28278 + Interview Questions in Maths in Class 12 Page 27 InterviewSolution

1301.	Find all common tangents of the pairs of circles x^(2) +y^(2) +4x + 2y -4 =0 and x^(2)+y^(2) -4x -2y +4=0
Answer» ANSWER :`y-2 =0, y-3 =0 , x-1 =0,3x +4Y -5=0`

Discussion

1302.	Inverse of the matrix [[cos 2 theta,-sin 2 theta],[sin 2 theta , cos 2 theta]] is
Answer» `[[COS2THETA,-SIN2THETA],[sin2theta,cos2theta]]` is `[[cos2theta,sin2theta],[sin2theta,-cos2theta]]` is `[[cos2theta,sin2theta],[sin2theta,cos2theta]]` is `[[cos2theta,sin2theta],[-sin2theta,cos2theta]]` is Answer :D

Discussion

1303.	Let X_(1),X_(2),…….X_(n) be n observations,and let bar(x) be theirarithmeticmeanand sigma^(2) be theirvariance . Statement 1 : Arithmeticmeanof x_(1)+ 2,x_(2) + 2,x_(3) + 2,…..,x_(n) + 2 is bar(x) + 2 Statement2 : Varianceof x_(1)
Answer» Statemnet 1is TURE , STATEMENT 2 is ture, Statement 2 is a correct EXPLANATION for Statement 1 Statement 1 is ture Statement2 is FALSE Statement 1 is falsefalse, Statement2 is ture Statement 1 is ture , Statement2 is true, Statement 2 is correct explanationfor Statement 1 Answer :B

Discussion

1304.	Letx_(1),x_(2),………,x_(n)be n observation , and letbar(x)be thrirarithmeticmeanand sigma^(2)be theirvariance. Statement1 : Variance of 2x_(1),2x_(2),…..,2x_(n) is 4sigma^(2). Statement 2 : Arithmetic meanof 2x_(1),2x_(2),......,2x_(n) is 4 bar(x).
Answer» Statemnet 1is ture , Statement 2 is ture, Statement 2 is a correct EXPLANATION for Statement 1 Statement 1 is ture Statement2 is FALSE Statement 1 is falsefalse, Statement2 is ture Statement 1 is ture , Statement2 is true, Statement 2 is correct EXPLANATIONFOR Statement 1 Answer :B

Discussion

1305.	The plane (x)/(a)+(y)/(b)+(z)/(c )=3 meets the co-ordinate axes in A,B,C. The centroid of the triangle ABC is
Answer» `((a)/(3),(B)/(3),(C )/(3))` `((3)/(a),(3)/(b),(3)/(c ))` `((1)/(a),(1)/(b),(1)/(c ))` `(a,b,c)` ANSWER :D

Discussion

1306.	Determine the order and degree of the differential equation y' + y = e^(x)
Answer» ANSWER :ORDER 1; DEGREE 1

Discussion

1307.	Find the numerically greatest terms in the expansion of(3 + (2x)/(5))^12 whenx = 3/4
Answer» ANSWER :`T_2 = 12/10 .3^12`

Discussion

1308.	Write minors and cofactors of the elements of following determinant \|{:(1,-2),(4,3):}\|
Answer» ANSWER :`M_(11)=3,M_(12)=4,M_(21)=-2,M_(22)=1` `A_(11)=3,A_(12)-4,A_(21)=2,A_(22)=1`

Discussion

1309.	Let alpha be a complex p^(th) root of unity with alpha ne 1 . Let p numbers r_(1) , r_(2)…..r_(p) are selected one by one with replacement from a set S where S { 1 , 2 , 3 ..np} , p in N andn in N . Then probability that alpha_(bar r_(1)) , alpha_(barr _(2)) + ... + alpha_(bar r_(p)) = 0 is
Answer» INDEPENDENT of only Independent of both Independent of only `2//9` ANSWER :C

Discussion

1310.	An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of thefoci of the ellipse, the radius of the incircle of traingle OCS_(1) be 1 unit, adn OS_(1)=6 units The equation ofthe director circle of E is
Answer» `x^(2)+y^(2)=48.5` `x^(2)+y^(2)=sqrt(97)` `x^(2)+y^(2)=97` `x^(2)+y^(2)=sqrt(48.5)` Solution : `:.OS_(1)=ae=6,OC=b` Also,` CS_(1)=a` `:. "Area of " DeltaOCS_(1)=(1)/(2)=(OS_(1))xx(OC)=3b` `:.`Semi-perimeter of `DeltaOCS_(1)=(1)/(2)=(OS_(1)+OC+CS_(1))` `=(1)/(2)(6+a+b) ""(1)` `:.` In radius of `DeltaOCS_(1) ","( "Using" r=(Delta)/(S))` =` (3b)/((1)/(2)(6+a+b))=1""("Using"r=(Delta)/(S))` `or 5b=6+a""(2)` Also, `b^(2)=a^(2)-a^(2)e^(2)=a^(2)-36""(3)` From (2), we get `25(a^(2)-36)=36+a^(2)+12a` `or 2a^(2)-a-78=0` `a=(13)/(2),-6` `:. a=(13)/(2) and b=(5)/(2)` Area or ellipse `=piab=(65pi)/(4)` sq. UNIT Perimeter of `DeltaOCS_(1)=6+a+b=6+(13)/(2)+(5)/(2)=15` UNITS The equation of DIRECTOR circle is `x^(2)+y^(2)=a^(2)+b^(2)` or `x^(2)+y^(2)=(97)/(2)`

Discussion

1311.	An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of thefoci of the ellipse, the radius of the incircle of traingle OCS_(1) be 1 unit, adn OS_(1)=6 units The area of ellipe (E) is
Answer» `65pi//4` `64pi//5` `64pi` `65pi` Solution : `:.OS_(1)=ae=6,OC=b` Also,` CS_(1)=a` `:. "AREA of " DeltaOCS_(1)=(1)/(2)=(OS_(1))xx(OC)=3b` `:.`Semi-perimeter of `DeltaOCS_(1)=(1)/(2)=(OS_(1)+OC+CS_(1))` `=(1)/(2)(6+a+b) ""(1)` `:.` In radius of `DeltaOCS_(1) ","( "Using" r=(Delta)/(S))` =` (3b)/((1)/(2)(6+a+b))=1""("Using"r=(Delta)/(S))` `or 5b=6+a""(2)` Also, `b^(2)=a^(2)-a^(2)e^(2)=a^(2)-36""(3)` From (2), we GET `25(a^(2)-36)=36+a^(2)+12a` `or 2a^(2)-a-78=0` `a=(13)/(2),-6` `:. a=(13)/(2) and b=(5)/(2)` Area or ellipse `=piab=(65pi)/(4)` sq. unit Perimeter of `DeltaOCS_(1)=6+a+b=6+(13)/(2)+(5)/(2)=15` UNITS The equation of director circle is `x^(2)+y^(2)=a^(2)+b^(2)` or `x^(2)+y^(2)=(97)/(2)`

Discussion

1312.	f(x)= {((1)/(e^(4x) + 1)",",x ne 0),(0",",x = 0):} Examine the continuity of f(x) at x= 0
Answer» ANSWER :DISCONTINUOUS at X= 0

Discussion

1313.	Let S be a non-empty subset of R. consider the following statement : P: There is a rational number xinS such that xgt0. which of the following statements is the negation of the statement P?
Answer» `x in S` and `x LE 0 RARR x` is not rational There is rational number `x in S` such that `XLE0`. There is no rational number `x in S` such that `xle0`. Every rational number `x in S` SATISFIES `xle0` Solution :P: There is a rational BUMBER `x in S` such that `x gt0` `~p `: Every rational number `x in S` satisfies `xle0`

Discussion

1314.	If 1/2lt\|x\|lt1 then which of the following are real ?
Answer» `SQRT(3)`when `x GT1` `2-sqrt(3)` when `0ltx lt 1` `2+sqrt(3)` when `0lt x lt 1` `-(1)/sqrt(3)` when `x gt2` Answer :a,b,d

Discussion

1315.	Find the number of 5 letter words that can be formed using the letters of the word “NATURE' that begin and end with vowel when repetitions are allowed.
Answer» ANSWER :`6^4`

Discussion

1316.	The value of 2^(n)n!(1.3.5.....(2n-1)) is
Answer» `(2N)!` `(4N)!` `((2n)!)/(N)` `n!` ANSWER :A

Discussion

1317.	The perimeter of rectangle ABCD is 96 cm. The ratio of the side lengths AB : BC is 3:5. What is the length, in centimeters of bar(AB)?
Answer» 6 18 30 36 Answer :B

Discussion

1318.	If f(x) = (X^(2) -1)^(7), then f^((14))(x) is equal to
Answer» 0 2! 7! 14! ANSWER :D

Discussion

1319.	Obtain the parametric equation of each of the following circles. 4(x^(2)+y^(2))=9
Answer» Answer :` x= (3)/(2) COS THETA , y =(3)/(2)sin theta`

Discussion

1320.	A die is rolled twice. Getting a number greater than 4 is called a 'Success'. Let the random variable X is equal to the number of successes then mean of X is
Answer» `(1)/(3)` `(2)/(3)` `(3)/(4)` `(1)/(4)` Answer :B

Discussion

1321.	The value of int_(1)^(a)[x] f' (x) dx, a gt 1, where [x] denotes the greatest integer not exceeding x is
Answer» `AF(a)-{F(1)+f(2)+....+ f([a])}` `[a]f(a)-{f(1)+f(2)+....+f([a])}` `[a]f([a])-{f(1)+f(2)+....+f(a)}` `af([a])-{f(1)+f(2)+....+f(a)}` Answer :B

Discussion

1322.	Solve as directed : Convert to linear inequality and solve for natural numbers: (x-2) (x-3) lt (x +3) (x-1)
Answer» SOLUTION : (x-2) (x-3) `lt` (x +3) (x-1) `RARR x^2 - 5X + 6 lt x^2 + 2X-3` `rArr -5x + 6 lt 2x - 3` `rArr -5x - 2x lt -3 -6 `rArr -7X lt -9 `rArr x gt 9/7` If x `in` N the solution set is S = { 2,3,4…….}

Discussion

1323.	If y = (3x^(2) - 9x + 5)^(9) find (dy)/(dx).
Answer» ANSWER :`27(3X^(2)-9x+5)^(8)(2x-3)`

Discussion

1324.	Show that the focal chord of the parabola y^(2)=4ax, which makes an angle alpha with the x-axis, is of length 4a cosec^(2) alpha.
Answer» Answer :`=a{4 cot^(2) alpha +4}=4A COSEC^(2) alpha""[because t_2 +t_1 =2 cot alpha and t_1 t_2 =-1]`

Discussion

1325.	Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2). f(3) is equal to
Answer» F(0) 4+f(0) 9+f(0) 16+f(0) ANSWER :d

Discussion

1326.	A random variable X takes four values with probabilities (1+3x)/(4), (1-x), (1+2x)/(4) and (1-4x)/(4). Find the set of values of x for the variable X to have probability distribution.
Answer» ANSWER :`-(1)/(3) le X le (1)/(4)`

Discussion

1327.	Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15^(@) with the ground. Let d be the distance (in m) between their poles, then (2 - sqrt(3))d = ______________
Answer» ANSWER :`5.00`

Discussion

1328.	A questionpapercontains6questioneachhavinganalternative. Thenumberofwaysthatanexaminecananswer oneor morequestion is
Answer» 243 242 729 728 Answer :D

Discussion

1329.	A=[aij]_(mxxn) is a square matrix, ifa) m=nb) m>nc) m< n d) none of these
Answer» mltn mgtn m=n None of these. Answer :C

Discussion

1330.	Find the transpose of each of each of the following matrics: [[5],[1/2],[-1]]
Answer» SOLUTION :`[[5,1/2,-1]]`

Discussion

1331.	A number x is chosen at random from the set {1,2,3,4,. . . . ,100} . Define the events A =the chosen number x satisfies((x - 10) (x - 50))/((x - 30)) ge 0 . Then P(A) is
Answer» `0 . 71` `0 . 70` `0 . 51` `0 . 20` ANSWER :A

Discussion

1332.	The roots of (z-1)^n=i(z+1)^n are plotted on the argand plane they are
Answer» on X = 0 concyclic on a PARABOLA on y = 0 Answer :A

Discussion

1333.	Dot product of a vector vec(a) with hati+hatj-3hatk,hati+3hatj-2hatk and 2hati+hatj+4hatk are 0, 5 and 8 respectively. Find the vector.
Answer» ANSWER :`hati+2hatj+hatk`

Discussion

1334.	The sum to infinite terms of the series (3)/(10)+(3.7)/(10.15)+(3.7.9)/(10.15.20)+..." to " oo is
Answer» `root4(125)-1` `(5sqrt(5))/(3sqrt(3))-(8)/(5)` `root(3)(4)-(4)/(3)` `SQRT((5)/(3))-(6)/(5)` Answer :B

Discussion

1335.	If [x] represents greatest integer le x then int_(0)^(sqrt(2))[x^(2)]dx=
Answer» `2-SQRT(2)` `2+sqrt(2)` `sqrt(2)+1` `sqrt(2)-1` ANSWER :D

Discussion

1336.	Following is the graph of y = f'(x) and f(0) = 0 . (a) What type of function y = f'(x) is ? Odd or even? (b) What type of function y = f(x) is ? Odd or even? (c) What is the value of int_(-a)^(a) f(x) dx? (d) Has y = f(x) point of inflection? (e) What is the nature of y = f(x)? Monotonic or non-monotonic?
Answer» Solution :(a) The graph ofy = f'(x) is symmetrical about the y-axis, so f(x) is an even FUNCTION. (b) f(0) = 0, so f(x) is an odd function [derivative of an odd function is even]. (c) Asf(x) is odd, so `UNDERSET(-a)overset(a) int f(x) dx = 0` (d) `f''(x) gt 0 as x lt 0 and f''(x) lt 0 "as " x gt 0`. THEREFORE, x = 0 is the point of INFLEXION. (e) ` f'(x) le 0, forallx,` so f(x) is always decreasing.

Discussion

1337.	If a line is perpendicular to z-axis and makes an angle measuring 60^0 with x-axis, then the angle it makes with y-axis measures_____.
Answer» `30^0` `60^0` `90^0` `120^0` ANSWER :C

Discussion

1338.	If (3,0) is the focus and y axis is the tangent at vertex. Then the equation of the parabola is
Answer» `x^2 = 12X` `y^2 = 12x` `y^2 = 3X` `x^2 = 3x` ANSWER :B

Discussion

1339.	Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for whichAtleast one root lies in (0, (1)/(2))
Answer» Answer :`alpha in (-OO, 2)uu(3, oo)`

Discussion

1340.	If f(x)=x^4+ 3x ^2 - 6x-2then thecoefficientofx^3inf(x+1) is
Answer» 24 `-24` `4` `-4` ANSWER :C

Discussion

1341.	The values of p and q for which the function f(x)={{:(,(sin(p+1)x+sinx)/(x),x lt 0),(,(qroot(x+x^(2))-sqrtx)/(x^(3//2)),x gt 0):} is continuous for all x in R, are
Answer» `p=3/2,q=1/2` `p=1/2,q=3/2` `p=1/2,q=-3/2` `p=5/2,q=1/2` ANSWER :A

Discussion

1342.	Let A(4,3),B(-4,3) and C(0,-5) be the vertices of triangle and P(5,0) let L,M and N be the feet of the perpendiculars drawn from P onto the sides BC,CA and AB respectively then
Answer» <P>area of `Delta LMN` is 5 sq. units the centroid of `DeltaLMN` does not exist the ORTHOCENTRE of `DeltaLMN` is the ORIGIN `L,M` and `N` are collinear Solution :`P` lies on circumcircle So `L,M,N` are collinear (i.e. Simson's line)

Discussion

1343.	Given eight distinguishable rings, the number of possible five ring arrangements on the four fingers (not the thumb) of one hand is (the order of the rings on each finger is significant, but it not required that such that each finger have a ring) is
Answer» `.^(8)C_(5)xx4^(5)` `.^(8)C_(5)xx4^(5)xx5!` `(.^(8)C_(5))^(2)xx5!` NONE of these Answer :C

Discussion

1344.	Integrate the following functions sqrt(x^2+4x+1)
Answer» SOLUTION :`INT SQRT(x^2+4x+1) DX` =`int sqrt(x^2+4x+4-(sqrt3)^2) dx` =`int sqrt((x+2)^2-(sqrt3)^2) dx` `(x+2)/2 sqrt((x+2)-(sqrt3)^2-(sqrt)^2/2 log\|x+2+sqrt(x^2+4x+1)\|+c` =`(x+2)/2 sqrt(x^2+4x+1)-3/2 log\|x+2+sqrt(x^2+4x=1)\|+c`

Discussion

1345.	The solution of(x^(2) y^(3) + x^(2)) + (y^(2) x^(3) + y^(2)) dy = 0 is
Answer» `(X^(3) + 1) (y^(3) + 1) = C` `(x^(3)-1) (y^(3)-1) =c` `(x^(3)-1) (y^(3)+1) = c` `(x^(3) +1) (y^(3) -1) =c` ANSWER :A

Discussion

1346.	Write the number of solution of the following system of equation. x-2y=0
Answer» SOLUTION :INFINITE

Discussion

1347.	The region M consists of all the points (x, y) satisfying the inequalities y ge 0, y lex and yle 2 - x. The region N which varies with the parameter t consists of all points which satisfy tle xlet + 1 AAt in [0, 1], then min(ar(M cap N)) is
Answer» `1/2` SQ. UNITS `3/4` sq. units `7/8` units `16/3` sq. units Answer :B

Discussion

1348.	A (-1,2-3), B(5,0,-6), C(0,4,-1) are three points, Show that direction cosines of the bisectors oflfloorBAC are proportional to (25,8,5)and (-11,20,23).
Answer» ANSWER :`(-11,20,23)`

Discussion

1349.	Let the nine different lettersA, B, C… I in {1, 2, 3, …, 9}. Then find the probability that product (A - 1)(B - 1) … (I - 9) is an even number.
Answer» Solution :Given set of NUMBER is {1, 2, ……, 9} in which 4 are EVEN and 5 are odd, so in the given product it is not possible to arrange to substract only even number from odd number, there must be at least one factor involving substraction of an odd number from another odd number. So at least one of the factor is even. Hence, product is ALWAYS even. `THEREFORE` Required probability = 1

Discussion

1350.	Find the general value of sin^-1(sqrt3/2)
Answer»

Discussion

Explore topic-wise InterviewSolutions in .

Find all common tangents of the pairs of circles x^(2) +y^(2) +4x + 2y -4 =0 and x^(2)+y^(2) -4x -2y +4=0

Inverse of the matrix [[cos 2 theta,-sin 2 theta],[sin 2 theta , cos 2 theta]] is

Let X_(1),X_(2),…….X_(n) be n observations,and let bar(x) be theirarithmeticmeanand sigma^(2) be theirvariance . Statement 1 : Arithmeticmeanof x_(1)+ 2,x_(2) + 2,x_(3) + 2,…..,x_(n) + 2 is bar(x) + 2 Statement2 : Varianceof x_(1)

Letx_(1),x_(2),………,x_(n)be n observation , and letbar(x)be thrirarithmeticmeanand sigma^(2)be theirvariance. Statement1 : Variance of 2x_(1),2x_(2),…..,2x_(n) is 4sigma^(2). Statement 2 : Arithmetic meanof 2x_(1),2x_(2),......,2x_(n) is 4 bar(x).

The plane (x)/(a)+(y)/(b)+(z)/(c )=3 meets the co-ordinate axes in A,B,C. The centroid of the triangle ABC is

Determine the order and degree of the differential equation y' + y = e^(x)

Find the numerically greatest terms in the expansion of(3 + (2x)/(5))^12 whenx = 3/4

Write minors and cofactors of the elements of following determinant |{:(1,-2),(4,3):}|

Let alpha be a complex p^(th) root of unity with alpha ne 1 . Let p numbers r_(1) , r_(2)…..r_(p) are selected one by one with replacement from a set S where S { 1 , 2 , 3 ..np} , p in N andn in N . Then probability that alpha_(bar r_(1)) , alpha_(barr _(2)) + ... + alpha_(bar r_(p)) = 0 is

An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of thefoci of the ellipse, the radius of the incircle of traingle OCS_(1) be 1 unit, adn OS_(1)=6 units The equation ofthe director circle of E is

An ellipse E,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1, centred at point O has AB and CD as its major and minor axes, respectively. Let S_(1) be one of thefoci of the ellipse, the radius of the incircle of traingle OCS_(1) be 1 unit, adn OS_(1)=6 units The area of ellipe (E) is

f(x)= {((1)/(e^(4x) + 1)",",x ne 0),(0",",x = 0):} Examine the continuity of f(x) at x= 0

Let S be a non-empty subset of R. consider the following statement : P: There is a rational number xinS such that xgt0. which of the following statements is the negation of the statement P?

If 1/2lt|x|lt1 then which of the following are real ?

Find the number of 5 letter words that can be formed using the letters of the word “NATURE' that begin and end with vowel when repetitions are allowed.

The value of 2^(n)n!(1.3.5.....(2n-1)) is

The perimeter of rectangle ABCD is 96 cm. The ratio of the side lengths AB : BC is 3:5. What is the length, in centimeters of bar(AB)?

If f(x) = (X^(2) -1)^(7), then f^((14))(x) is equal to

Obtain the parametric equation of each of the following circles. 4(x^(2)+y^(2))=9

A die is rolled twice. Getting a number greater than 4 is called a 'Success'. Let the random variable X is equal to the number of successes then mean of X is

The value of int_(1)^(a)[x] f' (x) dx, a gt 1, where [x] denotes the greatest integer not exceeding x is

Solve as directed : Convert to linear inequality and solve for natural numbers: (x-2) (x-3) lt (x +3) (x-1)

If y = (3x^(2) - 9x + 5)^(9) find (dy)/(dx).

Show that the focal chord of the parabola y^(2)=4ax, which makes an angle alpha with the x-axis, is of length 4a cosec^(2) alpha.

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2). f(3) is equal to

A random variable X takes four values with probabilities (1+3x)/(4), (1-x), (1+2x)/(4) and (1-4x)/(4). Find the set of values of x for the variable X to have probability distribution.

Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15^(@) with the ground. Let d be the distance (in m) between their poles, then (2 - sqrt(3))d = ______________

A questionpapercontains6questioneachhavinganalternative. Thenumberofwaysthatanexaminecananswer oneor morequestion is

A=[aij]_(mxxn) is a square matrix, ifa) m=nb) m>nc) m< n d) none of these

Find the transpose of each of each of the following matrics: [[5],[1/2],[-1]]

A number x is chosen at random from the set {1,2,3,4,. . . . ,100} . Define the events A =the chosen number x satisfies((x - 10) (x - 50))/((x - 30)) ge 0 . Then P(A) is

The roots of (z-1)^n=i(z+1)^n are plotted on the argand plane they are

Dot product of a vector vec(a) with hati+hatj-3hatk,hati+3hatj-2hatk and 2hati+hatj+4hatk are 0, 5 and 8 respectively. Find the vector.

The sum to infinite terms of the series (3)/(10)+(3.7)/(10.15)+(3.7.9)/(10.15.20)+..." to " oo is

If [x] represents greatest integer le x then int_(0)^(sqrt(2))[x^(2)]dx=

If a line is perpendicular to z-axis and makes an angle measuring 60^0 with x-axis, then the angle it makes with y-axis measures_____.

If (3,0) is the focus and y axis is the tangent at vertex. Then the equation of the parabola is

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for whichAtleast one root lies in (0, (1)/(2))

If f(x)=x^4+ 3x ^2 - 6x-2then thecoefficientofx^3inf(x+1) is

The values of p and q for which the function f(x)={{:(,(sin(p+1)x+sinx)/(x),x lt 0),(,(qroot(x+x^(2))-sqrtx)/(x^(3//2)),x gt 0):} is continuous for all x in R, are

Let A(4,3),B(-4,3) and C(0,-5) be the vertices of triangle and P(5,0) let L,M and N be the feet of the perpendiculars drawn from P onto the sides BC,CA and AB respectively then

Given eight distinguishable rings, the number of possible five ring arrangements on the four fingers (not the thumb) of one hand is (the order of the rings on each finger is significant, but it not required that such that each finger have a ring) is

Integrate the following functions sqrt(x^2+4x+1)

The solution of(x^(2) y^(3) + x^(2)) + (y^(2) x^(3) + y^(2)) dy = 0 is

Write the number of solution of the following system of equation. x-2y=0

The region M consists of all the points (x, y) satisfying the inequalities y ge 0, y lex and yle 2 - x. The region N which varies with the parameter t consists of all points which satisfy tle xlet + 1 AAt in [0, 1], then min(ar(M cap N)) is

A (-1,2-3), B(5,0,-6), C(0,4,-1) are three points, Show that direction cosines of the bisectors oflfloorBAC are proportional to (25,8,5)and (-11,20,23).

Let the nine different lettersA, B, C… I in {1, 2, 3, …, 9}. Then find the probability that product (A - 1)(B - 1) … (I - 9) is an even number.

Find the general value of sin^-1(sqrt3/2)