/2)` `[ 0, pi/2)` `[0, pi/2]` `[0,1]` ANSWER :B

Discussion

6447.	Find the points on the line x+y=4 which lie at a unit distance from the line 4x+ 3y=10.
Answer» Answer :the REQUIRED points are `(3, 1) and (-7, 11).`

Discussion

6448.	Evaluate the following limits. Lt_(xto2)(x-2)/(x^(3)-8)
Answer» ANSWER :`1/12`

Discussion

6449.	Find equation of the circle which touches circle x^(2) + y^(2) - 2x - 4y - 20 = 0of point (5,5) externally and radius is 5 unit.
Answer» Answer :`x^(2) + y^(2) - 18X - 16y + 120 = 0`

Discussion

6450.	Value of the rotation of point P on unit circle increase in multiple of 2pi then value of sine and cosine does not change .
Answer» ANSWER :TRUE STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

Write the first six terms of the sequences given by(i)a_(1)=a_(2)=1, a_(n)=a_(n-1)+a_(n-2)(n ge 3)(ii)a_(1)=4, a_(n+1)=2na_(n)

The possible values of a such that the equation x^(2)+2ax+a= sqrt(a^(2)+x -(1)/(16))-(1)/(16), x ge -a, has two distinct real root are given by

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 5. . .A

A cubic function of x has maximum 10 and minimum -5/2, when x = -3 and x = 2 respectively. Find the function.

If A={1,3,5,6}, the number of elements in P{P(A)} is

Value of 'K' so that equation 16x^2+24xy+ly^2+kx--12y-21=0. Represents a pair of parallel lines is

Without using tables, give the valueof the following : "sec"(15pi)/(4)

If A=580^(0) then -sqrt(1+sinA)-sqrt(1-sinA)=

The equation of the pair of perpendicular lines passing through origin and forming an isosceles triangle with the line 2x+3y=6, is

Leta gt 2be a constant . If there are just 18 positive integers satisfying the inequality (x- a) ( x-2a) (x-a^(2))lt 2then the value of a is …………

Four digit numbers are formed from the digits = [4 = 24 2, 5,6, 7, 8 (without repetition of digits).Q How many of there are exactly divisible by 7.

Four digit numbers are formed from the digits = [4 = 24 2, 5,6, 7, 8 (without repetition of digits).Q How many of there are odd.

Consider the points A (1,-1,3), B(2,-4,5) and C(5,-13,11).Find AB, BC and AC

The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and vec(d) are two vectors satisfying vec(b) xx vec(c )= vec(b) xx vec(d) and vec(a).vec(d)= 0. Then the vector vec(d) is equal to

If (x+iy)^(3) = u + iy, then show that u/x + v/y = 4(x^(2)-y^(2))

If "tan" (x)/(2) cot h ((x)/(2)) = 1 then cos x cos hx =

If Lt_(ntooo)a_(n)=l" where "a_(n+1)=sqrt(2+a_(n)),n = 1,2,3...., find the value of l.

The numbers of bacteria increases at the rate of 4% every hour. If there were 40 beacteria present originally, then how many bacteria will be present at the end of 4^(th) hour ? How many bacteria will be there in 4^(th) hour?

Series (1)/(log_(2)^(2)) + (1)/(log_(4)^(4)) + (1)/(log_(8)^(4)) + …..+ (1)/(log_(2^(n))4)=……….

If f(x) = cos (log_(e) x), then f(x)f(y) -1/2[f(x/y) + f(xy)] has value

Find equaiton of hyperbola satisfying given conditons Foci of hyperbola will be foci of eppipse (x^(2))/(25) + (y^(2))/(9) = 1 having eccentricity 2.

In Delta ABC, if cos^2 A+ cos^2 B+cos^2 C=1, then the triangle is

If cos x= tan y, cos y= tan z' cos z= tan x then

Identify the quantifier in the following statements. There exists a capital city for every state of India.

IF in a Delta ABC, r_3=r_1+r_2+r, then angle A+ angle B=

Write down all the subsets of the following sets {a,b}

Sameer throws , an ordinary die . What is the probability that he throws 2

If f(x)=(25-x^(4))^(1//4) for 0 lt x lt sqrt5 then f(f((1)/(2)))=

Find the mean deviation from the mean for the following data : (i)13,15,16,15,18,15,14,18,17,10 (ii)38,70,48,40,42,55,63,46,54,44 (iii)37,48,50,23,47,58,29,27,31,40

Thethird vertex of trianglewhose centroid is origin and two vertex are (0,-2,5) and (-2,-2,-1) is

Find the coordinates of the vertices and the foci and the length of the latus rectum of the ellipse 9x^(2)+25y^(2)=225.

If sin theta, cos theta, tan theta are in GP then cos^(9)theta + cos^(6) theta + 3 cos^(5) theta=

Let the area of triangle ABC be ((sqrt(3)-1))/(2),b=2 and c=(sqrt(3)-1), and angleA the measure of the angle C is

Find the derivative of sin x at x = 0.

If from the point P (f,g,h) perpendicular PL, PM be drawn to YZ and ZX planes then the equation of the plane OLM is

If bara is parallel to barbxxbarc then (baraxxbarb).(baraxxbarc))=

If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^(2), thenD=|(x^(N_(1)),y^(N_(2))),(z^(N_(3)),w^(N_(4)))|(N_(1),N_(2),N_(3),N_(4)inN)

Range of (|x-4|)/(x-4) is

Expand (1)/((1+3x)^(2)) in powers of x. Find a condition on x for which the expansion is valid.

If the perimeter of a certain sectorof a circle is equal to the lengthof the arc of the semicircle having the same radius , find the angle of the sector in degrees .

The straight lines represented by (y-mx)^2=a^2(1+m^2) and (y-nx)^2 =a^2(1+n^2) form a

The real value of theta for which the expression (1+I cos theta)/(1-2i cos theta)is a real number is

If U_(n) = sin n theta.sec^(n)theta, V_(n)=cosnthetasec^(n)theta for n=0,1,2,……. Then V_(n)-V_(n-1) + U_(n-1) tan theta = ?

sin (- (11pi)/(3))

The value of (sin 55^(@) - cos 55^(@))/(sin 10^(@)) is

The range of y = sin^(-1)((x^(2))/(1+x^(2))) is

Find the points on the line x+y=4 which lie at a unit distance from the line 4x+ 3y=10.

Evaluate the following limits. Lt_(xto2)(x-2)/(x^(3)-8)

Find equation of the circle which touches circle x^(2) + y^(2) - 2x - 4y - 20 = 0of point (5,5) externally and radius is 5 unit.

Value of the rotation of point P on unit circle increase in multiple of 2pi then value of sine and cosine does not change .