14949 + Interview Questions in Maths in Class 11 Page 273 InterviewSolution

13601.	The point on y-axis which is equidistant to (2,0,6), (-6,2,4) is
Answer» (1,2,0) (0,4,0) (0,-4,0) (-1,2,0) ANSWER :B

Discussion

13602.	Find the derivative of the w.r.t.x sin mx.cos nx
Answer» Answer :`m COS MX cos NX - N SIN mx sin nx `

Discussion

13603.	Write the negation of statement "every naturalnumber is an integer"?
Answer» ANSWER :EVERY NATURAL NUMBER is not an INTEGER

Discussion

13604.	If A be one A.M and p, q be two G.M.'s between two numbers then 2A is equal to…..
Answer» <P>`(p^(3) + Q^(3))/(pq)` `(p^(3)-q^(3))/(pq)` `(p^(2) + q^(2))/(2)` `(pq)/(2)` ANSWER :A

Discussion

13605.	If 2x^(2)-5xy+3y^(2)=0 represents two adjacent sides of a parallelogram and x+y+2=0 is equation of one of diagonal then other diagonal is
Answer» 9x-11y=0 9x+11y=0 11x-9y=0 11x+9y=0 Answer :A

Discussion

13606.	Solve the general vlaue. tan theta + 4 cot 2 theta + 1=0
Answer» ANSWER :`N PI - (pi)/(4)`

Discussion

13607.	Write the negation of statement sqrt(2) is not a complex number.
Answer» ANSWER :`SQRT2` is a COMPLEX NUMBER

Discussion

13608.	Solve the equation for0 le x le 2pi. sin theta cos theta = (1)/(2)
Answer» ANSWER :`(PI)/(4), (5PI)/(4)`

Discussion

13609.	with usual notation find the sum C_(0) + ""^(3)C_(1) + ""^(5)C_(2) + …+(2n+1)C_(n) where C_(r) is representing ""^(n)C_(r)
Answer» ANSWER :`N.2^(n)`

Discussion

13610.	Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find the slope of the line.
Answer» ANSWER : `1/(2)`

Discussion

13611.	While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. he obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance .
Answer» ANSWER :43.81

Discussion

13612.	If""^(n)C_r :""^(n)C_(r+1)=1 : 2 and^(n)C_(r+1): ""^(n)C_(r+2)= 2 : 3determine the values of n and r.
Answer» ANSWER :` N= 14, r=4`

Discussion

13613.	Write the following sets in roster form: C = {x : x isa two-digit natural number such that the sum of its digits is 8}
Answer» Answer :`C = {17, 26, 35, 44, 53, 62, 71, 80}`

Discussion

13614.	In DeltaABC,(b-c)/r_1+(c-a)/r_2+(a-b)/r_3=
Answer» ` 1` ` 3` ` 4` `0 ` ANSWER :D

Discussion

13615.	Write the principal solution of cot x=(-sqrt3) ?
Answer» Answer :`(5PI)/(6), (11pi)/(6) ,NPI + (5pi)/(6), n in Z`

Discussion

13616.	Expandthe expression (1-2x)^5
Answer» ANSWER :`1-10x + 40x^2 - 80x^3 + 80x^4 - 32x^5`

Discussion

13617.	The values of 'theta' satisfying sin5theta=sin3theta-sintheta and 0ltthetalt(pi)/(2)
Answer» `(pi)/(6),(pi)/(3)` `(pi)/(6),(pi)/(4)` `(pi)/(4),(pi)/(3)` `(pi)/(4),(pi)/(2)` ANSWER :B

Discussion

13618.	If barp = (2,1,3), barq = (-2,3,1), barr = (3,-2,4) and barj is the unit vector in the direction of Y -axis, then (2barp+3barq -4barr). barj =
Answer» 18 19 20 21 Answer :B

Discussion

13619.	Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the median through A
Answer» ANSWER : `y=4`

Discussion

13620.	Statement-I : f(x)=sqrt3sinx+cosx has a greatest value when x=pi/6 Statement-II : If xgt0,xy=1 the minimum value of x + y is 2 Which of the above statements is true
Answer» only I only II both I,II neither I nor II Answer :B

