14949 + Interview Questions in Maths in Class 11 Page 138 InterviewSolution

6851.	If thetalt22 1^(@)/2 then sqrt(2+sqrt(2+sqrt(2+2cos4theta)))=
Answer» `1/4` `2costheta` `2"COS"theta/2` `2"cos"theta/4` ANSWER :C

Discussion

6852.	If y = "Tan"^(-1)((1)/(cos^2 x + cos x + 1)) + "Tan"^(-1)(1/(cos^2x + 3 cos x + 3))+ ….upto n term then f^(1)(0) =
Answer» 0 1 `PI/2` `pi` ANSWER :A

Discussion

6853.	A = { x in N\| x^(3) =x } is singleton set.
Answer» ANSWER :TRUE STATEMENT

Discussion

6854.	Find the cosines of the angles made by bara = 2bari+3barj+6bark with the X, Y, Z - axes.
Answer» ANSWER :`6/7`

Discussion

6855.	Does the point (3, 0) lie on the curve 3x^(2)+y^(2)-4x+7=0?
Answer» ANSWER : No

Discussion

6856.	…….of the following is not the eccentricity of hyperbola.
Answer» `sqrt((9)/(5))` `sqrt((1)/(9))` `3sqrt((1)/(8)` 2 Answer :B

Discussion

6857.	Out of the following sentence, which is true?
Answer» `cos1ltcos1^(@)` `cos1gtcos1^(@)` `cos1=cos1^(@)` `(PI)/(180)cos1=cos1^(@)` ANSWER :A

Discussion

6858.	If 630^@ lt A lt 720^(@) , \|tan A\|=12//5, " then " tan A//2=
Answer» `3/2` `-3/2` `2/3` `-2/3` ANSWER :D

Discussion

6859.	Write and simplify the term involving x^5 in the expansion of (x- 1/x)^11 .
Answer» ANSWER :`-165 x^5`

Discussion

6860.	If x and y are positve acute such that (x + y) and (x - y) satisfy the equation ta^(2) theta - 4 tan theta + 1 = 0then
Answer» `X=(pi)/6, y=(pi)/6` `y=(pi)/4, x=(pi)/3` `x=(pi)/4, y=(pi)/6` `x=(pi)/3, y=(pi)/3` Answer :A

Discussion

6861.	Evaluate the following limits. Lt_(xto0)(tan2x)/(tan4x)
Answer» ANSWER :`1/2`

Discussion

6862.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cap (B cup D)
Answer» ANSWER :`={4, 5}`

Discussion

6863.	The period of the function satisfying the relationf(x) + f(x+ 3) = 0, AA x in Ris
Answer» ANSWER :6

Discussion

6864.	There are 10 lamps in a hall, Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminted, Thinking Process : Total numbers of ways to lightned room is out of given n bulbs at least one or all bulls are lightened. we get total number of ways using following fromula.
Answer» ANSWER :` = 1023`

Discussion

6865.	A group of 4 boys and 3 girls are arranged atrandom , one after the other. Probability thatgirls and boys occupy alternate seats is ,
Answer» `(1)/(34)` `(1)/(35)` `(1)/(33)` `(1)/(32)` ANSWER :B

Discussion

6866.	A card is drawn from a pack of cards . Findthe probability that it is a red card
Answer» <P> ANSWER :`=(1)/(2)=P(B)`

Discussion

6867.	How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Answer» ANSWER :108

Discussion

6868.	Let cos beta is the geometric mean between sin alpha and cos alpha, where 0 lt alpha lt betalt pi//2 , then cos 2beta is equal to
Answer» `-2sin^2(PI/4-alpha)` `-2cos^2(pi/4+alpha)` `2sin^2((pi)/4+alpha)` `2cos^2(pi/4-alpha)` ANSWER :A::B

Discussion

6869.	Let A = { a, b }, B ={a, b, c}. Is A ⊂ B ? What is A ∪ B ?
Answer» ANSWER :YES, `A ∪ B = { a, b, C }`

Discussion

6870.	If ((x)/(3)+ 1, y- (2)/(3))= ((5)/(3), (1)/(3)), find the value of x and y.
Answer» ANSWER :x=2, y= 1

Discussion

6871.	Express (1-3i)/(1+2i) in the form x+iy
Answer» ANSWER :`-1 -i`

Discussion

6872.	Find the angle throughwhich the axes be rotated to remove the xy term from the equations x^(2) + 4xy + y^(2) - 2x + 2y - 6 = 0
Answer» ANSWER :`(PI)/(4)`

Discussion

6873.	Find the orthocentre of the triangle whose angular points are (0, 0), (2, -1), (-1, 3). [Note. Orthocentre is the point of intersection of the altitudes]
Answer» ANSWER : `(-4, -3)`

Discussion

6874.	Find the equation of the line through the points (1,-1) and (3,5).
Answer» ANSWER :`-3X + y + 4 = 0 `

Discussion

6875.	Find the slope of the line, which makes an angle of 30° with the positive direction of Y -axis measured anticlockwise.
Answer» ANSWER :`= TAN(60°)= - SQRT(3)`

Discussion

6876.	Find the number of ways in which 6 men and 5 women can dine around a circular table if no two women are to sit together.
Answer» ANSWER :`5!xx6!`

Discussion

6877.	Passing through (0, 0) with slope m.
Answer» ANSWER :`y = MX`

Discussion

6878.	Write the following sets in roster form : A= { x : x is a prime natural numbers 10 lt x lt 20}
Answer» ANSWER :`A= {11, 13, 17, 19}`

Discussion

6879.	sin "" (pi)/(7) sin "" (2pi)/(7) sin "" (4pi )/(7)=
Answer» `(SQRT7)/(8)` `(sqrt7)/(4)` `(sqrt7)/(2)` `sqrt7` ANSWER :A

Discussion

6880.	Two systems of rectangular axes have the same origin. If plane cut the intercepts a,b,c on co-ordinate axes for 1st system aned intercepts a', b'', c' on 2nd system then pick the correct alternatives
Answer» `(1)/( a ^(2)) + (1)/( b ^(2) ) + (1 )/( C ^(2)) - (1)/(a^('2)) - (1)/(b^('2)) - (1)/(c ^('2)) =0` `(1)/( a ^(2)) + (1)/( b ^(2) ) + (1 )/( c ^(2)) + (1)/(a^('2)) + (1)/(b^('2)) + (1)/(c ^('2)) =0` `x/1 +y/1 = (z)/(r ^(2))` `(1)/( a ^(2)) - (1)/( b ^(2) ) - (1 )/( c ^(2)) + (1)/(a^('2)) - (1)/(b^('2)) - (1)/(c ^('2)) =0` ANSWER :A

Discussion

6881.	Solve the following equations and write general solutions sin 3 theta - sin theta = 4 cos^(2) theta - 2
Answer» ANSWER :`(2n+1)(PI)/(4)` or `(2n+1)(pi)/(2)`

Discussion

6882.	Maximum value of sin^(4) x+ cos^(4)xis
Answer» 1 2 `(3)/(4)` `(5)/(4)` ANSWER :1

Discussion

6883.	A function f is defined as follows,is it continuous?f(x)={0,xlt0x,0lexlt1x^2 -2 ,1lexlt2x+35x -x,xge2
Answer» ANSWER :YES

Discussion

6884.	Find the domain and range of the following real functions: f(x)= -\|x\|
Answer» ANSWER :`R_(F)`

Discussion

6885.	If y =(logx)^(x) then (dy)/(dx) =
Answer» `(LOGX)^(X)[LOG(logx)+1/(logx)]` `(logx)^(x)[log(logx)-1/(logx)]` `-(logx)^(x)[log(logx)+1/(logx)]` `-(logx)^(x)[log(logx)-1/(logx)]` ANSWER :A

Discussion

6886.	Find the values of a if f(x) = 2x^(x) - a e^(-x) + (2a +1) x-3 is increasing for all values of x.
Answer» ANSWER :`a GE 0`

Discussion

6887.	Find the locus of the point such that its distance from the x-axis is half its distance from the y-axis.
Answer» ANSWER : `2y=+-x`

