14949 + Interview Questions in Maths in Class 11 Page 19 InterviewSolution

901.	Write the conctrapositive and converse of the followig statements. (i) if x is a prime number, then x is odd. (ii)if the two lines are parallel, then they do not intersect in the same plane. (iii) something is cold imlies that it has low temperature. (iv) you cannot comprehend geometry if you do not know how to reson duductively. (v) x is an even number implies that x is divisible by 4.
Answer» Solution :(i) Given statement : if x is a prime number, then x is odd. CONTRAPOSITIVE : if x is not odd then x is not a prime number. Converse: if a number x is odd then x is a prime number . (ii) Given statement : if two lines are parallel,then they do not intersect in the same plane. Contrapositive : if two lines interset in a plane , then they are not parallel . converse: if two lines do not intersect in a plane, then they are parallel. (III) Given statement : something is COLD implies that it has low TEMPERATURE. Contrapositive : if something is not at low temperature, then it is not cold. Converse: if something is at low temperature , then it is cold. (iv) Given statement : you cannot comprehend geometry if you do not know how to REASON deductively. Contrapositive : if you know how to reason deductively , then you can comprehend geometry. Converse: if you do not know how to reason deductively , then you cannot comprehend geometry. (v) Given statement : x is an number implies that x is divisibile by 4. Contrapositive : x is not divisible by 4, then x is not an even number . Converse: If x is divisible 4, then x is an even number.

Discussion

902.	If sin x coshy = cos theta, cos x sinhy = sin theta then sinh^2 y =
Answer» `cos H^(2) x` `cos^(2) x` `cos h^(3) x` `sin h^(2) x` Answer :B

Discussion

903.	Obtain equation of circle in(x- 1)^(2) + y^(2) = 4
Answer» ANSWER :CENTRE (1,0),, RADIUS 2

Discussion

904.	Maximum value of (1)/(sqrt((7)sin x+ sqrt( 29) cos x+7))
Answer» `13` `1` `1//13` `49` ANSWER :B

Discussion

905.	Themaximum area of the rectangle whose sides pass through the vertices if a given rectangleof sides a and b is
Answer» `2(AB)` `(1)/(2)(a+B)^(2)` `(1)/(2)(a^(2)+b^(2))` `(1)/(2)(a^(2)-b^(2))` ANSWER :B

Discussion

906.	If the expansion of (x-1/(x^(2)))^(2n) contains a term independent of x , then n is a multiple of 2 .
Answer» ANSWER :FALSE

Discussion

907.	9^(7) +7^(9) is divisible by …………
Answer» 6 24 64 72 Answer :C

Discussion

908.	Find component statement of the following compound statements and check whether they are true or false.Socrates was mathematician OR Socrates was philosopher.
Answer» ANSWER :1

Discussion

909.	If A and Bare two independenteventsthen P((A)/(B)) =
Answer» <P>0 1 `P(A) ` `P(B)` ANSWER :C

Discussion

910.	Find component statement of the following compound statements and check whether they are true or false. Kanpur city is in India and 7xx5=35
Answer» ANSWER :1

Discussion

911.	Find component statement of the following compound statements and check whether they are true or false. 5 is an integer and 5^(2)=25
Answer» ANSWER :1

Discussion

912.	Find component statement of the following compound statements and check whether they are true or false.(30)^(2)=9 and (-3)^(2)=9
Answer» ANSWER :1

Discussion

913.	Find (dy)/(dx) if y = x ^(y)
Answer» ANSWER :`(y ^(2))/( X (1 - LOG y ))`

Discussion

914.	If x, y in Q_(1) and 4 ^(sin x) + 3 ^((1)/(cos y)) = 115 . 16^(sin x) - 2 . 3 ^((1)/(cos y)) = 2 " then " (y)/(x) =
Answer» ANSWER :2

Discussion

915.	Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p ^^ q
Answer» ANSWER :TRUE

Discussion

916.	The sum of 30 terms of a series in A.P., whose last term is 98, is 1635. Find the first term and the common difference.
Answer» Answer :First TERMS = 11 Common DIFFERENCE =3

Discussion

917.	A model rocket is launched from the ground. The height 'h' reached by the rocket after t seconds from lift off is given by h(t) = -5t^(2) + 100t, 0 le t le 20. At what time the rocket is 495 feet above the ground?
Answer» Answer :` THEREFORE 11 or 9 ` sec , the rocket is 495 feet above that ground .

