14949 + Interview Questions in Maths in Class 11 Page 217 InterviewSolution

10801.	Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Answer» ANSWER :3050

Discussion

10802.	An analysis of daily wagesof casual laboures in two firmsA and B belonging to the sameindustry gives the following result : If the combined mean is Rs 116.82 find the standard deviation of wages of all casual labourers in the two firms taken in together .
Answer» ANSWER :`SIGMA = 8.25`

Discussion

10803.	Let A ={ 2,4,6,8,10} . Determine the truth value of each of the following : AA x in A,x is an even number.
Answer» ANSWER :TRUE

Discussion

10804.	If alpha in (0, pi/2) , then sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)) is always greater than or equal to (x != 0, -1)
Answer» 2 1 `2 TAN ALPHA` `2 Sec^(2) alpha` Answer :C

Discussion

10805.	A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i09ii) 12.
Answer» ANSWER :(i) `1/12` (II) `1/12`

Discussion

10806.	Observe the following statements: Assertion (A) : 2 cosh 3 cosh5 = cosh8 + cosh2 Reason (R ) : 2cosh alpha cosh beta = cosh (alpha+beta)- cosh(alpha-beta) Then the true statement among the following is
Answer» 1)A is true, R is true, `R rArr A` 2)A is false, R is true 3)A is true, R is false 4)A is false, R is false Answer :C

Discussion

10807.	If xis real , then the minimum value of (x^(2)-3x+4)/(x^(2)+3x+4)is :
Answer» 7 `-1/7` `-7` `1/7` ANSWER :D

Discussion

10808.	If z^(1) =2 -I, z_(2)=1+i, find \|(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)\|
Answer» ANSWER :`SQRT(2)`

Discussion

10809.	Show that the function f(x)=[cos(x^(10)+1)]^(1//3), x in Ris continuous function.
Answer» ANSWER :there is no POINT of discontinouity

Discussion

10810.	(i) Obtain the binomial expansion of (2- sqrt(3) )^(6) in the form a+b sqrt(3), where a and b are integers. State the corresponding result for the expansion ( 2+ sqrt(3) )^(6)
Answer» ANSWER :`1351 - 780 SQRT(3) , 1351 + 780 SQRT3`

Discussion

10811.	Find the component statements of the following and check whether they are true or not: sqrt(2) is a rational number or an irrational number.
Answer» ANSWER :TRUE.

Discussion

10812.	( cos2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =
Answer» 0 1 `1/2` 2 Answer :C

Discussion

10813.	If sum_(r=1)^(n)Cos^(-1)x_(r)=0," then "sum_(r=1)^(n)x_(r) equals to
Answer» 0 N `(n(n+1))/2` `n/2` ANSWER :B

Discussion

10814.	Find the mean, variance and standard deviation using short-cut method
Answer» ANSWER :93, 105.58, 10.27

Discussion

10815.	If z = x + iy and x +iy= (a+ib)/(a-ib) then x^2+y^2=1.
Answer» ANSWER :1

Discussion

10816.	If sin alpha=A sin(alpha + beta), A ne 0,then: The value of tan alpha is:
Answer» `(A SIN BETA)/(1-A COS beta)` `(A sin beta)/(1+A cos beta)` `(A cos beta)/(1-A sin beta)` `(A cos beta)/(1+A cos beta)` ANSWER :A

Discussion

10817.	Find the orthocentre of the triangle formed by the vertices (-2,-1),(6,-1),(2,5)
Answer» ANSWER :`(2,5/3)`

Discussion

10818.	Find the values of sin (-1110^(@))
Answer» Answer :` = - sin (3 XX 360 + 30^(@)) = - sin 30^(@) = - 1/2 `

Discussion

10819.	Find the co-ordinates of the orthocentre of a triangle whose vertices are (3,-1), (-1,2) and (0,0).
Answer» ANSWER :`"ORTHOCENTRE"=(-3,-4)`

Discussion

10820.	List all the elements of the following sets : A = {x : x is an odd natural number}
Answer» ANSWER :`A = {1, 3, 5, . . . }`

Discussion

10821.	Find the values of and p, if the equation x cos+ y sin = p is the normal form of the line sqrt3x + y + 2 = 0 .
Answer» ANSWER :`(7 PI)/6, 1`

Discussion

10822.	1 + 4 + 7 + 10 + … + x = 590, then the value of x is
Answer» 55 58 61 None of these ANSWER :B

Discussion

10823.	...........are the total numbers of ways to make a password of 5 digit for computer which contains 2 digits from computer which alphabet from 26 alphabets.
Answer» ANSWER :17,57, 600.

Discussion

10824.	A box contains 5 blue and 4 white balls. A person select two balls randomly from it. The probability that both the balls are of same colour is .....
Answer» `(4)/(9)` `(5)/(18)` `(5)/(108)` `(1)/(6)` ANSWER :A

Discussion

10825.	If A is any square matrix. Observe the following lists and matching from List - I to List - II is {:("List-I","List-II"),((A)A^(2)=A,"(1) Orthogonal matrix"),((B)A^(2)=I,"(2) Symmetric matrix"),((C)A^(2)=0,"(3) Idempotent matrix"),((D)A.A^(T)=A^(T)A=I,"(4) Nilpotent matrix"),(,"(5) Involutory matrix"):}
Answer» `{:(A,B,C,D),(2,5,4,1):}` `{:(A,B,C,D),(3,2,4,1):}` `{:(A,B,C,D),(3,5,4,1):}` `{:(A,B,C,D),(3,5,4,2):}` ANSWER :C

Discussion

10826.	Find the equation of pair of lines joining the origin to the points of intersection of the 2x+3y-2=0 and 2x^(2)-5xy-15y^(2)+4x+6y=0. Find the angle between them.
Answer» ANSWER :`(PI)/(2)`

Discussion

10827.	Find theperiodsof the followingfunctions sin (5 x+3) sin (x+11) 5 sin 4 x cos (4x+9)/(5)
Answer» ANSWER :A::B::C

Discussion

10828.	Which of the following sentences are statements? Give reasons for your answer The sum of all interior angles of a triangle is 180^(@).
Answer» Answer :This SENTENCE is ALWAYS true and therefore, it is a statement.

Discussion

10829.	Prove that Lim_(x to 0) (\|x\|)/x , x != 0does not exist .
Answer» ANSWER :` :'R.H.L != L.H.L:. Lim_(x to 0) F(x)` does not EXIST .

Discussion

10830.	The sides of a triangle inscribed in a given circle subtend angles alpha, beta, gamma at the centre then minimum value of Arithmetic mean of cos(alpha+pi//2), cos beta+pi//2)cos (gamma+pi//2)
Answer» `(SQRT(3))/(2)` `(2PI)/(3)` `(sqrt(2))/(3)` `-(sqrt(3))/(2)` ANSWER :D

Discussion

10831.	Given that tantheta=a/b find sin2thetaand cos2theta
Answer» SOLUTION :`(2AB)/(a^2+b^2) , `(b^2-a^2)/(b^2+a^2)`

Discussion

10832.	If tan alpha = (P)/(q) "where" alpha = 6 beta, alpha being an acute angle then (1)/(2) ["p cosec" 2 beta - q sec 2 beta] is equal to
Answer» `sqrt(p^(2) + Q^(2))` `sqrt(p^(2) - q^(2))` `sqrt(2P^(2) + q^(2))` `2 sqrt(p^(2) + q^(2))` Answer :A

Discussion

10833.	If (tan 3 A)/(tan A) = k, (k ne 1) then
Answer» `(cos A)/(cos 3 A) = (k^(2)-1)/(2K)` `(sin 3A)/(sin A) = (2k)/(k-1)` `k lt (1)/(3)` `k gt 3` Answer :B::C::D

Discussion

10834.	The sine of the angle between the straight line (x-2)/(3) = (y-3)/(4) = (z-4)/(5) and the pane 2x - 2y + z=5 is
Answer» `(sqrt5)/(3)` `(2SQRT2)/(5)` `(1)/(5sqrt2)` `(2sqrt3)/(5)` Answer :C

Discussion

10835.	A die is thrown, find the probability of following events : A number greater than or equal to 3 will appear.
Answer» ANSWER :`(2)/(3)`

Discussion

10836.	The value of sec x+2 cot 2x sin x lines in
Answer» [-1,1] [-2,2] [-3,3] [-4,4] ANSWER :B

Discussion

10837.	If cos x =- 3/5, x lies in the third quadrant, find the vlaues of other five trigonometric functions.
Answer» ANSWER :`3/4`