Discussion

13621.	Sove that \|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))\|^(2)=\|(1+a^(2)+a^(4),1+ab+a^(2)b^(2),1+ac+a^(2)c^(2)),(1+ab+a^(2)b^(2),1+b^(2)+b^(4),1+bc+b^(2)c^(2)),(1+ac+a^(2)c^(2),1+ba+b^(2)c^(2),1+c^(2)+c^(4))\|and hence show RHS determinent is =(a-b)^(2)(b-c)^(2)(c-a)^(2)
Answer» ANSWER : RHS DETERMINENT is `=(a-b)^(2)(b-c)^(2)(c-a)^(2)`

Discussion

13622.	If n is odd then n^2 is odd ' compound statement is false .
Answer» ANSWER :FALSE STATEMENT

Discussion

13623.	If the lines y = 3x + 1 " and " 2y = x + 3 are equally inclined to the liney = mx + 4,find the value of m.
Answer» Answer :`(1 PM 5 SQRT 2)/7`

Discussion

13624.	If x sin(a+y) = siny then (dy)/(dx) is equal to
Answer» `(SIN^2(a+y))/(SINA)` `(sina)/(sin^2(a+y))` `(sin(a+y))/(sina)` `(sina)/(sin(a+y))` ANSWER :A

Discussion

13625.	Find the derivative of the following functions from first principle: cos(x-(pi)/(8))
Answer» ANSWER :`-SIN(X-(PI)/(8))`

Discussion

13626.	Two vertices ofa triangle are (5,-1) and (-2,3). If the orthocentre of the triangle is the origin, find the third vertex.
Answer» ANSWER :`A=(-4,-7)`

Discussion

13627.	Write the sample space in each of the following : A coin is tossed four times.
Answer» ANSWER :{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}

Discussion

13628.	If the system of equations 3x-2y+z=0, lamdax-14y+15z=0,x+2y-3z=0 have non zero solution zero lamda=
Answer» Both A and R are TRUE and R is the correct EXPLANATION of A Both A and R are true and R is not correct explanation of A A is true but R is FALSE A is false but R is true ANSWER :A

Discussion

13629.	How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?
Answer» ANSWER :120

Discussion

13630.	Evaluate overset(13) underset(n=1) sum (i^(n)+i^(n+1)) , wheren in N.
Answer» ANSWER :`i-1`

Discussion

13631.	How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel?
Answer» ANSWER :(i) 30, (II) 360

Discussion

13632.	If bara = 2bari - barj, barb = 4barj + bark, barc = 3bark then (2bara +barb+barc). (-barb+2barc) xx barc =
Answer» 48 28 `-28` `-48` ANSWER :D

Discussion

13633.	If z_(1) and z_(2) are two complex numbers such that \|z_(1)\|= \|z_(2)\|, then is it necessary that z_(1) = z_(2)
Answer» ANSWER :`a_(1)=a_(2) and b_(1)= b_(2)`

Discussion

13634.	Daily absence from a school during three weeksis recorded as follows : Draw a graph , illustratingthe above data . Calculatethe 5 - daysmovingaverage and plot them on the samegraph.
Answer» Answer :TREND value are` 29, 32 , 36 . 8 , 41.2 , 46.2 , 50 . 8 , 53. 6 , 54 , 57.6 , 56.2 , 53.8.`

Discussion

13635.	The relation between D_(5) and Q_(2) is :
Answer» (a)`D_(5) gt Q_(2)` (b)`D_(5) NE Q_(2)` (C)`D_(5) = Q_(2)` (d)` Q_(2) = D_(5)` Answer :C

Discussion

13636.	A person in aballoon, who has ascended verticallly from flat land at the sea level, observes the angle of depression of a ship at anchor to be 30^(@). After descending verticallly 600 metres, he finds the angle of depression to be 15^(@). The horizontal distance of the ship from the foot of ascent in metres is
Answer» `300(3+sqrt(3))` `300(3+2sqrt(3))` `150(3+2sqrt(3))` `150(3-2sqrt(3))` ANSWER :B

Discussion

13637.	Semi vertical angle of cone is alpha . Plane intersects vertical axis at an angle beta . If alpha = beta then cross section of cone is parabola.
Answer» ANSWER :TRUE STATEMENT

