14949 + Interview Questions in Maths in Class 11 Page 283 InterviewSolution

14101.	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^(2)cos((pi)/(4)))/(sinx)
Answer» Answer :`(X COS""(PI)/(4)(2sinx-x cosx))/(SQRT2 sin^(2)x)`

Discussion

14102.	Find the derivative of (4x+5sinx)
Answer»

Discussion

14103.	How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
Answer» ANSWER :Hence, Using the first 10 LETTERS of the English alphabet, 5040 LETTER - code can can be forned.

Discussion

14104.	If the equation x^(4) + 4x^(3) - 2x^(2) - 12 x + k = 0 has 4 real roots, then find set of values of k.
Answer» ANSWER :`-7 lt K lt 9 RARR k in (-7, 9)`

Discussion

14105.	Identify the Quantifiers in the following statements: There exists a triangle which is not equilateral.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

14106.	The mean and variance of 8 observations are respectively 9 and 9.25. If six observations are 4,6,7,8,12 and 13 then find the remaining two observations.
Answer» SOLUTION :NA

Discussion

14107.	Solve the general vlaue. 3-2cos theta -4sin theta - cos 2 theta + sin 2 theta =0
Answer» ANSWER :`N PI + (-1) ^(n) (pi)/(2) , 2 n pi, 2 n pi + (pi)/(2) `

Discussion

14108.	Solve cosx=(1)/(2).
Answer» ANSWER :`x=2npipm(PI)/(3),N INZ`

Discussion

14109.	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)/(px^(2)+qx+r)
Answer» ANSWER :`(-APX^(2)-2bpx+ar-bq)/((PX^(2)+qx+r)^(2))`

Discussion

14110.	Find the derivative of (1)/(ax^(2)+bx+c)
Answer» ANSWER :`(-(2ax+b))/((AX^(2)+bx+c)^(2))`

Discussion

14111.	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): ((1+(1)/(x))/(1-(1)/(x)))
Answer» ANSWER :`(-2)/((x-1)^(2)), x NE 0, 1`

Discussion

14112.	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)/(cx+d)
Answer» ANSWER :`(ad-bc)/((cx+ax)^(2))`

Discussion

14113.	If sinx + cos x = sqrt7/2 where x in 1^(st) quadrant , then tan""(x)/2 is equal to
Answer» `(3-sqrt7)/3` `(sqrt7-2)/3` `(4-sqrt7)/4` NONE of these Answer :B

Discussion

14114.	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)(vx+d)^(2)
Answer» ANSWER :`2C(ax+b)(cx+d)+a(cx+d)^(2)`

Discussion

14115.	Find the derivative of (px+q)((r)/(x)+s)
Answer» ANSWER :`(-QR)/(X^(2))+PS`

Discussion

14116.	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+a)
Answer» ANSWER :1

Discussion

14117.	A line passing through the point A(3bar(i)+bar(j)-bar(k)) and parallel to 2bar(i)-bar(j)+2bar(k). If P is a point such that AP=15 then bar(OP) is
Answer» `(3bar(i)+BAR(J)+bar(K)) PM5(2bar(i)+bar(j)+2bar(k))` `(3bar(i)+bar(j)+bar(k))pm5(2bar(i)-bar(j)+2bar(k))` `(3bar(i)+bar(j)-bar(k)) pm5 (2bar(i)-bar(j)-2bar(k))` `(3bar(i)+bar(j)-bar(k))pm15(2bar(i)-bar(j)-2bar(k))` Answer :B

Discussion

14118.	From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Cosec ^(2) theta =
Answer» `COT ^(2) alpha + cot ^(2) BETA + cot ^(2) GAMMA ` `COSEC ^(2) alpha + cosec ^(2) beta + cosec ^(2) gamma` `cosec alpha + cosec beta + cosec gamma ` ` cot ^(2) alpha - cot ^(2) beta - cot ^(2) gamma ` Answer :C

Discussion

14119.	Find the derivative of (cosx)/(1+sinx)
Answer» ANSWER :`(-1)/(1+sinx)`

Discussion

14120.	From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Sin thetamust be equal to
Answer» `(abc)/(SQRT (a ^(2) + B ^(2) c ^(2) sqrt (b^(2) b ^(2) + b ^(2) c ^(2) + c ^(a) a ^(2))))` `(AB + BC + ca)/(a ^(2) + b ^(2) + c ^(2))` `( a + b + c)/( a ^(2) +b ^(2) +c ^(2)) ` `(abc)/( sqrt (a ^(2) +b ^(2) + c ^(2)))` Answer :B

Discussion

14121.	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): "cosec "xcotx
Answer» ANSWER :`-"COSEC"^(3)X-"cosec "xcot^(2)x`

Discussion

14122.	From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Equation of plane OMN must be
Answer» `x/a - y/b + z/c =0` `x/a + y/b - z/c =0` `x/a - y/b + z/c =0` `x/a- y/b - z/c =0` ANSWER :A

Discussion

14123.	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)
Answer» ANSWER :`COS(x+a)`

Discussion

14124.	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)^(n)
Answer» ANSWER :`(ax+b)^(n-1)(cx+d)^(m-1)[MC(ax+b)+NA(cx+d)]`

Discussion

14125.	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)
Answer» ANSWER :`NA(ax+b)^(n-1)`

Discussion

14126.	Find the derivative of 4sqrtx-2
Answer» ANSWER :`(2)/(SQRTX)`

Discussion

14127.	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)/(x^(4))-(b)/(x^(2))+cosx
Answer» Answer :`(-4A)/(X^(5))+(2b)/(x^(3))-sinx`

Discussion

14128.	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): (px^(2)+qx+r)/(ax+b)
Answer» ANSWER :`(APX^(2)+2bpx+bq-ar)/((ax+b)^(2))`

Discussion

14129.	Find the values of a, b so that the function defined by f(x)={{:(5,if x le 2),(ax+b,if2lt x lt 10 "is"),(21,if x ge 10):}continuous function
Answer» ANSWER :a=2,b=1

Discussion

14130.	Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0 Find the vertices of the triangle
Answer» SOLUTION :(1,1), (-6,-6), (2,0)

Discussion

14131.	A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 m, the rate of increases in the area of the wave ring is
Answer» `0.75pi` sq.cm/sec 30 sq.cm/sec `30PI` sq.m/sec `0.4 PI` sq.cm/sec Answer :C

Discussion

14132.	Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2)
Answer» Answer :`(6x ^(2) COT ^(-1) X ^(3))/( 1 + x ^(6))`

Discussion

14133.	Find equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.
Answer» ANSWER :`X^(2)+y^(2)-ax-by=0`

Discussion

14134.	Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^(2)+3x+1) is
Answer» ANSWER :3

Discussion

14135.	Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x - 3y + 4 = 0 .
Answer» ANSWER :`(6/5, 7/5)`

Discussion

14136.	Evaluate (sqrt3+ sqrt2 )^6- ( sqrt3- sqrt2)^6 .
Answer» ANSWER :396`SQRT6`

Discussion

14137.	Sum of the measure of an angle of cyclic quadrilateral ABCD is .........radian.
Answer» ANSWER :`PI` RADIAN

Discussion

14138.	The volume of Parallelopiped with edges bara+barb,barb+barc,barc+bara is V_(1) and with edgs bara barb barc is V_(2) then V_(1)//V_(2)=
Answer» 2 3 1 4 Answer :A

Discussion

14139.	Show that thelines form an equilateral triangle and find its area (x+2a)^(2)-3y^(2)=0,x-a=0
Answer» ANSWER :`3sqrt(3)a^(2)` SQ. UNITS

Discussion

14140.	bar(AB) is diameter of circle with centre (4,2) . If point A is (-3,2) . Then second end point is ..............
Answer» ANSWER :(11,2)

Discussion

14141.	Iftan(pi//4 + theta ) + tan (pi//4 - theta ) =3 , " then " tan^(2)(pi//4 + theta ) + tan^(2)(pi//4 - theta ) =
Answer» 0 a 3A `a^(3)-3a` ANSWER :D

Discussion

14142.	If the increase in the side of a square is 4% Then find the approximate percentage of increase in the area of the square.
Answer» ANSWER :8

Discussion

14143.	Consider the experiment of rolling die. Let A be the event 'getting a prime number'. B be the event 'getting an odd number'. Write the sets representing the events (i) A or B (ii) A and B (iii) A but not B (iv) 'not A'.
Answer» ANSWER :`C NN D = PHI`

Discussion

14144.	Find the mean and variance for each of the data :First 10 multiple of 3.
Answer» ANSWER :74.25

Discussion

14145.	Solve the following equations : 9x^(2)+4=0
Answer» ANSWER :`(2)/(3)I,-(2)/(5)i`

Discussion

14146.	For all sets A and B, A - (A cap B)= A - B.
Answer» ANSWER :R.H.S.

Discussion

14147.	For any triangle ABC, prove that : a(cosC-cosB)=2(b-c)cos^(2)""(A)/(2)
Answer» ANSWER :`2(b-c)COS^(2)((A)/(2))`

Discussion

14148.	Let P = {theta , sin theta - cos theta = sqrt(2)cos theta} and Q = {theta , sin theta + cos theta = sqrt(2) sin theta) be two sets. Then
Answer» <P>`PcancesubQandQ-P!=cancelO` `Q cancelsub P` `P cancelsub` P = Q Answer :D

Discussion

14149.	Prove that, 3sin""(pi)/(6)sec""(pi)/(3)-4sin""(5pi)/(6)cot""(pi)/(4)=1
Answer» ANSWER :`=2-4 XX 1/2 =1 =R.H.S.`

Discussion

14150.	Let 0 lt A, B lt (pi)/(2) satisfying the equation 3 sin ^(2) A + 2 sin ^(2) B =1 and 3 sin 2A - 2 sin B =0 then A +2B =
Answer» `0` `pi//2` `pi//6` `3pi//2` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

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^(2)cos((pi)/(4)))/(sinx)

Find the derivative of (4x+5sinx)

How many 4-letter code can be formed using the first 10 letters of the English﻿ alphabet, if no letter can be repeated?﻿

If the equation x^(4) + 4x^(3) - 2x^(2) - 12 x + k = 0 has 4 real roots, then find set of values of k.

Identify the Quantifiers in the following statements: There exists a triangle which is not equilateral.

The mean and variance of 8 observations are respectively 9 and 9.25. If six observations are 4,6,7,8,12 and 13 then find the remaining two observations.

Solve the general vlaue. 3-2cos theta -4sin theta - cos 2 theta + sin 2 theta =0

Solve cosx=(1)/(2).

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)/(px^(2)+qx+r)

Find the derivative of (1)/(ax^(2)+bx+c)

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): ((1+(1)/(x))/(1-(1)/(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): (ax+b)/(cx+d)

If sinx + cos x = sqrt7/2 where x in 1^(st) quadrant , then tan""(x)/2 is equal to

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)(vx+d)^(2)

Find the derivative of (px+q)((r)/(x)+s)

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+a)

A line passing through the point A(3bar(i)+bar(j)-bar(k)) and parallel to 2bar(i)-bar(j)+2bar(k). If P is a point such that AP=15 then bar(OP) is

From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Cosec ^(2) theta =

Find the derivative of (cosx)/(1+sinx)

From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Sin thetamust be equal to

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): "cosec "xcotx

From any point P (a,b,c) perpendiculars PM &PN drawn to zx and xy-plane respectively. Let alpha, beta, gamma be the angles which OP makes with coordinate planes and theta be the angle which OP makes with the plane OMN must be Equation of plane OMN must be

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)

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)^(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)

Find the derivative of 4sqrtx-2

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)/(x^(4))-(b)/(x^(2))+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): (px^(2)+qx+r)/(ax+b)

Find the values of a, b so that the function defined by f(x)={{:(5,if x le 2),(ax+b,if2lt x lt 10 "is"),(21,if x ge 10):}continuous function

Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0 Find the vertices of the triangle

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 m, the rate of increases in the area of the wave ring is

Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2)

Find equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^(2)+3x+1) is

Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x - 3y + 4 = 0 .

Evaluate (sqrt3+ sqrt2 )^6- ( sqrt3- sqrt2)^6 .

Sum of the measure of an angle of cyclic quadrilateral ABCD is .........radian.

The volume of Parallelopiped with edges bara+barb,barb+barc,barc+bara is V_(1) and with edgs bara barb barc is V_(2) then V_(1)//V_(2)=

Show that thelines form an equilateral triangle and find its area (x+2a)^(2)-3y^(2)=0,x-a=0

bar(AB) is diameter of circle with centre (4,2) . If point A is (-3,2) . Then second end point is ..............

Iftan(pi//4 + theta ) + tan (pi//4 - theta ) =3 , " then " tan^(2)(pi//4 + theta ) + tan^(2)(pi//4 - theta ) =

If the increase in the side of a square is 4% Then find the approximate percentage of increase in the area of the square.

Consider the experiment of rolling die. Let A be the event 'getting a prime number'. B be the event 'getting an odd number'. Write the sets representing the events (i) A or B (ii) A and B (iii) A but not B (iv) 'not A'.

Find the mean and variance for each of the data :First 10 multiple of 3.

Solve the following equations : 9x^(2)+4=0

For all sets A and B, A - (A cap B)= A - B.

For any triangle ABC, prove that : a(cosC-cosB)=2(b-c)cos^(2)""(A)/(2)

Let P = {theta , sin theta - cos theta = sqrt(2)cos theta} and Q = {theta , sin theta + cos theta = sqrt(2) sin theta) be two sets. Then

Prove that, 3sin""(pi)/(6)sec""(pi)/(3)-4sin""(5pi)/(6)cot""(pi)/(4)=1

Let 0 lt A, B lt (pi)/(2) satisfying the equation 3 sin ^(2) A + 2 sin ^(2) B =1 and 3 sin 2A - 2 sin B =0 then A +2B =

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?