Discussion

10838.	P(n) : 4n + 1 , for n= ………….it is not a prime number
Answer» 1 3 7 11 Answer :D

Discussion

10839.	Evaluate the following limits. Lt_(xto0)(tan(tanx)-tanx)/(x^(2)tanx)
Answer» ANSWER :`1/3`

Discussion

10840.	If fL R to R is defined by f(x) = x^(4)+4, then find f^(-1)(-4).
Answer» ANSWER :`INFTY`

Discussion

10841.	If \|z-1\|^(2)=\|z\|^(2)+1 then in the grand plane, z lines an.....
Answer» `x^(2)+y^(2)=1` Imaginary axis Real axis `2x+3=0` ANSWER :B

Discussion

10842.	Write down in terms of x and n, the term containingx^3 in the expansion of (1- (x)/(n) )^(n) by the binomial theorem. if this term equals (7)/(8) when x=-2, and n is a positive integer, calculate the value of n.
Answer» Answer :`(- (N -1) (n-2))/( 6n^2) . X^(3) ; n =8`

Discussion

10843.	Evaluate""^(11)C_(2).
Answer» ANSWER :` 55`

Discussion

10844.	If sinA+sin2A=x, cosA+cos2A=y then cosA=
Answer» `X^(2)+y^(2)+2` `1/2(x^(2)+y^(2)-2)` `1/2(x^(2)+y^(2)+2)` `2(x^(2)+y^(2)+2)` ANSWER :B

Discussion

10845.	Compute (8!)/(6! xx 2!)
Answer» ANSWER :28

Discussion

10846.	Three numbers are in A.P. and their sum is 15. If 1,4 and 19 be added to these numbers respectively the number are in G.P. Find the numbers .
Answer» ANSWER :2,5,8, or 26,5,-16

Discussion

10847.	List all the elements of the following sets : B = {x : x is an integer, -(1)/(2)ltxlt(9)/(2)}
Answer» Answer :`={0, 1, 2, 3, 4}`

Discussion

10848.	If the origin is shifted to the point (1,2) then what will be the transform equation of the following equations, it is given that the new and old axes are parallel :(i) x^(2)+y^(2)-2x-4y=0(ii) 2x^(2)-y^(2)-4x+4y-3=0(iii) x^(2)+xy-2y^(2)-4x+7y-5=0(iv) 3x+y=6
Answer» ANSWER :`(i) X^(2)+Y^(2)=5` `(II) 2X^(2)-Y^(2)=1` `(iii) X^(2)+XY-2Y^(2)=0` `(iv) 3X+Y=1`

Discussion

10849.	If DeltaABC in a triangle in which sqrt(3) sin C=2 secA-tanA and one of sides is of length 2- then
Answer» `angleC=(pi)/(2)` `angleB=(pi)/(6)` triangle is Iscosceles rightangled Max area of TRIANGLES is `2 sqrt(3)` Answer :A::C::D

Discussion

10850.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. (A cap B)cap (B cup C)
Answer» ANSWER :`={4, 5}`

Discussion

Explore topic-wise InterviewSolutions in .

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

An analysis of daily wagesof casual laboures in two firmsA and B belonging to the sameindustry gives the following result : If the combined mean is Rs 116.82 find the standard deviation of wages of all casual labourers in the two firms taken in together .

Let A ={ 2,4,6,8,10} . Determine the truth value of each of the following : AA x in A,x is an even number.

If alpha in (0, pi/2) , then sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)) is always greater than or equal to (x != 0, -1)

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i09ii) 12.

Observe the following statements: Assertion (A) : 2 cosh 3 cosh5 = cosh8 + cosh2 Reason (R ) : 2cosh alpha cosh beta = cosh (alpha+beta)- cosh(alpha-beta) Then the true statement among the following is

If xis real , then the minimum value of (x^(2)-3x+4)/(x^(2)+3x+4)is :

If z^(1) =2 -I, z_(2)=1+i, find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

Show that the function f(x)=[cos(x^(10)+1)]^(1//3), x in Ris continuous function.