Discussion

13638.	Write the first four terms of the sequence whose nth term is given (2^(n))/(n^(2))
Answer» ANSWER :`(1)/(2) , 1, (8)/(9) ,1 `

Discussion

13639.	Show that Lim_(x to 0 ) 1/xdoes not exist .
Answer» ANSWER :`Lim_(X to 0 ) f(x) = oo and Lim _(x to 0 ) f(x) = 0 `

Discussion

13640.	If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
Answer» ANSWER :`R - Q` = The SET of irrational NUMBERS.

Discussion

13641.	A plane is parallel to two lines whose direction ratios are (1,0,-1) and (-1, 1,0) and it contains the point (1, 1, 1). If it cuts coordinate axesatA, B, C. If V is the volumeof the tetrahedron OABC then2V is
Answer» ANSWER :9

Discussion

13642.	Let U = {1,2,3,4,5,6,7}, A = {1,5,6} and B = {1,2,6,7}.Find A' and B'
Answer» SOLUTION :{2,3,4,7},{3,4,5}

Discussion

13643.	In Delta ABC if b+c:c+a:a+b=11:12:13, then cos A: cos B: cos C=
Answer» ` 7 : 9 : 4` ` 7 : 19 : 25 ` ` 7 :2: 24` ` 7 :9 : 23` ANSWER :B

Discussion

13644.	Statement I: If sin alpha = 12/13, (0 lt alpha lt pi/2) and cos beta =-3/5,(pi lt beta lt (3pi)/2), then sin(alpha + beta) = 56/65 Statement II : If theta and phi, are angles in the first quadrant such that tan theta =1/7 and sin phi =1/sqrt(10), then theta + 2phi = 45^(@) Which of the above statements is correct?
Answer» Only I Only II Both I & II NEITHER I nor II ANSWER :B

Discussion

13645.	lim_(xrarr1)(x+x^(2)+x^(3)+...+x^(10)-10)/(x-1)
Answer» ANSWER :55

Discussion

13646.	(x+1)/((x-1)^(2)(x-2))=
Answer» 0 1 3 4 Answer :B

Discussion

13647.	For what values of k the equation sinx+cos(k+x)+cos(k-x)=2 has real solution?
Answer» `n PI -(pi)/6 le k le n pi+(pi)/6, n in Z` `npi+(pi)/3le k le n pi -(pi)/3, n in Z` `n pi+(pi)/2 le k le n pi -(pi)/2, NINZ` `n pi +(pi)/4 le k le n pi-(pi)/4, n in Z` ANSWER :A

Discussion

13648.	If a and b are positive quantities such that a gt b, the minimum value of a sec theta - b tan theta is
Answer» 2AB `SQRT(a^(2)-B^(2))` a-b `sqrt(a^(2)+b^(2))` ANSWER :A

Discussion

13649.	Inverse of (7,0) does not exists.
Answer» ANSWER :FALSE STATEMENT

Discussion

13650.	Using symbols sub" and " cancelsub fill in the following blanks : {""}………..{1, 4, 8}
Answer» ANSWER :`SUB`

Discussion

Explore topic-wise InterviewSolutions in .

The point on y-axis which is equidistant to (2,0,6), (-6,2,4) is

Find the derivative of the w.r.t.x sin mx.cos nx

Write the negation of statement "every naturalnumber is an integer"?

If A be one A.M and p, q be two G.M.'s between two numbers then 2A is equal to…..

If 2x^(2)-5xy+3y^(2)=0 represents two adjacent sides of a parallelogram and x+y+2=0 is equation of one of diagonal then other diagonal is

Solve the general vlaue. tan theta + 4 cot 2 theta + 1=0

Write the negation of statement sqrt(2) is not a complex number.

Solve the equation for0 le x le 2pi. sin theta cos theta = (1)/(2)

with usual notation find the sum C_(0) + ""^(3)C_(1) + ""^(5)C_(2) + …+(2n+1)C_(n) where C_(r) is representing ""^(n)C_(r)

Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find the slope of the line.

While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. he obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance .

If""^(n)C_r :""^(n)C_(r+1)=1 : 2 and^(n)C_(r+1): ""^(n)C_(r+2)= 2 : 3determine the values of n and r.

Write the following sets in roster form: C = {x : x isa two-digit natural number such that the sum of its digits is 8}

In DeltaABC,(b-c)/r_1+(c-a)/r_2+(a-b)/r_3=

Write the principal solution of cot x=(-sqrt3) ?

Expandthe expression (1-2x)^5

The values of 'theta' satisfying sin5theta=sin3theta-sintheta and 0ltthetalt(pi)/(2)

If barp = (2,1,3), barq = (-2,3,1), barr = (3,-2,4) and barj is the unit vector in the direction of Y -axis, then (2barp+3barq -4barr). barj =

Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the median through A

Statement-I : f(x)=sqrt3sinx+cosx has a greatest value when x=pi/6 Statement-II : If xgt0,xy=1 the minimum value of x + y is 2 Which of the above statements is true

Sove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|^(2)=|(1+a^(2)+a^(4),1+ab+a^(2)b^(2),1+ac+a^(2)c^(2)),(1+ab+a^(2)b^(2),1+b^(2)+b^(4),1+bc+b^(2)c^(2)),(1+ac+a^(2)c^(2),1+ba+b^(2)c^(2),1+c^(2)+c^(4))|and hence show RHS determinent is =(a-b)^(2)(b-c)^(2)(c-a)^(2)

If n is odd then n^2 is odd ' compound statement is false .

If the lines y = 3x + 1 " and " 2y = x + 3 are equally inclined to the liney = mx + 4,find the value of m.

If x sin(a+y) = siny then (dy)/(dx) is equal to

Find the derivative of the following functions from first principle: cos(x-(pi)/(8))

Two vertices ofa triangle are (5,-1) and (-2,3). If the orthocentre of the triangle is the origin, find the third vertex.

Write the sample space in each of the following : A coin is tossed four times.

If the system of equations 3x-2y+z=0, lamdax-14y+15z=0,x+2y-3z=0 have non zero solution zero lamda=

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9﻿ which are divisible by 10 and no digit is repeated ?﻿

Evaluate overset(13) underset(n=1) sum (i^(n)+i^(n+1)) , wheren in N.

How many words, with or without meaning can be made from the letters of the﻿ word MONDAY, assuming that no letter is repeated, if.﻿ (i) 4 letters are used at a time,﻿ (ii) all letters are used at a time,﻿ (iii) all letters are used but first letter is a vowel?

If bara = 2bari - barj, barb = 4barj + bark, barc = 3bark then (2bara +barb+barc). (-barb+2barc) xx barc =

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)|, then is it necessary that z_(1) = z_(2)

Daily absence from a school during three weeksis recorded as follows : Draw a graph , illustratingthe above data . Calculatethe 5 - daysmovingaverage and plot them on the samegraph.

The relation between D_(5) and Q_(2) is :

Semi vertical angle of cone is alpha . Plane intersects vertical axis at an angle beta . If alpha = beta then cross section of cone is parabola.

Write the first four terms of the sequence whose nth term is given (2^(n))/(n^(2))

Show that Lim_(x to 0 ) 1/xdoes not exist .

If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

A plane is parallel to two lines whose direction ratios are (1,0,-1) and (-1, 1,0) and it contains the point (1, 1, 1). If it cuts coordinate axesatA, B, C. If V is the volumeof the tetrahedron OABC then2V is

Let U = {1,2,3,4,5,6,7}, A = {1,5,6} and B = {1,2,6,7}.Find A' and B'

In Delta ABC if b+c:c+a:a+b=11:12:13, then cos A: cos B: cos C=

lim_(xrarr1)(x+x^(2)+x^(3)+...+x^(10)-10)/(x-1)

(x+1)/((x-1)^(2)(x-2))=

For what values of k the equation sinx+cos(k+x)+cos(k-x)=2 has real solution?

If a and b are positive quantities such that a gt b, the minimum value of a sec theta - b tan theta is

Inverse of (7,0) does not exists.

Using symbols sub" and " cancelsub fill in the following blanks : {""}………..{1, 4, 8}

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel?