14949 + Interview Questions in Maths in Class 11 Page 238 InterviewSolution

11851.	If a line passing through the point P(1,1) makes an angle theta with the positive direction of x-axiss meets the coordinate axes at A and B such that AB=OP, O being the origin , then tantheta+cottheta=
Answer» 2 `1-sqrt3` `1+sqrt3` 1 Answer :C

Discussion

11852.	If z ne 1 and (z^(2))/(z-1) is real, then the point represented by the complex number z lies
Answer» EITHER on the real AXIS or on a circle PASSING through the origin on a circle with centre at the origin either on the real axis or on a circle not passing through the origin on the IMAGINARY axis Answer :A

Discussion

11853.	If the odds in favour of an event are 4 to 5 , find the probability that it will occur .
Answer» ANSWER :`=(4)/(9)`.

Discussion

11854.	y = sin^(-1)2x+Tan^(-1)3x + Cos^(-1)2x+Cot^(-1)3x then (dy)/(dx)
Answer» 0 1 `2/SQRT(1-x^2)+3/(sqrt(1+9x^2))` 3 Answer :A

Discussion

11855.	cot7(1^@)/2-cot37(1^@)/2-cot52(1^@)/2+cot82(1^@)/2 =
Answer» `4sqrt2` 4 2 1 Answer :A

Discussion

11856.	Consider the sets phi, A={1,3}, B={1,5,9}, C={1,3,5,7,9}. Insert the symbol subset or cancel(subset) between each of the following pair of sets. (i) phi ....B (ii) A....B (iii) A.....C (iv) B.....C
Answer» ANSWER :`cancelsub`

Discussion

11857.	If alpha,beta,gamma, are lengths of the altitudes of a triangle ABC with area Delta , then Delta^2/R^2(1/alpha^2+1/beta^2+1/gamma^2)=
Answer» `sin^(2)A+sinB+sin^(2)C` `cos^(2)A+cos^(2)B+cos^(2)C` `TAN^(2)A+tan^(2)B+tan^(2)C` `cot^(2)A+ cot^(2)B+cot^(2)C` ANSWER :A

Discussion

11858.	Evaluate the following limits. Lt_(xto1)[(x-1)/(x^(2)-x)]
Answer» ANSWER :1

Discussion

11859.	2tan^(-1)(cosx)=tan^(-1)(2cosecx) then x=
Answer» 1)`pi//4` `2)pi//6` 3)`pi//2` 4)no solution Answer :A

Discussion

11860.	A point is in the XZ-plane. What can you say about its y coordinate ?
Answer» ANSWER :y -COORDINATE is ZERO

Discussion

11861.	Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then the value of m and n are………..
Answer» `7, 6` `6, 3` `6, 4` `7, 4` ANSWER :C

Discussion

11862.	Length of major axis of ellipse 25x^2+9y^2=1 is ........ .
Answer» ANSWER :`2/3`

Discussion

11863.	The period of the function f(x) = lambda\| sin x\| + lambda^(2) \| cos x\| + g (lambda) is (lambdai)/(2), if lambda is
Answer» `1` `2` `3` `1//2` ANSWER :A

Discussion

11864.	The chord through (1, -2) cuts the curve 3x^(2)-y^(2)-2x+4y=0 in P and Q. Then PQ subtends at the origin an angle of
Answer» ANSWER :`pi//2`

Discussion

11865.	Solution of x^(2)+x+1=0 is
Answer» `+-i` `+-2I` `OMEGA` and `omega^(2)` `-omega` and `omega^(2)` ANSWER :C

Discussion

11866.	Assertion (A): A(x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)). The projection of AB on the line with D.C's (l,m,n) is l(x_(2)-x_(1)) +m(y_(2)-y_(1))+n(z_(2)-z_(1)) Reason (R ) : The projection of the join of A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) on yz plane is sqrt((y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2))
Answer» Both A and R are ture and R is the correct EXPLANATION of A Both A and R are true but R is not the correct explanation of A A is true but R is FLASE A is flase but R is true Answer :B

Discussion

11867.	The sum of infinite terms of the series cot^(-1)(2^(2)+1/2)+cot^(-1)(2^(3)+1/2^(2))+cot^(-1)(2^(4)+1/2^(3))+…=cot^(-1)k then k =
Answer» ANSWER :2