(i) Obtain the binomial expansion of (2- sqrt(3) )^(6) in the form a+b sqrt(3), where a and b are integers. State the corresponding result for the expansion ( 2+ sqrt(3) )^(6)

Find the component statements of the following and check whether they are true or not: sqrt(2) is a rational number or an irrational number.

( cos2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

If sum_(r=1)^(n)Cos^(-1)x_(r)=0," then "sum_(r=1)^(n)x_(r) equals to

Find the mean, variance and standard deviation using short-cut method

If z = x + iy and x +iy= (a+ib)/(a-ib) then x^2+y^2=1.

If sin alpha=A sin(alpha + beta), A ne 0,then: The value of tan alpha is:

Find the orthocentre of the triangle formed by the vertices (-2,-1),(6,-1),(2,5)

Find the values of sin (-1110^(@))

Find the co-ordinates of the orthocentre of a triangle whose vertices are (3,-1), (-1,2) and (0,0).

List all the elements of the following sets : A = {x : x is an odd natural number}

Find the values of and p, if the equation x cos+ y sin = p is the normal form of the line sqrt3x + y + 2 = 0 .

1 + 4 + 7 + 10 + … + x = 590, then the value of x is

...........are the total numbers of ways to make a password of 5 digit for computer which contains 2 digits from computer which alphabet from 26 alphabets.

A box contains 5 blue and 4 white balls. A person select two balls randomly from it. The probability that both the balls are of same colour is .....

Find the equation of pair of lines joining the origin to the points of intersection of the 2x+3y-2=0 and 2x^(2)-5xy-15y^(2)+4x+6y=0. Find the angle between them.

Find theperiodsof the followingfunctions sin (5 x+3) sin (x+11) 5 sin 4 x cos (4x+9)/(5)

Which of the following sentences are statements? Give reasons for your answer The sum of all interior angles of a triangle is 180^(@).

Prove that Lim_(x to 0) (|x|)/x , x != 0does not exist .

The sides of a triangle inscribed in a given circle subtend angles alpha, beta, gamma at the centre then minimum value of Arithmetic mean of cos(alpha+pi//2), cos beta+pi//2)cos (gamma+pi//2)

Given that tantheta=a/b find sin2thetaand cos2theta

If tan alpha = (P)/(q) "where" alpha = 6 beta, alpha being an acute angle then (1)/(2) ["p cosec" 2 beta - q sec 2 beta] is equal to

If (tan 3 A)/(tan A) = k, (k ne 1) then

The sine of the angle between the straight line (x-2)/(3) = (y-3)/(4) = (z-4)/(5) and the pane 2x - 2y + z=5 is

A die is thrown, find the probability of following events : A number greater than or equal to 3 will appear.

The value of sec x+2 cot 2x sin x lines in

If cos x =- 3/5, x lies in the third quadrant, find the vlaues of other five trigonometric functions.

P(n) : 4n + 1 , for n= ………….it is not a prime number

Evaluate the following limits. Lt_(xto0)(tan(tanx)-tanx)/(x^(2)tanx)

If fL R to R is defined by f(x) = x^(4)+4, then find f^(-1)(-4).

If |z-1|^(2)=|z|^(2)+1 then in the grand plane, z lines an.....

Write down in terms of x and n, the term containingx^3 in the expansion of (1- (x)/(n) )^(n) by the binomial theorem. if this term equals (7)/(8) when x=-2, and n is a positive integer, calculate the value of n.

Evaluate""^(11)C_(2).

If sinA+sin2A=x, cosA+cos2A=y then cosA=

Compute (8!)/(6! xx 2!)

Three numbers are in A.P. and their sum is 15. If 1,4 and 19 be added to these numbers respectively the number are in G.P. Find the numbers .

List all the elements of the following sets : B = {x : x is an integer, -(1)/(2)ltxlt(9)/(2)}

If the origin is shifted to the point (1,2) then what will be the transform equation of the following equations, it is given that the new and old axes are parallel :(i) x^(2)+y^(2)-2x-4y=0(ii) 2x^(2)-y^(2)-4x+4y-3=0(iii) x^(2)+xy-2y^(2)-4x+7y-5=0(iv) 3x+y=6

If DeltaABC in a triangle in which sqrt(3) sin C=2 secA-tanA and one of sides is of length 2- then

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. (A cap B)cap (B cup C)