Discussion

918.	If f: R rarr [0, oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), and f(x) is periodic then its period is
Answer» 12 14 11 10 Answer :A

Discussion

919.	Find the coordinates of the orthocentre of the triangle whose vertices are (1, 2), (2, 3) and (4, 3).
Answer» ANSWER : `(1, 6)`

Discussion

920.	Find the equatin to the parabola whose axis is parallel to the y-xis and which passes through the point (0,4), (1.9)," and "(-2,6) and determine its latus rectum.
Answer» ANSWER :`y=2x^(2)+3x+4,(1)/(2)`

Discussion

921.	Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p vv q
Answer» ANSWER :All are TRUE EXCEPT (IV)

Discussion

922.	Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p vv(~q)
Answer» ANSWER :All are TRUE EXCEPT (IV)

Discussion

923.	Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : (~p)vv(~q)
Answer» ANSWER :All are TRUE EXCEPT (IV)

Discussion

924.	Evaluate the following limits. Lt_(xto2)(2x^(2)-7x-4)/((2x-1)(sqrtx-2))
Answer» ANSWER :`5/3(2+sqrt2)`

Discussion

925.	If a^2x^4+b^2y^4=c^6 then the maximum value of xy is
Answer» `(c^(3))/(2AB)` `(c^(3))/(sqrt(2ab))` `(c^(3))/(AB)` `(c^(3))/(sqrt(ab))` ANSWER :B

Discussion

926.	Let f(1)=1 and f(n)=2 sum_(r=1)^(n-1)f(r) then sum_(n=1)^(m)f(n)=
Answer» `3^(m)-1` `3^(m)` `3^(m-1)` `3^(m-2)` ANSWER :C

Discussion

927.	Statement-1: If A = (300)^( 600) , B =600!, C= (200)^(600) , then A gt B gt C. Statement-2: ((n)/(2) )^(n) gt n! gt ((n)/(3) )^(n) for n gt 6.
Answer» Statement-1 is TRUE, Statement-2 is true, Statement-2 is not a CORRECT EXPLANATION for Statement-1. Statement-1 is true, Statement-2 is FALSE Statement-1 is false, Statement-2 is true Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation for Statement-1 Answer :D

Discussion

928.	Solve the following equations : 21x^(2)+9x+1=0
Answer» ANSWER :`-(9)/(42)+-(SQRT(3))/(42)i`

Discussion

929.	In a triangle ABC, if A,B, C are in A.P and b:c =sqrt3:sqrt2, then
Answer» `60^(@)` `75^(@)` `45^(@)` `120^(@)` ANSWER :B

Discussion

930.	Equation of circle passing through A(-1,-3), B (3,0) and touching line 4x + 3y - 12 = 0at B , is
Answer» `x^(2) + y^(2) - 2x - 3y - 3 = 0 ` `x^(2) + y^(2) - 2x- 3y - 3= 0 ` `x^(2) + y^(2) - 2x - 3y + 3 = 0` `x^(2) + y^(2) - 2x + 3y - 3= 0 ` Solution :N/A

Discussion

931.	Find the perpendicular distance between the lines 9x+40y-20=0, 9x+40y+21=0
Answer» ANSWER :1

Discussion

932.	If A, B, C are the angles of a triangle such that cot ""A/2 = 3 tan ""C/2, then sin a, sin B, sin Care in
Answer» A.P. G.P. H.P. A.G.P. ANSWER :A

Discussion

933.	Evaluate Lt_(xtoa)(x-a)^(x-a)
Answer» ANSWER :1

Discussion

934.	Find out whether the points (0, 7, 10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.
Answer» ANSWER :No

Discussion

935.	Vertex A of Delta ABC moves in such way that tanB+tanC =constant, when BC is fixed the locus of orthocentre of DeltaABC is a
Answer» Striaght line Parabola Ellipse Circle Answer :D

Discussion

936.	The value of the determinant Delta = \|((1 - a_(1)^(3) b_(1)^(3))/(1 - a_(1) b_(1)),(1 - a_(1)^(3) b_(2)^(3))/(1 - a_(1) b_(2)),(1 - a_(1)^(3) b_(3)^(3))/(1 - a_(1) b_(3))),((1 - a_(2)^(3) b_(1)^(3))/(1 - a_(2) b_(1)),(1 - a_(2)^(3) b_(2)^(3))/(1 - a_(2) b_(2)),(1 - a_(2)^(3) b_(3)^(3))/(1 - a_(2) b_(3))),((1 - a_(3)^(3) b_(1)^(3))/(1 - a_(3) b_(1)),(1 - a_(3)^(3) b_(2)^(3))/(1 - a_(3) b_(2)),(1 - a_(3)^(3) b_(3)^(3))/(1 - a_(3) b_(3)))\|, is
Answer» 0 DEPENDENT only on `a_(1), a_(2), a_(3)` dependent only `b_(1), b_(2), b_(3)` dependent on `a_(1), a_(2), a_(3) b_(1), b_(2), b_(3)` Answer :D