Discussion

11868.	Expand (2+x+x^(2) )^(3).
Answer» ANSWER :`=8+12x+18x^(2) + 13x^(3) + 9X^(4) + 3x^(5) + X^(6)`.

Discussion

11869.	2 sin x = \|x\| + ahas no solution for a in ((k sqrt(k))/(k)- 3, infty) then K is
Answer» 3 5 7 9 Answer :A

Discussion

11870.	The mean and standard deviation of six observation are 8 and 4 respectively. If each observation is multiplied by 3, Find the new mean and new standard deviation of the resulting obervations.
Answer» ANSWER :24, 12

Discussion

11871.	Evaluate the following limits : Lt_(xtooo)(1+2/x)^(3x)
Answer» ANSWER :`E^(6)`

Discussion

11872.	Write down all the subsets of the following sets : { phi }
Answer» ANSWER :`PHI, { phi }`

Discussion

11873.	Find the sum: (1)/(3) + (2)/(3^(2)) + (1)/(3^(3)) + (2)/(3^(4)) + (1)/(3^(5)) + (2)/(3^(6)) + …..oo
Answer» ANSWER :`(5)/(8)`s

Discussion

11874.	A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)," are the vetice of a triangle, then equation " \|{:(x,y,l),(x_1,y_1,1),(x_2,y_2,1):}\|+\|{:(x,y,l),(x_1,y_1,1),(x_3,y_3,1):}\|=o represents
Answer» the mediam through A the ALTITUDE through A the perpendicualr BISECTOR of BC the LINE JOING the centroid with a vertex Answer :A,D

Discussion

11875.	p implies q is false when .
Answer» <P>p and Q are TRUE p and q are FALSE p is true and q is false p is false and q is true Answer :C

Discussion

11876.	If bara,barb,barc " are unit vectors such that " bara+barb+barc=bar0, " then find the least value of " bara.barb+barb.barc+barc.bara.
Answer» ANSWER :`-(3)/2`

Discussion

11877.	If alpha,beta be the roots of x^(2)-px+q=0, find the value of alpha^(5)beta^(7)+alpha^(7)beta^(5) in terms of p and q.
Answer» ANSWER :`Q^(5)(p^(2)-2Q)`

Discussion

11878.	Find the angle between the lines whose slopes are -3 and -1/(2).
Answer» ANSWER : `theta=45^(@)`

Discussion

11879.	The ratio in which the line 3x+ 4y + 2 =0 divides the distance between the lines 3x + 4y + 5 =0 and 3x + 4y - 5 =0 is
Answer» `1:2` `3:7` `2:3` `2:5` ANSWER :B

Discussion

11880.	If p is the perpendicular distance from the origin to the straight line x/a+y/b=1, then 1/(a^(2))+1/(b^(2))=
Answer» <P>`1/p` `1/(p^(2))` `2/p` `2/(p^(2))` ANSWER :B

Discussion

11881.	If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=
Answer» A nA `(n+1)A` 0 Answer :B

Discussion

11882.	For a set of five true- or -false questionsno students has written the all - correct answer ,and no two students have given the same sequence of answer. What is the maximum number of students in the class , for this to be possible?
Answer» ANSWER :` 31 `

Discussion

11883.	Find equation of the line parallel to the line 3x-4y+2=0 and passing through the point (-2,3).
Answer» ANSWER :REQUIRED LINE if `3x-4y+18=0`.

Discussion

11884.	What is the 20^("th")term of the sequence defined by a_n=(n-1) (2-n) (3+n) ?
Answer» ANSWER :`- 7866`

Discussion

11885.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax+b)^(n)(cx+d)^(m)
Answer» ANSWER :`(ax+b)^(n-1)(cx+d)^(m-1)[MC(ax+b)+NA(cx+d)]`

Discussion

11886.	Theperpendicular distance from origin to the line passing through P(1,2) such that bisects the path intercepted between the axes is
Answer» `SQRT(5)` `4` `4//sqrt(5)` `sqrt(5)//4` ANSWER :C

Discussion

11887.	Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = {omega_(1), omega_(2), omega_(3), omega_(4), omega_(5), omega_(6), omega_(7)} Assignment omega_(1)" "omega_(2)" "omega_(3)" "omega_(4)" "omega_(5)" "omega_(6)' (a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (b) 1/7 1/7 1/7 1/7 1/7 1/7 1/7 (c) 0.1 0.2 0.3 0.4 0.5 - 0.6 - 0.7 (d) -0.1 0.2 0.3 0.4 -0.2 0.1 0.3 (e) 1/14 2/14 3/14 4/14 5/14 6/14 15/14
Answer» ANSWER :(a) YES, (B) Yes, (C) No, (d) No, (E) No.