Discussion

6888.	Evaluate the following limits. Lt_(xtoa)(tan(x-a))/(x^(2)-a^(2))(ane0)
Answer» ANSWER :`1/(2A)`

Discussion

6889.	(1+tan alpha tan beta)^(2) + (tan alpha -tan beta)^(2) =
Answer» `TAN^(2) alpha tan^(2) BETA` `sec^(2)alpha sec^(2) beta` `tan^(2) alpha sec^(2) beta` `sec^(2) alpha cot^(2) beta` Answer :B

Discussion

6890.	Find the mean deviation from the short cut method.
Answer» SOLUTION :NA

Discussion

6891.	if TanA=1/2, tanB=1/3 then cos2A-sin2B=
Answer» 0 1 2 3 Answer :A

Discussion

6892.	Write the negation of the following statements: p: For every real number x,x^(2)ltx.
Answer» ANSWER :`X^(2)GEX`

Discussion

6893.	If the ends of the base of an isosceles triangle are at (2,0) and (0,1) , and the equaiton of one side is x=2 then the orthocenter of the triangle is
Answer» `(3//2,3//2)` `(5//4,1)` `(3//4,1)` `(4//3,7//12)` ANSWER :D

Discussion

6894.	(i) "sin" 2theta=….........(in terms of "tan" theta). (ii) cos 2theta…..........(in terms of "tan" theta). (iii) "tan" 2theta…........(in terms of "tan" theta).
Answer» Answer :(i) `(2"tan" theta)/(1+"tan"^(2)theta)` (II) `(1-"tan"^(2)theta)/(1+"tan"^(2)theta)` (III) `(2"tan" theta)/(1-"tan"^(2)theta)`

Discussion

6895.	Construct a 3xx2 matrix A=[a_(ij)], whose elements are given by (i) a_(ij)=i+j (ii) a_(ij)=1/2\|i-3j\|
Answer» ANSWER :(i) `[(2,3),(3,4),(4,5)]` (II) `[(1,5//2),(1//2,2),(0,3//2)]`

Discussion

6896.	The value of tan^(-1)(tan((3pi)/4))=
Answer» 1)`(3pi)/4` 2)`(PI)/4` 3)`(-(3pi)/4)` 4)`-(pi)/4` ANSWER :D

Discussion

6897.	Consider a line with equation x - sqrt 3 y + 4 =0 Reduce the given equation into normal form and find the length of the perpendicular from the origin on the line and the angle made by this perpendicular with the x- axis.
Answer» SOLUTION :`X COS ((2pi)/3) +sin (2pi/3)=2:2,(2pi)/3`

Discussion

6898.	Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+betabar(b). If the vectors bar(i)-2bar(j)+bar(k), 3bar(i)+2bar(j)-bar(k) and bar(c) are coplanar then alpha/beta equals
Answer» -1 2 3 -3 Answer :D

Discussion

6899.	If f(x)=g(x)(x-a)^(2), where g(a)ne0, and g is continuous at x=a , then
Answer» F is INCREASING in the NEIGHBOURHOOD of a if `g(a)gt0` f is increasing in the neighbourhood of a if `g(a)LT0` f is DECREASING in the neighbourhood of a if `g(a)gt0` f is decreasing in the neighbourhood of a if `g(a)lt0` Answer :A::D

Discussion

6900.	If A^(2)=2A-I then for n!=2,A^(n)=
Answer» `NA-(n-1)I` `nA-I` `nA-(n-2)I` `nA-2I` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If thetalt22 1^(@)/2 then sqrt(2+sqrt(2+sqrt(2+2cos4theta)))=

If y = "Tan"^(-1)((1)/(cos^2 x + cos x + 1)) + "Tan"^(-1)(1/(cos^2x + 3 cos x + 3))+ ….upto n term then f^(1)(0) =

A = { x in N| x^(3) =x } is singleton set.

Find the cosines of the angles made by bara = 2bari+3barj+6bark with the X, Y, Z - axes.

Does the point (3, 0) lie on the curve 3x^(2)+y^(2)-4x+7=0?

…….of the following is not the eccentricity of hyperbola.

Out of the following sentence, which is true?

If 630^@ lt A lt 720^(@) , |tan A|=12//5, " then " tan A//2=

Write and simplify the term involving x^5 in the expansion of (x- 1/x)^11 .