Discussion

937.	Find the 6^(th) term in expansion of (z^(2)+(2z)/3+1/9)^(5)
Answer» ANSWER :`(28)/(27) 3^(5)`

Discussion

938.	Three persons have 4 coats, 5 waistcoats ,and 6 hats. Find in how many ways can they put on the clothes.
Answer» ANSWER :` ""^(4)P_3 XX ""^(5)P_3 = 172800`

Discussion

939.	The probability of hitting a target by three persons A,B,C are given by (1)/(2),(1)/(3) and (1)/(4) respectively. If all of them try to hit simultaneously.Find the probability that,(i)None of them hit the target.(ii)At least one of them will hit the target .(iii)Exactly one of them will hit the target(iv)Exactly two of them will hit the target(v)At least two of them will hit the target.
Answer» ANSWER :(i)`(1)/(4)` (ii)`(3)/(4)` (iii)`(1)/(4)` (iv)`(7)/(24)`

Discussion

940.	Evaluate root(3)(0.08034).
Answer» Solution :LET `x = ROOT(3)(0.08034).` Then, log `x = 1/3` log (0.08034). `= 1/3 (bar(2).9049) = 1/3(-2 + 0.9049) = 1/3(-1.0951)` `= -0.3650 = -1 + (1 - 0.3650) = bar(1).6350` `rArr` x = ANTILOG `(bar(1).6350) = 0.4315.`

Discussion

941.	If M and N are any two events, the probability that at least one of them occurs is
Answer» <P>`P(M)+P(N)-2P(McapN)` `P(M)+P(N)-P(McapN)` `P(M)+P(N)+P(McapN)` `P(M)+P(N)+2P(McapN)` ANSWER :B

Discussion

942.	If A(2,-1) and B(6,5) are two points the ratio in which the foot of the perpendicular from (4,1) to AB divides it is
Answer» `8:15` `5:8` `-5:8` `-8:5` ANSWER :D

Discussion

943.	For all integers n ge 1, which of the following is divisible by 9 ?
Answer» `8^(N) +1` `4^(n) - 3n-1` `3^(2n) + 3n+1` `10^(n)+1` Answer :B

Discussion

944.	Find the value of AO) so that the function f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) is continuous at x = 0.
Answer» ANSWER :`a^(2) COS a + 2A SIN a`

Discussion

945.	Redefine the function f(x)= \|x-2\| + \|2 + x\|, -3 le x le 3
Answer» Answer :`{:(-2X",",-3 LE X lt -2),(4",",-2 le x lt 2),(2",",2 le x le 3):}`

Discussion

946.	The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that (i) it will get at least one of the awards (ii) it will get only one of the awards.
Answer» ANSWER : (i)0.64 (II)0.44

Discussion

947.	Differentiate the following function w.r.t. x: cot nx
Answer» ANSWER :`-N COSEC^(2) NX`

Discussion

948.	A bag contains tickets numbered 1 to 20 . Twotickets are drawn . Find the probability that both numbers are odd .
Answer» ANSWER :`(""^(10)C_(2))/(""^(20)C_(2))=(9)/(38)`

Discussion

949.	A mirror and source of light are kept at the origin and at a point on the positive x-axis respectively. A ray of light from the sources strikes the mirror and is reflected. If (1,-1,1) are the d.r's of a normal to the plane, then the d.c's of the reflected ray are:
Answer» `((-1)/(3), (-2)/(3), (2)/(3))` `((1)/(3), (2)/(3), (2)/(3))` `((1)/(3), (-2)/(3), (2)/(3))` `(-(1)/(SQRT(3)), (-1)/(sqrt(3)), (1)/(sqrt(3)))` ANSWER :A

Discussion

950.	((44),(r-2)) = ((44),(r+2)), then r = ……
Answer» 33 11 22 44 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If sin x coshy = cos theta, cos x sinhy = sin theta then sinh^2 y =

Obtain equation of circle in(x- 1)^(2) + y^(2) = 4

Maximum value of (1)/(sqrt((7)sin x+ sqrt( 29) cos x+7))

Themaximum area of the rectangle whose sides pass through the vertices if a given rectangleof sides a and b is

If the expansion of (x-1/(x^(2)))^(2n) contains a term independent of x , then n is a multiple of 2 .