Discussion

11888.	Statement-I: If x cos theta = y cos(120^(@) + theta) = zcos(theta + 240^(@)), then xy + yz + xz=0 Statement II: If cosalpha + cos(120^(@) + alpha) + cos(120^(@)-alpha)=0 Then which of the above statements is/are correct ?
Answer» Only I Only II Both I and II Neither I nor II Answer :C

Discussion

11889.	For the non null sets A and B , Acup(AcapB)' =…. .
Answer» ANSWER :U

Discussion

11890.	f:R-{0}rarrR-{0},f(x)=4x^3+3x^2+3x+4" then "x^3 f(1/x)= .......
Answer» ANSWER :F(X)

Discussion

11891.	If y = mx + 1 is tangentto the parabola y = 2 sqrt(x) , then find the value of m
Answer» ANSWER :1

Discussion

11892.	Find the equation of lineintersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.
Answer» ANSWER :`X - SQRT3 y + 2 sqrt3 = 0 `

Discussion

11893.	State whether each of the following set is finite or infinite: The set of letters in the English alphabet
Answer» ANSWER :FINITE

Discussion

11894.	If cos 3 x + sin (2 x - (7 pi)/(6)) = - 2 then x is equal to (k in Z)
Answer» `(PI)/3(6k+1)` `(pi)/3(6k-1)` `(pi)/3(2k+1)` `(pi)/3(2k-1)` ANSWER :D

Discussion

11895.	If y = sqrt(x + sqrt(x + sqrt(x + .....oo)))then (dy)/(dx) =
Answer» `1/(2y-1)` `(X)/(x+2y)` `1/(SQRT(1+4x))` `y/(2x+y)` ANSWER :A

Discussion

11896.	If f(x) = {{:(x+1, "when" , x lt 2),(2x-1, "when" ,x ge 2):}, then f'(2) is................ .
Answer» 0 1 2 does not exist Answer :D

Discussion

11897.	IQ of a person is given by the formula IQ= (MA)/(CA) xx 100, where MA is mental age and CA is chronological age. If 80 le IQ le 140 for a group of 12 years old children, find the range of their mental age.
Answer» ANSWER :`9.6 LE MA le 16.8`

Discussion

11898.	Write down the negation of following compound statements. All real numbers are rationals or irrationals.
Answer» ANSWER :not IRRATIONALS.

Discussion

11899.	Write the first five terms of each of the sequencesand obtain the corresponding series: a_1=-1,a_(n)=(a_(n-1))/n, n ge 2
Answer» ANSWER :`(-1) + (-(1)/(2)) + (-(1)/(6)) + (-(1)/(24)) + (-(1)/(120)) +` ……

Discussion

11900.	Find the number of 4-letter words with or without meaning which can be formed out of the letters of the word KENY when, The repetition of letters is not allowed. E is at first place.
Answer» ANSWER :24, 6,

Discussion

Explore topic-wise InterviewSolutions in .

If a line passing through the point P(1,1) makes an angle theta with the positive direction of x-axiss meets the coordinate axes at A and B such that AB=OP, O being the origin , then tantheta+cottheta=

If z ne 1 and (z^(2))/(z-1) is real, then the point represented by the complex number z lies

If the odds in favour of an event are 4 to 5 , find the probability that it will occur .

y = sin^(-1)2x+Tan^(-1)3x + Cos^(-1)2x+Cot^(-1)3x then (dy)/(dx)

cot7(1^@)/2-cot37(1^@)/2-cot52(1^@)/2+cot82(1^@)/2 =

Consider the sets phi, A={1,3}, B={1,5,9}, C={1,3,5,7,9}. Insert the symbol subset or cancel(subset) between each of the following pair of sets. (i) phi ....B (ii) A....B (iii) A.....C (iv) B.....C

If alpha,beta,gamma, are lengths of the altitudes of a triangle ABC with area Delta , then Delta^2/R^2(1/alpha^2+1/beta^2+1/gamma^2)=

Evaluate the following limits. Lt_(xto1)[(x-1)/(x^(2)-x)]

2tan^(-1)(cosx)=tan^(-1)(2cosecx) then x=

A point is in the XZ-plane. What can you say about its y coordinate ?

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then the value of m and n are………..

Length of major axis of ellipse 25x^2+9y^2=1 is ........ .

The period of the function f(x) = lambda| sin x| + lambda^(2) | cos x| + g (lambda) is (lambdai)/(2), if lambda is

The chord through (1, -2) cuts the curve 3x^(2)-y^(2)-2x+4y=0 in P and Q. Then PQ subtends at the origin an angle of

Solution of x^(2)+x+1=0 is

The sum of infinite terms of the series cot^(-1)(2^(2)+1/2)+cot^(-1)(2^(3)+1/2^(2))+cot^(-1)(2^(4)+1/2^(3))+…=cot^(-1)k then k =

Expand (2+x+x^(2) )^(3).

2 sin x = |x| + ahas no solution for a in ((k sqrt(k))/(k)- 3, infty) then K is

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

Evaluate the following limits : Lt_(xtooo)(1+2/x)^(3x)

Write down all the subsets of the following sets : { phi }

Find the sum: (1)/(3) + (2)/(3^(2)) + (1)/(3^(3)) + (2)/(3^(4)) + (1)/(3^(5)) + (2)/(3^(6)) + …..oo

A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)," are the vetice of a triangle, then equation " |{:(x,y,l),(x_1,y_1,1),(x_2,y_2,1):}|+|{:(x,y,l),(x_1,y_1,1),(x_3,y_3,1):}|=o represents

p implies q is false when .

If bara,barb,barc " are unit vectors such that " bara+barb+barc=bar0, " then find the least value of " bara.barb+barb.barc+barc.bara.

If alpha,beta be the roots of x^(2)-px+q=0, find the value of alpha^(5)beta^(7)+alpha^(7)beta^(5) in terms of p and q.

Find the angle between the lines whose slopes are -3 and -1/(2).

The ratio in which the line 3x+ 4y + 2 =0 divides the distance between the lines 3x + 4y + 5 =0 and 3x + 4y - 5 =0 is

If p is the perpendicular distance from the origin to the straight line x/a+y/b=1, then 1/(a^(2))+1/(b^(2))=

If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

For a set of five true- or -false questionsno students has written the all - correct answer ,and no two students have given the same sequence of answer. What is the maximum number of students in the class , for this to be possible?

Find equation of the line parallel to the line 3x-4y+2=0 and passing through the point (-2,3).

What is the 20^("th")term of the sequence defined by a_n=(n-1) (2-n) (3+n) ?

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax+b)^(n)(cx+d)^(m)

Theperpendicular distance from origin to the line passing through P(1,2) such that bisects the path intercepted between the axes is

Statement-I: If x cos theta = y cos(120^(@) + theta) = zcos(theta + 240^(@)), then xy + yz + xz=0 Statement II: If cosalpha + cos(120^(@) + alpha) + cos(120^(@)-alpha)=0 Then which of the above statements is/are correct ?

For the non null sets A and B , Acup(AcapB)' =…. .

f:R-{0}rarrR-{0},f(x)=4x^3+3x^2+3x+4" then "x^3 f(1/x)= .......

If y = mx + 1 is tangentto the parabola y = 2 sqrt(x) , then find the value of m

Find the equation of lineintersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

State whether each of the following set is finite or infinite: The set of letters in the English alphabet

If cos 3 x + sin (2 x - (7 pi)/(6)) = - 2 then x is equal to (k in Z)

If y = sqrt(x + sqrt(x + sqrt(x + .....oo)))then (dy)/(dx) =

If f(x) = {{:(x+1, "when" , x lt 2),(2x-1, "when" ,x ge 2):}, then f'(2) is................ .

IQ of a person is given by the formula IQ= (MA)/(CA) xx 100, where MA is mental age and CA is chronological age. If 80 le IQ le 140 for a group of 12 years old children, find the range of their mental age.

Write down the negation of following compound statements. All real numbers are rationals or irrationals.

Write the first five terms of each of the sequencesand obtain the corresponding series: a_1=-1,a_(n)=(a_(n-1))/n, n ge 2

Find the number of 4-letter words with or without meaning which can be formed out of the letters of the word KENY when, The repetition of letters is not allowed. E is at first place.