14949 + Interview Questions in Maths in Class 11 Page 282 InterviewSolution

14051.	If p = sin (A-B) sin (C-D) q = sin (B-C) sin (A-D) , r = sin (C-A) sin (B- D) then
Answer» <P>`p + q - r =0` `p+ q + r=0` `p - q + r=0` `p ^(3) + q ^(3) + r ^(3) = 3 PQR` Answer :B::D

Discussion

14052.	If thetaltpi/16 then sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=
Answer» 2 4 8 16 Answer :A

Discussion

14053.	If A sub B then A cap B = ..........
Answer» ANSWER :A

Discussion

14054.	If z=(1+7i)/((2-i)^(2) then......
Answer» `\|Z\|=2` `\|z\|=(1)/(2)` `arg(z)=(pi)/(4)` `arg(z)=(3PI)/(4)` ANSWER :D

Discussion

14055.	Identify the quantifier in the following statements and write thenegation of the statements. For every real numbers x,x is less than x+1.
Answer» Answer :The quantifier for the given statement is 'For every' It is true NEGATION of the given statement is ~p:For every real NUMBER X,x is not less than x +1

Discussion

14056.	If cos theta _(1) = 2 cos theta _(2),then tan (( theta _(1) + theta _(2))/(2)) tan (( theta _(1) - theta _(2))/(2)) is equal to
Answer» `1/3` `-1/3` 1 `-1` ANSWER :B

Discussion

14057.	Simplify the following sqrt(-18).sqrt(-2)
Answer» ANSWER :`-6`

Discussion

14058.	What is the geometric property possessed by the straight lines of each system given by y = mx + 8
Answer» SOLUTION :A FAMILY of LINE with y - INTERCEPT 8

Discussion

14059.	200 cuboidal logs of woods are arranged in such a way that there is 20 logs in the lower row, then 19 logs in the second row. There are 18 logs in the third row and so on. How many logs are there in the upper most row?
Answer» ANSWER :16 ROW, 5 LOGS

Discussion

14060.	Find: (i) the 7th term of 2,4,8,... (ii) the 9th term of 1,(1)/(2),(1)/(2^(2)), ... (iii) the nth term of (15)/(8) ,(3)/(8) ,(3)/(40)
Answer» Answer :(i) 128 (ii) `(1)/(126)` (iii) `(15)/(8) ((1)/(5))^(n-1)`

Discussion

14061.	The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.
Answer» ANSWER :`(1)/(20)xx400=20=2^(2)XX5`

Discussion

14062.	Asserton (A): Ifa gt 0, thenrange ofd+ a cos (x+ bx) is [d-=a,d+a] Reason(R ) : The periodof d+ a cos ( x+hx ) is (2pi)/( 1+b) Thenwhichone of thefollowingiscorrect ?
Answer» A is TRUER istrueand R is CORRECTEXPLANATION of A A is trueR istrueand Ris not correctexplanatinof A A istrueR isfalse A isfalseR istrue . Answer :2

Discussion

14063.	Evaluate the following limits. lim_(xto2)1/(x-2)-4/(x^(2)-4)
Answer» ANSWER :`1/4`

Discussion

14064.	If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3,2), then the equation of the line will be
Answer» `2X + 3Y =12` `3X + 2Y =12` `4x -3y =12` `5x-2y=10` Answer :A

Discussion

14065.	Which of the following quantities is/are positive?
Answer» `cos(TAN^(-1)(tan4))` `sin(cot^(-1)(cot4))` `tan(cos^(-1)(cos5))` `cot(sin^(-1)(sin4))` Answer :A::B::C

Discussion

14066.	A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45^@. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30^@. Then the speed ( in m//s) of the bird is
Answer» `14.64m//s` `16.4m//w` `12.64m//s` `15.64m//s` ANSWER :A