If x and y are positve acute such that (x + y) and (x - y) satisfy the equation ta^(2) theta - 4 tan theta + 1 = 0then

Evaluate the following limits. Lt_(xto0)(tan2x)/(tan4x)

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cap (B cup D)

The period of the function satisfying the relationf(x) + f(x+ 3) = 0, AA x in Ris

A group of 4 boys and 3 girls are arranged atrandom , one after the other. Probability thatgirls and boys occupy alternate seats is ,

A card is drawn from a pack of cards . Findthe probability that it is a red card

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the﻿ digits can be repeated?﻿

Let cos beta is the geometric mean between sin alpha and cos alpha, where 0 lt alpha lt betalt pi//2 , then cos 2beta is equal to

Let A = { a, b }, B ={a, b, c}. Is A ⊂ B ? What is A ∪ B ?

If ((x)/(3)+ 1, y- (2)/(3))= ((5)/(3), (1)/(3)), find the value of x and y.

Express (1-3i)/(1+2i) in the form x+iy

Find the angle throughwhich the axes be rotated to remove the xy term from the equations x^(2) + 4xy + y^(2) - 2x + 2y - 6 = 0

Find the orthocentre of the triangle whose angular points are (0, 0), (2, -1), (-1, 3). [Note. Orthocentre is the point of intersection of the altitudes]

Find the equation of the line through the points (1,-1) and (3,5).

Find the slope of the line, which makes an angle of 30° with the positive direction of Y -axis measured anticlockwise.

Find the number of ways in which 6 men and 5 women can dine around a circular table if no two women are to sit together.

Passing through (0, 0) with slope m.

Write the following sets in roster form : A= { x : x is a prime natural numbers 10 lt x lt 20}

sin "" (pi)/(7) sin "" (2pi)/(7) sin "" (4pi )/(7)=

Two systems of rectangular axes have the same origin. If plane cut the intercepts a,b,c on co-ordinate axes for 1st system aned intercepts a', b'', c' on 2nd system then pick the correct alternatives

Solve the following equations and write general solutions sin 3 theta - sin theta = 4 cos^(2) theta - 2

Maximum value of sin^(4) x+ cos^(4)xis

A function f is defined as follows,is it continuous?f(x)={0,xlt0x,0lexlt1x^2 -2 ,1lexlt2x+35x -x,xge2

Find the domain and range of the following real functions: f(x)= -|x|

If y =(logx)^(x) then (dy)/(dx) =

Find the values of a if f(x) = 2x^(x) - a e^(-x) + (2a +1) x-3 is increasing for all values of x.

Find the locus of the point such that its distance from the x-axis is half its distance from the y-axis.

Evaluate the following limits. Lt_(xtoa)(tan(x-a))/(x^(2)-a^(2))(ane0)

(1+tan alpha tan beta)^(2) + (tan alpha -tan beta)^(2) =

Find the mean deviation from the short cut method.

if TanA=1/2, tanB=1/3 then cos2A-sin2B=

Write the negation of the following statements: p: For every real number x,x^(2)ltx.

If the ends of the base of an isosceles triangle are at (2,0) and (0,1) , and the equaiton of one side is x=2 then the orthocenter of the triangle is

(i) "sin" 2theta=….........(in terms of "tan" theta). (ii) cos 2theta…..........(in terms of "tan" theta). (iii) "tan" 2theta…........(in terms of "tan" theta).

Construct a 3xx2 matrix A=[a_(ij)], whose elements are given by (i) a_(ij)=i+j (ii) a_(ij)=1/2|i-3j|

The value of tan^(-1)(tan((3pi)/4))=

Consider a line with equation x - sqrt 3 y + 4 =0 Reduce the given equation into normal form and find the length of the perpendicular from the origin on the line and the angle made by this perpendicular with the x- axis.

Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+betabar(b). If the vectors bar(i)-2bar(j)+bar(k), 3bar(i)+2bar(j)-bar(k) and bar(c) are coplanar then alpha/beta equals

If f(x)=g(x)(x-a)^(2), where g(a)ne0, and g is continuous at x=a , then

If A^(2)=2A-I then for n!=2,A^(n)=

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?