14949 + Interview Questions in Maths in Class 11 Page 152 InterviewSolution

7551.	If the feet of the perpendiculars from (3, 4, 5) to the coordinates axesare A, B, C and the angle between AB and AC is cos^(-1)((9)/(a)) then a =
Answer» `5sqrt(34)` `3sqrt(34)` `SQRT(34)` 25 Answer :A

Discussion

7552.	The value of the sum1.2.3+2.3.4+3.4.5+… upto n terms is equal to
Answer» `N (n+1) (n+2) (3n+5)//12` `n (n+1) (n+2) (n+3)//4` `2n(n+1) (n+2) (n+3)` `n (n+1) (n+2) (3n+1)//12` Answer :B

Discussion

7553.	Express sqrt3-i in polar form using the polar form of sqrt3+i
Answer» Answer :`2(COS(-PI)/6) + ISING(-pi)/6)`

Discussion

7554.	In Delta ABC, if c(a+b) cos B//2=b (a+c) cos C//2, then the triangle is
Answer» isosceles Right ANGLED Equilateral Right angled isosceles Answer :A

Discussion

7555.	Find the area of the triangle bounded by the straight line 3x+4y=12 and the coordinate axis.
Answer»

Discussion

7556.	Find the gradient of the straight line joining between two points (4,8) and (-6,-2)
Answer»

Discussion

7557.	Solve for x: a) \|\|x-1\|+2\|le4\|, b) (x-4)/(x+2) le \|(x+2)/(x-1)\|
Answer» Solution :a) `\|\|x-1\|+2\|le4\| rArr -4 le\|x-1\|+2le4` `rArr -6 le\|x-1\|le2` `rArr \|x-1\|le2 rArr -2 le-1 le2` `rArr -1 lexle3 rArr x in [-1.3]` b) Case I: Given inequation will be SATISFIED for all x such that `(x-4)/(x+2) le0 rArr x in (-2,4)-{1}`............(i) (Note: {1} is not in domain of RHS) Case 2: `(x-4)/(x+2) lt 0 rArr x in(-infty, -2) cup (4, infty)`.................(ii) Given inequation becomes `(x-2)/(x-1) ge (x-4)/(x+2)` or `(x-2)/(x-1) le (x-4)/(x+2)` On solving we geton solving we get `x in (-2,4//5) cup (1, infty)``x in (-2,0) cup (1,5//2)` taking intersection with (ii) we gettaking intersection with (ii), we get `x in (4, infty)`...........(III) `x in PHI` Hence, solution of the original inequation : `x in (-2,infty)-{1}` (taking union of (i) and (ii)

Discussion

7558.	Write the following sets in the set builder form : D= {10, 11, 12, 13, 14, 15}
Answer» ANSWER :`D= {X : x in N, 9 LT x lt 16}`

Discussion

7559.	If "tan"^(-1)(sqrt(1+x^(2))-1)/x=4^(@) then
Answer» `x=tan2^(@)` `x=tan4^(@)` `x=tan(1//4)^(@)` `x=tan8^(@)` ANSWER :D

Discussion

7560.	The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
Answer» a = 0, b = 7 a = 5, b = 2 a = 1, b = 6 a = 3, b = 4 Answer :D

Discussion

7561.	Evaluate the following limits : Lim_( xto 1) (x^(1//4)-1)/(x^(1//3) -1)
Answer» ANSWER :`3/4`

Discussion

7562.	Distance of the point (3, 4, 5) from the origin (0, 0, 0) is
Answer» `sqrt50` 3 4 5 Answer :A

Discussion

7563.	Calculate the mean deviation about median for the following data :
Answer» ANSWER :10.16

Discussion

7564.	Find the tangents to the ellipse x ^(2) + 9y ^(2) = 3, which are (i) parallel (ii) perpendicular to the line 3x + 4y =9.
Answer» Answer :`3x + 4y PM sqrt ((17)/(3)) = 0 and 3Y - 4X pm sqrt51 =0`

Discussion

7565.	Find the vector equation of the plane passing through the intersection of the planes barr.(2bari +2barj-3bark) = 7, barr. = (2bari+5barj+3bark) = 9 " and through the point " (2,1,3).
Answer» ANSWER :`BARR.(38bari+68barj+3bark)=153`

Discussion

7566.	For any real theta, the maximum value of cos^(2) ( cos theta) + sin^(2) (sin theta) is
Answer» 1 `1+sin^(2)1` `1+cos^(2)1` Does not exist Answer :B

Discussion

7567.	If the lines 2x+ y-3 = 0, 5x+ky - 3=0 and 3x -y -2 =0 are concurrent, find the value of k.
Answer» ANSWER :`k=-2`

Discussion

7568.	Find the derivative of f (x) w.r.t. g(x) for the f (x) = log x, g (x) = a ^(x)
Answer» ANSWER :`(1)/( X.a ^(x) (LOG a ) ^(2))`

Discussion

7569.	In the function f(x) satisfies lim_(xto1)(f(x)-2)/(x^(2)-1)=pi evaluate lim_(xto1)f(x).
Answer» ANSWER :2

Discussion

7570.	The point dividing the join of (3, -2, 1) and (-2, 3, 11) in the ratio 2:3 is :
Answer» (1, 1, 4) (1, 0, 5) (2, 3, 5) (0, 6, -1) ANSWER :b

Discussion

7571.	If bara=bari+barj+bark,barb=bari+barj,barc=bari and bar(baraxxbarb)xxbarc = lamdabara+ μbarb then lamda+μ =
Answer» `-1` 0 1 2 Answer :B

Discussion

7572.	Write the first four terms of the sequence whose nth term is given sin^(n) 30^(@)
Answer» ANSWER :`(1)/(2) , (1)/(4),(1)/(8) , (1)/(16)`

Discussion

7573.	How many different amounts can be formed with one-one coin of Rs 1, Rs 2, Rs 5 and Rs 10?
Answer» ANSWER :15

Discussion

7574.	If sec theta + tan theta=1, then root of the equation (a-2b+c)x^(2) + (b-2c+a)x + (c-2a+b)=0 is:
Answer» `SEC theta` `TAN theta` `sin theta` `cot theta` ANSWER :A

Discussion

7575.	Find the value of (a^2 + sqrta^2 - 1)^4 + (a^2 - sqrta^2 - 1)^4 .
Answer» ANSWER :`2a^8` + `12a^6` - `10a^4` -`4a^2` + 2

Discussion

7576.	Area of triangle is 75 cm^(2)and twoof itssides 20 cm, 15cm,theirincludedangle is
Answer» `30 ^(@) or 150 ^(@) ` ` 60 ^(@)or 120 ^(@) ` ` 30 ^(@) or 135^(@) ` `30 ^(@) or 120 ^(@) ` ANSWER :A

Discussion

7577.	Consider the equation of the ellipse 3x^2+2y^2 = 6.Find e, foci, directrices, length of major axis and minor axis and length oflatus rectum of the above ellipse
Answer» SOLUTION :`[1/sqrt3, (0,1),(0,-1),y-3=0, y+3=0,2sqrt3,2sqrt2,4/sqrt3]`

Discussion

7578.	Locus of point for which the sum of squares of distance from the coordinate axes is 8 units is
Answer» `x^(2)+y^(2)+z^(2) = 8` `x^(2)+y^(2)+z^(2) = 16` `x^(2)+y^(2)+z^(2) = 4` `x^(2)+y^(2)+z^(2) = 64` Answer :A

Discussion

7579.	Write the first term of the sequence, whose nth term is a_n=(n)/(n+1).
Answer» ANSWER :`1/2,2/3,3/4,4/5,5/6`

Discussion

7580.	Which of the following statements is are correct Statement -I : For any vector bara,(bara.bari)bari+(bara.barj)barj+(bara.bark)bark = bara. Statement -II : For any vector bara, (bara.barj)bark+(bara.bark)bari+(bara.bari)barj = bar0
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor IIis true Answer :A

Discussion

7581.	If f(x)=cos^(-1)(x-x^(2))+sqrt((1-(1)/(\|x\|)))+(1)/([x^(2)-1]) then domain of f(x) ( where [.] G.I.F) is
Answer» `( SQRT(2), (1+sqrt(5))/(2)]` `(-sqrt(2), (1-sqrt(5))/(2))` `(-sqrt(2), (1+sqrt(5))/(2)]` `[ sqrt(7), (sqrt(7))/(2)]` ANSWER :A

