14949 + Interview Questions in Maths in Class 11 Page 178 InterviewSolution

8851.	The sum of two numbers is 20 . If the product of the square of one number and cube of the other is maximum , then the numbers are
Answer» 8,12 12,9 4,16 7,13 Answer :A

Discussion

8852.	Show that tan (45^(@) - A) = (1 - tanA)/(1 + tanA)
Answer» ANSWER :`(1 - TAN A)/(1 + tan A)`

Discussion

8853.	A relation R from set A= {1, 3, 5, 7} to B= {2, 4, 6, 8} definded as follows: (x, y) in R hArr x gt y. Express R as set of ordered pairs.
Answer» ANSWER :`R= {(3,2) (5,2) (5,4) (7,2) (7,4) (7,6)}`

Discussion

8854.	d/(dx){sec^(-1)""(1)/(sqrt(1-x^2))+cot^(-1)""(sqrt(1-x^2))/x} =
Answer» `1/(SQRT(1-x^2))` `(-1)/(sqrt(1-x^2))` `(2)/(sqrt(1-x^2))` `(-2)/(sqrt(1-x^2))` ANSWER :C

Discussion

8855.	Rewrite each of the following statements in the form p if and only if q: q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
Answer» ANSWER :If you GET GRADE A if and only if you do all the home WORK regularly.

Discussion

8856.	Find six angles for which sin theta=-(sqrt(3))/(2).
Answer» ANSWER :`240^(@),300^(@),600^(@),660^(@),960^(@),1020^(@)`

Discussion

8857.	If a= ( b-c)sec theta " then "tan theta =
Answer» ` ( 2sqrt(bc))/( b-c) SIN ""(A)/(2) ` ` ( 2sqrt(bc))/( b+c) sin ""(A)/(2) ` ` ( 2sqrt(bc))/( b+c) COT""(A)/(2) ` ` ( 2sqrt(bc))/( b+c) TAN""(A)/(2) ` ANSWER :A

Discussion

8858.	A ray of light is incident along a line which meets another line 7x-y+1=0, at the point (0,1). The ray is then reflected from this point along the line y+2x=1. Then the equation of the line of incidence of the ray of light is
Answer» `41x-25y+25=0` `41x+25y-25=0` `41x-38y+38=0` `41x+38y-38=0` ANSWER :C

Discussion

8859.	Find the derivative of the following functions: 2tanx-7secx
Answer» ANSWER :`2SEC^(2)X-7sec x TANX`

Discussion

8860.	If sqrt(1+sinA)+sqrt(1-sinA)=2"sin"A/2" then"A/2 in
Answer» `(2NPI+pi/4, 2npi+(3PI)/4)` `(2npi-pi/4, 2npi+pi/4)` `(2npi-pi/2, 2npi+pi/2)` `(2npi+pi/4, 2npi+(5PI)/4)` ANSWER :A

Discussion

8861.	In triangle ABC, a=5,b=4, and cos(A+B)=(31)/(32). In this triangle c=
Answer» `SQRT(6)` 36 6 `(sqrt(319))/(2)` Answer :D

Discussion

8862.	Find the sum of the series to n terms and to infinity : (1)/(1.3)+ (1)/(3.5) +(1)/(5.7) +(1)/(7.9)+...
Answer» ANSWER :`S_(N)= (n)/(2n+1), S_(OO)=(1)/(2)`

Discussion

8863.	The mean and variance of 7 observations are 8 and 16 respectively. If five of the observation are 2, 4, 10, 12, 14. Find the remaining two observation.
Answer» ANSWER :6, 8

Discussion

8864.	If tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(-1)""6/x, then the value of x^(4) is
Answer» ANSWER :9

Discussion

8865.	If the equation x^(2)+py^(2)+y=a^(2) represents a pair of perpendicular lines then its point of intersection is
Answer» (1,a) (1,-a) (0,a) (0,2a) ANSWER :C

Discussion

8866.	If Delta=\|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}\| then \|{:(A_(1),A_(2),A_(3)),(B_(1),B_(2),B_(3)),(C_(1),C_(2),C_(3)):}\|=(A_(1),A_(2),A_(3) . . . . . " are cofactors of "a_(1),a_(2),a_(3) . . . . . )
Answer» `(DELTA^(2))/(2)` `2DELTA` `Delta^(2)` `Delta` ANSWER :C

Discussion

8867.	If the sums of the first 8 and 19 terms of an A.P. are 64 and 361 respectively, find (i) the common difference and (ii) the sum of n terms of the series.
Answer» ANSWER :d=2 , S=`N^(2)`

Discussion

8868.	Find the points of discontinuity of the function f, where f(x)={:{(x+2,if ,x ge2),(x^2,if,xlt2):}
Answer» ANSWER :`X in R`

Discussion

8869.	The vector equation of the plane passing through the points (1, -2, 5), (0, -5, -1), (-3, 5, 0) is
Answer» `BAR(r)=(1-s-t)(bar(i)-2bar(j)-5bar(K))+s(-5bar(j)-bar(k))+t(-3bar(i)+5bar(j))` `bar(r)=(1-s-t)(bar(i)+2bar(j)+3bar(k))+s(3bar(i)+2bar(j)+bar(k))+t(2bar(i)+bar(j)+3bar(k))` `bar(r)=(1-s-t)(bar(i)-2bar(j)+4bar(k))+s(-5bar(j)-bar(k))+t(-3bar(i)+5bar(j))` `bar(r)=(1-s-t)(bar(i)-2bar(j))+s(-5bar(j)-bar(k))+t(bar(i)+bar(j))` ANSWER :A

Discussion

8870.	Evaluate the following limits : Lim_(x to a) ((x+2)^(3//2) -(a+2)^(3//2))/(x-a)
Answer» ANSWER :`3/2 (a+2)^(1//2)`

Discussion

8871.	Ifa= 30, b = 18, c = 24then the descendingorder ofr_1, r_2,r_3is
Answer» ` r_1,r_3,r_2` ` r_3,r_2,r_1` ` r_2,r_3,r_1` ` r_1,r_2,r_3` ANSWER :A

Discussion

8872.	The triangle of maximum area that can be inscribed in a circle is
Answer» RIGHT ANGLED ISOSCELES right angled and isosceles EQUILATERAL ANSWER :D

Discussion

8873.	Rewrite each of the following statements in the form of conditional statements: The square of an odd number is odd.
Answer» ANSWER :ODD NUMBER.

Discussion

8874.	The value of lambda such that 2x^(2)-10xy+12y^(2)+5x+lambda y-3=0 represents a pair of lines is
Answer» `-10` `-9` -16 9 Answer :B

Discussion

8875.	Find a point on the x-axis, which is equidistant from the points (7,6) and (3, 4).
Answer» ANSWER :`(15/2, 0)`

Discussion

8876.	Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))/((sqrt(3) + 2i)-(sqrt(3)-isqrt(2))))
Answer» ANSWER :`0-I (7sqrt(2))/2`

Discussion

8877.	If 0 le x le 2pi and 2^(cosec^(2)x)sqrt(1/2y^(2)-y+1)lesqrt(2) then the number of ordered pairs of (x,y) is
Answer» ANSWER :2

Discussion

8878.	y = tantheta ( sin theta + cos theta) find (dy)/(d theta).
Answer» ANSWER :` SEC THETA`

Discussion

8879.	Which of the following is the contrapositive of the statement p implies q?
Answer» `qimpliesp` `~pimplies~q` `~qimplies~p` `pimplies~q` ANSWER :a

Discussion

8880.	Show that x = 7 and y = 8 touch the circle x^(2) + y^(2) - 4x - 6y -1 2 = 0 and find the points of contact.
Answer» ANSWER :`(7,3),(2,8)`

Discussion

8881.	Arrange the following in ascending order of their values (A) cosh2 + sinh2 (B) cosh2 - sinh2 (C ) cosh0 + sinh0 (D) (cosh2-sinh2)^(2)
Answer» A,B,D,C B,C,D,A D,B,C,A A,B,C,D ANSWER :C

Discussion

8882.	A coin is tossed thrice. Write the elements of an event that 3 heads are not obtained. Also give complement of that event.
Answer» ANSWER :`A'={(H,H,H)}`

Discussion

8883.	f(x) - log (x^(2) + 2) - log 3 in [-1, 1]
Answer» 0 1 `-1` does not exists Answer :A

Discussion

8884.	[bara barb barc]+[bara barc barb]=
Answer» `[BARA BARB BARC]` `2[bara barb barc]` `3[bara barb barc]` 0 Answer :D

Discussion

8885.	Calculate the variance and standard deviation of the observations : 11, 12, 13, . . . .. 20.
Answer» ANSWER :`SIGMA=2.87`, VARIANCE = `sigma^(2)=8.27`

Discussion

8886.	If the repetation is not allowed then we get .......... total numbers of 5 digits from the digits 0, 2,4,6 and 8.
Answer» ANSWER :96

Discussion

8887.	If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9bar(j)" then "bar(c)=
Answer» `2BAR(a)+BAR(B)` `bar(a)+2bar(b)` `bar(a)+3BAR(b)` `3bar(a)+bar(b)` ANSWER :D

Discussion

8888.	If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible by
Answer» `a-B` `a^(3) + b^(3)` `a+b` `a^(2) + b^(2)` ANSWER :C

Discussion

8889.	A family buys quantities of rice, wheat, fish, potato and coal whose prices are given below, in the ratio 3:1:3:2:2. Find the weighted aggregate price index.
Answer» ANSWER :`=118.60`

Discussion

8890.	If A= {-1, 2, 3} and B= {1, 3}, the determine B xxA
Answer» ANSWER :`{(1,-1), (1,2), (1,3),(3,-1), (3,2), (3,3)}`

Discussion

8891.	If 9x^(2)-24xy+ky^(2)-12x+16y-12=0 represents a pair of parallel lines, then
Answer» 2 4 8 16 Answer :D

Discussion

8892.	If the area of the triangle formed by the lines x=0, y=0, 3x+4y=a(a gt0) is 1, then
Answer» `SQRT(6)` `2sqrt(6)` `4sqrt(6)` `6sqrt(2)` ANSWER :B

Discussion

8893.	Equation of the line belonging to the system 3x+2y-8+lamda(2x-5y+1)=0 and having equal intercepts is
Answer» `x+y=0` `x+y=1` `x+y=2` `x+y=3` ANSWER :D

Discussion

8894.	If cos x = tan y, cot y = tan z and cot z = tan x, then sin x =
Answer» `(SQRT(5)+ 1)/(4)` `(sqrt(5)-1)/(4)` `sqrt(5) + 1)/(2)` `(sqrt(5) - 1)/(2)` Answer :D

Discussion

8895.	If alpha and beta are the roots of the equation 2x^(2)+3x+2=0, find the equation whose roots are alpha+1 and beta+1.
Answer» ANSWER :`2X^(2)-x+1=0`.

Discussion

8896.	If x = a cos^4 t , y = b sin^4 tthen (dy)/(dx) at t= pi/4 is
Answer» `(-B)/a` `b/a` `a/b` `(-a)/b` ANSWER :A

Discussion

8897.	If 270^(@) lt A lt 360^(@), 90^(@) lt B lt 180^(@) , cos A =5//13 , tan B=-15//8 " then " cos (A+B)=
Answer» `(140)/(221)` `(171)/(221)` `(140)/(171)` `(221)/(171)` ANSWER :B

Discussion

8898.	Evaluate the following limits : Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3)
Answer» ANSWER :`1/3`

Discussion

8899.	If (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_3), z_(3)) are the vertices of an equilateral triangle such that(x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2)=(x_(3)-2)^(3)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sumy_(1)+3sum z_(1)=
Answer» 6 18 24 60 Answer :d

Discussion

8900.	If the points (1,2) and (3,4) were to be on the opposite side of the line 3x-5y+a=0, then
Answer» `7ltalt11` `a=7` `a=11` `alt7` or ` agt11` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

The sum of two numbers is 20 . If the product of the square of one number and cube of the other is maximum , then the numbers are

Show that tan (45^(@) - A) = (1 - tanA)/(1 + tanA)

A relation R from set A= {1, 3, 5, 7} to B= {2, 4, 6, 8} definded as follows: (x, y) in R hArr x gt y. Express R as set of ordered pairs.

d/(dx){sec^(-1)""(1)/(sqrt(1-x^2))+cot^(-1)""(sqrt(1-x^2))/x} =

Rewrite each of the following statements in the form p if and only if q: q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Find six angles for which sin theta=-(sqrt(3))/(2).

If a= ( b-c)sec theta " then "tan theta =

A ray of light is incident along a line which meets another line 7x-y+1=0, at the point (0,1). The ray is then reflected from this point along the line y+2x=1. Then the equation of the line of incidence of the ray of light is

Find the derivative of the following functions: 2tanx-7secx

If sqrt(1+sinA)+sqrt(1-sinA)=2"sin"A/2" then"A/2 in

In triangle ABC, a=5,b=4, and cos(A+B)=(31)/(32). In this triangle c=

Find the sum of the series to n terms and to infinity : (1)/(1.3)+ (1)/(3.5) +(1)/(5.7) +(1)/(7.9)+...

The mean and variance of 7 observations are 8 and 16 respectively. If five of the observation are 2, 4, 10, 12, 14. Find the remaining two observation.

If tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(-1)""6/x, then the value of x^(4) is

If the equation x^(2)+py^(2)+y=a^(2) represents a pair of perpendicular lines then its point of intersection is

If Delta=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| then |{:(A_(1),A_(2),A_(3)),(B_(1),B_(2),B_(3)),(C_(1),C_(2),C_(3)):}|=(A_(1),A_(2),A_(3) . . . . . " are cofactors of "a_(1),a_(2),a_(3) . . . . . )

If the sums of the first 8 and 19 terms of an A.P. are 64 and 361 respectively, find (i) the common difference and (ii) the sum of n terms of the series.

Find the points of discontinuity of the function f, where f(x)={:{(x+2,if ,x ge2),(x^2,if,xlt2):}

The vector equation of the plane passing through the points (1, -2, 5), (0, -5, -1), (-3, 5, 0) is

Evaluate the following limits : Lim_(x to a) ((x+2)^(3//2) -(a+2)^(3//2))/(x-a)

Ifa= 30, b = 18, c = 24then the descendingorder ofr_1, r_2,r_3is

The triangle of maximum area that can be inscribed in a circle is

Rewrite each of the following statements in the form of conditional statements: The square of an odd number is odd.

The value of lambda such that 2x^(2)-10xy+12y^(2)+5x+lambda y-3=0 represents a pair of lines is

Find a point on the x-axis, which is equidistant from the points (7,6) and (3, 4).

Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))/((sqrt(3) + 2i)-(sqrt(3)-isqrt(2))))

If 0 le x le 2pi and 2^(cosec^(2)x)sqrt(1/2y^(2)-y+1)lesqrt(2) then the number of ordered pairs of (x,y) is

y = tantheta ( sin theta + cos theta) find (dy)/(d theta).

Which of the following is the contrapositive of the statement p implies q?

Show that x = 7 and y = 8 touch the circle x^(2) + y^(2) - 4x - 6y -1 2 = 0 and find the points of contact.

Arrange the following in ascending order of their values (A) cosh2 + sinh2 (B) cosh2 - sinh2 (C ) cosh0 + sinh0 (D) (cosh2-sinh2)^(2)

A coin is tossed thrice. Write the elements of an event that 3 heads are not obtained. Also give complement of that event.

f(x) - log (x^(2) + 2) - log 3 in [-1, 1]

[bara barb barc]+[bara barc barb]=

Calculate the variance and standard deviation of the observations : 11, 12, 13, . . . .. 20.

If the repetation is not allowed then we get .......... total numbers of 5 digits from the digits 0, 2,4,6 and 8.

If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9bar(j)" then "bar(c)=

If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible by

A family buys quantities of rice, wheat, fish, potato and coal whose prices are given below, in the ratio 3:1:3:2:2. Find the weighted aggregate price index.

If A= {-1, 2, 3} and B= {1, 3}, the determine B xxA

If 9x^(2)-24xy+ky^(2)-12x+16y-12=0 represents a pair of parallel lines, then

If the area of the triangle formed by the lines x=0, y=0, 3x+4y=a(a gt0) is 1, then

Equation of the line belonging to the system 3x+2y-8+lamda(2x-5y+1)=0 and having equal intercepts is

If cos x = tan y, cot y = tan z and cot z = tan x, then sin x =

If alpha and beta are the roots of the equation 2x^(2)+3x+2=0, find the equation whose roots are alpha+1 and beta+1.

If x = a cos^4 t , y = b sin^4 tthen (dy)/(dx) at t= pi/4 is

If 270^(@) lt A lt 360^(@), 90^(@) lt B lt 180^(@) , cos A =5//13 , tan B=-15//8 " then " cos (A+B)=

Evaluate the following limits : Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3)

If (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_3), z_(3)) are the vertices of an equilateral triangle such that(x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2)=(x_(3)-2)^(3)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sumy_(1)+3sum z_(1)=

If the points (1,2) and (3,4) were to be on the opposite side of the line 3x-5y+a=0, then