9^(7) +7^(9) is divisible by …………

Find component statement of the following compound statements and check whether they are true or false.Socrates was mathematician OR Socrates was philosopher.

If A and Bare two independenteventsthen P((A)/(B)) =

Find component statement of the following compound statements and check whether they are true or false. Kanpur city is in India and 7xx5=35

Find component statement of the following compound statements and check whether they are true or false. 5 is an integer and 5^(2)=25

Find component statement of the following compound statements and check whether they are true or false.(30)^(2)=9 and (-3)^(2)=9

Find (dy)/(dx) if y = x ^(y)

If x, y in Q_(1) and 4 ^(sin x) + 3 ^((1)/(cos y)) = 115 . 16^(sin x) - 2 . 3 ^((1)/(cos y)) = 2 " then " (y)/(x) =

Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p ^^ q

The sum of 30 terms of a series in A.P., whose last term is 98, is 1635. Find the first term and the common difference.

A model rocket is launched from the ground. The height 'h' reached by the rocket after t seconds from lift off is given by h(t) = -5t^(2) + 100t, 0 le t le 20. At what time the rocket is 495 feet above the ground?

If f: R rarr [0, oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), and f(x) is periodic then its period is

Find the coordinates of the orthocentre of the triangle whose vertices are (1, 2), (2, 3) and (4, 3).

Find the equatin to the parabola whose axis is parallel to the y-xis and which passes through the point (0,4), (1.9)," and "(-2,6) and determine its latus rectum.

Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p vv q

Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : p vv(~q)

Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true : (~p)vv(~q)

Evaluate the following limits. Lt_(xto2)(2x^(2)-7x-4)/((2x-1)(sqrtx-2))

If a^2x^4+b^2y^4=c^6 then the maximum value of xy is

Let f(1)=1 and f(n)=2 sum_(r=1)^(n-1)f(r) then sum_(n=1)^(m)f(n)=

Statement-1: If A = (300)^( 600) , B =600!, C= (200)^(600) , then A gt B gt C. Statement-2: ((n)/(2) )^(n) gt n! gt ((n)/(3) )^(n) for n gt 6.

Solve the following equations : 21x^(2)+9x+1=0

In a triangle ABC, if A,B, C are in A.P and b:c =sqrt3:sqrt2, then

Equation of circle passing through A(-1,-3), B (3,0) and touching line 4x + 3y - 12 = 0at B , is

Find the perpendicular distance between the lines 9x+40y-20=0, 9x+40y+21=0

If A, B, C are the angles of a triangle such that cot ""A/2 = 3 tan ""C/2, then sin a, sin B, sin Care in

Evaluate Lt_(xtoa)(x-a)^(x-a)

Find out whether the points (0, 7, 10), (-1,6,6) and (-4,9,6) are the vertices of a right angled triangle.

Vertex A of Delta ABC moves in such way that tanB+tanC =constant, when BC is fixed the locus of orthocentre of DeltaABC is a

Find the 6^(th) term in expansion of (z^(2)+(2z)/3+1/9)^(5)

Three persons have 4 coats, 5 waistcoats ,and 6 hats. Find in how many ways can they put on the clothes.

Evaluate root(3)(0.08034).

If M and N are any two events, the probability that at least one of them occurs is

If A(2,-1) and B(6,5) are two points the ratio in which the foot of the perpendicular from (4,1) to AB divides it is

For all integers n ge 1, which of the following is divisible by 9 ?

Find the value of AO) so that the function f(x) = ((a+x)^(2)sin(a+x)-a^(2)sin a)/(x) is continuous at x = 0.

Redefine the function f(x)= |x-2| + |2 + x|, -3 le x le 3

Differentiate the following function w.r.t. x: cot nx

A bag contains tickets numbered 1 to 20 . Twotickets are drawn . Find the probability that both numbers are odd .

A mirror and source of light are kept at the origin and at a point on the positive x-axis respectively. A ray of light from the sources strikes the mirror and is reflected. If (1,-1,1) are the d.r's of a normal to the plane, then the d.c's of the reflected ray are:

((44),(r-2)) = ((44),(r+2)), then r = ……