Discussion

7582.	Solve each of the following equations. 1. Solve x^(2) +x+1=0
Answer» ANSWER :`=(-1 + SQRT(3)i)/2`

Discussion

7583.	If A=[(1,1),(1,1)] and ninN then A^(n)=
Answer» `2^(N)A` `2^(n-1)A` `"n A"` `(n=1)A` ANSWER :B

Discussion

7584.	Find the vector equation of the line passing through the points bar(i)+bar(j)+bar(k) and bar(i)-bar(j)+bar(k).
Answer» `ALPHA+beta+gamma=0` `alpha+beta+gamma=1` `alpha+beta=gamma` `alpha^(2)+beta^(2)+beta^(2)=1` ANSWER :B

Discussion

7585.	If A={-1,1}, find A xx A xx A
Answer» ANSWER :`A XX A={(-1,-1),(,-1,1),(1,-1,),(1,1)}` `A xx A xx A={(-1,-1,-1),(,-1,-1,1),(,-1,1,-1),(,-1,1,1),(,1,-1,-1),(1,-1,1),(1,1,-1),(1,1,1)}`

Discussion

7586.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find D – C
Answer» ANSWER :`={5, 15, 20}`

Discussion

7587.	underset(x to 0)(Lt) [(1)/(1^(sin^(2)x))+(1)/(2^(sin^(2))x)+....+(1)/(n^(sin^(2))x)]^(Sin^(2)x)
Answer» `OO` 0 `(n+1)/(2)` n Answer :D

Discussion

7588.	Find the term independent of x in (2x^(2) - (1)/(x) )^(12).
Answer» ANSWER :`T_9, 7920`

Discussion

7589.	If P(AuuB)=0.65andP(AcapB)=0.15, find P(overline(A))+P(overline(B)).
Answer» ANSWER :`=1.2`

Discussion

7590.	If A and B are acute angles satisfying SinA = Sin^(2) B and 2Cos^(2) A= 3Cos^(2) B then A + B =
Answer» `60^(@)` `75^(@)` `80^(@)` `90^(@)` Answer :B

Discussion

7591.	In the interval (-3,3) the function f(x) =x/3+3/x,xne 0 is
Answer» increasing DECREASING neither increasing nor decreasing function partly increasing and partly decreasing ANSWER :B

Discussion

7592.	Find the modulus of (1+i)/(1-i)-(1-i)/(1+i).
Answer» ANSWER :2

Discussion

7593.	Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are :(i)included(ii)excluded.
Answer» ANSWER :(i)60480(II)60480

Discussion

7594.	Determine the x- intercept 'a' and the y-intercept 'b' of the following lines. Sketch each. 3x+5y-15=0,
Answer» ANSWER : `a=5, b=3`

Discussion

7595.	Find the domain and range of the function f(x)=(x^(2))/(1+x^(2)). Is the function one-to-one?
Answer» `R^(+)` and R R and [0, 1) [2, 5] and [0, 1) (2, 5) and (3, 5) Answer :B

Discussion

7596.	If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x+y=1, then the orthocentre of te triangle is
Answer» `(1/3,1/3)` `(2/3,2/3)` (1,1) (1,3) ANSWER :A

Discussion

7597.	Find the middle terms in the expansion of (3 - x^(3)/6)^(7)
Answer» ANSWER :`105/8` `x^9,.35/48 x^12`

Discussion

7598.	Find the multiplicative invers of each of the complex number -i
Answer» ANSWER :0 + I1

Discussion

7599.	If x=2\|t\| + 3t, y =2t\|t\| + 3t^(2) and y=f(x) hen find whether f(x)is injective where t in R
Answer» ANSWER :not an INJECTION

Discussion

7600.	Evaluate Lt_(x to 0)(x(e^x - 1))/(1 - cos x)
Answer» ANSWER :2

Discussion

Explore topic-wise InterviewSolutions in .

If the feet of the perpendiculars from (3, 4, 5) to the coordinates axesare A, B, C and the angle between AB and AC is cos^(-1)((9)/(a)) then a =

The value of the sum1.2.3+2.3.4+3.4.5+… upto n terms is equal to

Express sqrt3-i in polar form using the polar form of sqrt3+i

In Delta ABC, if c(a+b) cos B//2=b (a+c) cos C//2, then the triangle is

Find the area of the triangle bounded by the straight line 3x+4y=12 and the coordinate axis.