Discussion

14067.	The value of cos^(-1){1/(sqrt(2))("cos"(9pi)/10-"sin"(9pi)/10)} is
Answer» `(3PI)/20` `(7pi)/10` `(7pi)/20` `(17pi)/20` ANSWER :D

Discussion

14068.	If f(x)= tan x - x then The set of all the values of x in (0 ,2 pi) for which f(x) gt 0 is
Answer» `(0, PI)` `(pi, 2PI)` `(pi/2, (3PI)/(2))` None Answer :D

Discussion

14069.	Unit vector making angles pi/3, pi/3, (3pi)/4 with bar(i), bar(j), bar(k) is
Answer» `1/2bar(i)+1/2bar(J)-1/2bar(K)` `1/2bar(i)+1/2bar(j)-1/sqrt(2)BAR(k)` `1/2bar(i)-1/2bar(j)-1/sqrt(2)bar(k)` `bar(i)-bar(j)+bar(k)` ANSWER :A

Discussion

14070.	Let f(x) = (x - 1)(x - 2)(x - 3)…(x -n), n in N and f(')(n) = 5040. Then the value of n is …..
Answer»

Discussion

14071.	How many 4-digit numbers are there with no digit repeated?
Answer» ANSWER :4536

Discussion

14072.	A five figured number is formed by the digits 0,1,2,3,4, (without repetition). Find the probability that the number formed is divisible by 4.
Answer» ANSWER :`=(5)/(16)`.

Discussion

14073.	If A = sin 45^(@) + cos 45^(@) and B= sin 44^(@) + cos44^(@), then:
Answer» `A GT B` `A LT B` A = B A = 2B Answer :A

Discussion

14074.	When axes rotated through an angle alpha the transformed equation of x cos alpha + y sin alpha = p is
Answer» <P>X = p y = p x + p = 0 y + p = 0 Answer :A

Discussion

14075.	If f(2x+3y, 2x-7y)=20x, then f(x, y) equals
Answer» `7x-3y` `7x+3y` `3x-7y` `x-ky` ANSWER :B

Discussion

14076.	If theta_(2) and theta_(2) are the angles made by the lines (x^(2)+y^(2))(cos^(2) theta sin^(2)alpha+ sin^(2) theta)= (x tan alpha- y sin theta)^(2) with positive axis of x in the anticlock wise direction, if theta=(pi)/(6), tan theta_(1)+ tan theta_(2), equals
Answer» `(-(8)/(3)) SIN^(2) ALPHA` `(-8sqrt(3))"cosec" 2 alpha` `(-(8)/(3))"cosec" 2 alpha` `(-4 sqrt(3))"cosec" 2 alpha` Answer :C

Discussion

14077.	Find the roots of the equations. Q. 36x^(2)+23=60x.
Answer» ANSWER :`(5pmsqrt(2))/(6)`.

Discussion

14078.	If a sin x + b cos ( x+ theta) + b cos ( x-theta)=d, then the minimum of \| cos theta\| is equal to
Answer» `(1)/( 2 \|B\|) SQRT( d^(2) - a^(2) )` `(1)/( 2 \|a\|) sqrt( d^(2) - a^(2) )` `(1)/( 2 \|d\|) sqrt( d^(2) - a^(2) )` NONE of these Answer :A

Discussion

14079.	If sin alpha+ cos alpha= m then sin^(6)( alpha)+ cos^(6) (alpha)=
Answer» `(4-3(m^(2)-1)^(2))/(4)` `(4-3(m^(2)-1)^(2))/(4)` `(4+3(m^(2)+1)^(2))/(4)` `(4+3(m^(2)+1)^(2))/(4)` ANSWER :A

Discussion

14080.	Write the negation of the following statements: q: All cats scratch.
Answer» ANSWER :There EXISTS a CAT which does not SCRATCH.

Discussion

14081.	The radian measure of 15^(@) is…......
Answer» ANSWER :`(PI)/(12)`

Discussion

14082.	Using symbols sub" and " cancelsub fill in the following blanks : {2, 4, 6}…………{2, 4, 6, 8,…….,……}
Answer» ANSWER :`SUB`

Discussion

14083.	InDelta ABC , if a= sqrt3 + 1, b = 2, B = 45 ^(@),then A =
Answer» `30^(@)` `60v` `75^(@)` `45^(@)` Answer :C

Discussion

14084.	Write each of the statements in the form ''if p, then q'' p: It is necessary to have a password to log on to the server.
Answer» ANSWER :If you LOG on to the SERVER, then you have a PASSWORD.

Discussion

14085.	If lim_(x to 2)(tan(x-2){x^(2)+(k-2)x-2k})/(x^(2)-4x+4)=5 then k is equal to
Answer» 0 1 2 3 Answer :D

Discussion

14086.	Find the sum to n terms of the series in whose n^(th)terms is given by (2n-1)^2
Answer» ANSWER :`(N)/(3) (2n+1) (2n-1)`

Discussion

14087.	cos105^(@)+sin105^(@) = …………
Answer» `(1)/(2)` 1 `SQRT(2)` `(1)/(sqrt(2))` ANSWER :D

Discussion

14088.	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): (x+cosx)(x-tanx)
Answer» ANSWER :`-TAN^(2)X(x+cosx)+(x-tanx)(1-sinx)`

Discussion

14089.	Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .
Answer» ANSWER :(i)` a_(2)/b_(2), (II) = 0 `

Discussion

14090.	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^(2)+sinx)(p+qcosx)
Answer» Answer :`-Q sin x(AX^(2)+SINX)+(p+q cos x)(2ax +cosx)`

Discussion

14091.	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): (x^(3)+1)cosx
Answer» ANSWER :`-X^(2)sinx-sinx+2x COSX`

Discussion

14092.	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): x^(4)(5sinx-3cosx)
Answer» ANSWER :`x^(3)(5 x cos x+3x SIN x+20 sin x-12 COSX)`

Discussion

14093.	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): (sin(x+a))/(cosx)
Answer» ANSWER :`(COSA)/(COS^(2)X)`

Discussion

14094.	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): (a+bsinx)/(c+d cosx)
Answer» ANSWER :`(BC cos x+ad sin x+bd)/((c+d CSX)^(2))`

Discussion

14095.	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): sin^(n)x
Answer» ANSWER :`nsin^(n-1)xcosx`

Discussion

14096.	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): (secx-1)/(secx+1)
Answer» ANSWER :`(2secx TANX)/((secx+1)^(2))`

Discussion

14097.	Find the derivative of (sinx+cosx)/(sinx-cosx)
Answer» ANSWER :`(-2)/((sinx-cosx)^(2))`

Discussion

14098.	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): (x)/(sin^(n)x)
Answer» ANSWER :`(sinx-ncos X)/(SIN^(n+1)x)`

Discussion

14099.	Find the derivative of (x+secx)(x-tanx)
Answer» ANSWER :`(X+secx)(1-sec^(2)x)+(x-TANX).(1+secx tanx)`

Discussion

14100.	Find the derivative of (x)/(1+tanx)
Answer» ANSWER :`(1+tanx-X SEC^(2)x)/((1+tanx)^(2))`

Discussion

Explore topic-wise InterviewSolutions in .

If p = sin (A-B) sin (C-D) q = sin (B-C) sin (A-D) , r = sin (C-A) sin (B- D) then

If thetaltpi/16 then sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=

If A sub B then A cap B = ..........

If z=(1+7i)/((2-i)^(2) then......

Identify the quantifier in the following statements and write thenegation of the statements. For every real numbers x,x is less than x+1.

If cos theta _(1) = 2 cos theta _(2),then tan (( theta _(1) + theta _(2))/(2)) tan (( theta _(1) - theta _(2))/(2)) is equal to

Simplify the following sqrt(-18).sqrt(-2)

What is the geometric property possessed by the straight lines of each system given by y = mx + 8

200 cuboidal logs of woods are arranged in such a way that there is 20 logs in the lower row, then 19 logs in the second row. There are 18 logs in the third row and so on. How many logs are there in the upper most row?

Find: (i) the 7th term of 2,4,8,... (ii) the 9th term of 1,(1)/(2),(1)/(2^(2)), ... (iii) the nth term of (15)/(8) ,(3)/(8) ,(3)/(40)

The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.

Asserton (A): Ifa gt 0, thenrange ofd+ a cos (x+ bx) is [d-=a,d+a] Reason(R ) : The periodof d+ a cos ( x+hx ) is (2pi)/( 1+b) Thenwhichone of thefollowingiscorrect ?

Evaluate the following limits. lim_(xto2)1/(x-2)-4/(x^(2)-4)

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3,2), then the equation of the line will be

Which of the following quantities is/are positive?

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45^@. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30^@. Then the speed ( in m//s) of the bird is

The value of cos^(-1){1/(sqrt(2))("cos"(9pi)/10-"sin"(9pi)/10)} is

If f(x)= tan x - x then The set of all the values of x in (0 ,2 pi) for which f(x) gt 0 is

Unit vector making angles pi/3, pi/3, (3pi)/4 with bar(i), bar(j), bar(k) is

Let f(x) = (x - 1)(x - 2)(x - 3)…(x -n), n in N and f(')(n) = 5040. Then the value of n is …..

How many 4-digit numbers are there with no digit repeated?﻿

A five figured number is formed by the digits 0,1,2,3,4, (without repetition). Find the probability that the number formed is divisible by 4.

If A = sin 45^(@) + cos 45^(@) and B= sin 44^(@) + cos44^(@), then:

When axes rotated through an angle alpha the transformed equation of x cos alpha + y sin alpha = p is

If f(2x+3y, 2x-7y)=20x, then f(x, y) equals

If theta_(2) and theta_(2) are the angles made by the lines (x^(2)+y^(2))(cos^(2) theta sin^(2)alpha+ sin^(2) theta)= (x tan alpha- y sin theta)^(2) with positive axis of x in the anticlock wise direction, if theta=(pi)/(6), tan theta_(1)+ tan theta_(2), equals

Find the roots of the equations. Q. 36x^(2)+23=60x.

If a sin x + b cos ( x+ theta) + b cos ( x-theta)=d, then the minimum of | cos theta| is equal to

If sin alpha+ cos alpha= m then sin^(6)( alpha)+ cos^(6) (alpha)=

Write the negation of the following statements: q: All cats scratch.

The radian measure of 15^(@) is…......

Using symbols sub" and " cancelsub fill in the following blanks : {2, 4, 6}…………{2, 4, 6, 8,…….,……}

InDelta ABC , if a= sqrt3 + 1, b = 2, B = 45 ^(@),then A =

Write each of the statements in the form ''if p, then q'' p: It is necessary to have a password to log on to the server.

If lim_(x to 2)(tan(x-2){x^(2)+(k-2)x-2k})/(x^(2)-4x+4)=5 then k is equal to

Find the sum to n terms of the series in whose n^(th)terms is given by (2n-1)^2

cos105^(@)+sin105^(@) = …………

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): (x+cosx)(x-tanx)

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

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^(2)+sinx)(p+qcosx)

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): (x^(3)+1)cosx

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): x^(4)(5sinx-3cosx)

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): (sin(x+a))/(cosx)

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): (a+bsinx)/(c+d cosx)

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): sin^(n)x

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): (secx-1)/(secx+1)

Find the derivative of (sinx+cosx)/(sinx-cosx)

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): (x)/(sin^(n)x)

Find the derivative of (x+secx)(x-tanx)

Find the derivative of (x)/(1+tanx)

How many 4-digit numbers are there with no digit repeated?