Find the gradient of the straight line joining between two points (4,8) and (-6,-2)

Solve for x: a) ||x-1|+2|le4|, b) (x-4)/(x+2) le |(x+2)/(x-1)|

Write the following sets in the set builder form : D= {10, 11, 12, 13, 14, 15}

If "tan"^(-1)(sqrt(1+x^(2))-1)/x=4^(@) then

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

Evaluate the following limits : Lim_( xto 1) (x^(1//4)-1)/(x^(1//3) -1)

Distance of the point (3, 4, 5) from the origin (0, 0, 0) is

Calculate the mean deviation about median for the following data :

Find the tangents to the ellipse x ^(2) + 9y ^(2) = 3, which are (i) parallel (ii) perpendicular to the line 3x + 4y =9.

Find the vector equation of the plane passing through the intersection of the planes barr.(2bari +2barj-3bark) = 7, barr. = (2bari+5barj+3bark) = 9 " and through the point " (2,1,3).

For any real theta, the maximum value of cos^(2) ( cos theta) + sin^(2) (sin theta) is

If the lines 2x+ y-3 = 0, 5x+ky - 3=0 and 3x -y -2 =0 are concurrent, find the value of k.

Find the derivative of f (x) w.r.t. g(x) for the f (x) = log x, g (x) = a ^(x)

In the function f(x) satisfies lim_(xto1)(f(x)-2)/(x^(2)-1)=pi evaluate lim_(xto1)f(x).

The point dividing the join of (3, -2, 1) and (-2, 3, 11) in the ratio 2:3 is :

If bara=bari+barj+bark,barb=bari+barj,barc=bari and bar(baraxxbarb)xxbarc = lamdabara+ μbarb then lamda+μ =

Write the first four terms of the sequence whose nth term is given sin^(n) 30^(@)

How many different amounts can be formed with one-one coin of Rs 1, Rs 2, Rs 5 and Rs 10?

If sec theta + tan theta=1, then root of the equation (a-2b+c)x^(2) + (b-2c+a)x + (c-2a+b)=0 is:

Find the value of (a^2 + sqrta^2 - 1)^4 + (a^2 - sqrta^2 - 1)^4 .

Area of triangle is 75 cm^(2)and twoof itssides 20 cm, 15cm,theirincludedangle is

Consider the equation of the ellipse 3x^2+2y^2 = 6.Find e, foci, directrices, length of major axis and minor axis and length oflatus rectum of the above ellipse

Locus of point for which the sum of squares of distance from the coordinate axes is 8 units is

Write the first term of the sequence, whose nth term is a_n=(n)/(n+1).

Which of the following statements is are correct Statement -I : For any vector bara,(bara.bari)bari+(bara.barj)barj+(bara.bark)bark = bara. Statement -II : For any vector bara, (bara.barj)bark+(bara.bark)bari+(bara.bari)barj = bar0

If f(x)=cos^(-1)(x-x^(2))+sqrt((1-(1)/(|x|)))+(1)/([x^(2)-1]) then domain of f(x) ( where [.] G.I.F) is

Solve each of the following equations. 1. Solve x^(2) +x+1=0

If A=[(1,1),(1,1)] and ninN then A^(n)=

Find the vector equation of the line passing through the points bar(i)+bar(j)+bar(k) and bar(i)-bar(j)+bar(k).

If A={-1,1}, find A xx A xx A

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find D – C

underset(x to 0)(Lt) [(1)/(1^(sin^(2)x))+(1)/(2^(sin^(2))x)+....+(1)/(n^(sin^(2))x)]^(Sin^(2)x)

Find the term independent of x in (2x^(2) - (1)/(x) )^(12).

If P(AuuB)=0.65andP(AcapB)=0.15, find P(overline(A))+P(overline(B)).

If A and B are acute angles satisfying SinA = Sin^(2) B and 2Cos^(2) A= 3Cos^(2) B then A + B =

In the interval (-3,3) the function f(x) =x/3+3/x,xne 0 is

Find the modulus of (1+i)/(1-i)-(1-i)/(1+i).

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are :(i)included(ii)excluded.

Determine the x- intercept 'a' and the y-intercept 'b' of the following lines. Sketch each. 3x+5y-15=0,

Find the domain and range of the function f(x)=(x^(2))/(1+x^(2)). Is the function one-to-one?

If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x+y=1, then the orthocentre of te triangle is

Find the middle terms in the expansion of (3 - x^(3)/6)^(7)

Find the multiplicative invers of each of the complex number -i

If x=2|t| + 3t, y =2t|t| + 3t^(2) and y=f(x) hen find whether f(x)is injective where t in R

Evaluate Lt_(x to 0)(x(e^x - 1))/(1 - cos x)