14949 + Interview Questions in Maths in Class 11 Page 233 InterviewSolution

11601.	Write the negation of the following statements.Ashok reads news paper daily
Answer» Solution :Ashok does not read NEWS PAPER DAILY

Discussion

11602.	There are 12 true - false questions in an examination .How many seqences of answer are possible?
Answer» ANSWER :` 4096`

Discussion

11603.	The quadratic equations x^(2)-6x+a=0 and x^(2)-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3. then the common root is
Answer» 1 4 3 2 Answer :D

Discussion

11604.	If A={x\|x is the multiple of 4} and B = {x\|x is the multiple of 6} then A cap B= {………}
Answer» ANSWER :12

Discussion

11605.	A andB are mutually exclusive events and P(A)=3/5,P(B)=1/5then P(A OR B ) = …..
Answer» ANSWER :`4/5`

Discussion

11606.	Let f(x)=(1-tan x)/(4x-pi), x ne pi/4, x in [0,pi/2]." If f(x) is continuous in "[0,pi/4]," then "f(pi/4)is
Answer» 1 `1/2` `-(1)/(2)` -1 Answer :C

Discussion

11607.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – D
Answer» ANSWER :`={4, 8, 12, 16}`

Discussion

11608.	............are the numbers of words using the letters of word ROSE with its meaning or without its meaning.
Answer» ANSWER :24

Discussion

11609.	Expand (1+ax)^n upto the third term if n is a positive integer
Answer» SOLUTION :`[(1+ax)^N=1+nax+(n(n-1))/2x^2+...]`

Discussion

11610.	The P.V.'s of the vertices of a triangle are 2bar(i)+3bar(j)+4bar(k), 4bar(i)+6bar(j)+3bar(k), 3bar(i)+2bar(j)+3bar(k) P.V. of its orthocentre is
Answer» `2BAR(i)-3BAR(j)+4bar(k)` `2bar(i)+3bar(j)-4bar(k)` `2bar(i)+3bar(j)+4bar(k)` `-2bar(i)+3bar(j)+4bar(k)` ANSWER :C

Discussion

11611.	In a triangle ABC, the median to the side BC is of length 1/sqrt(11 - 6 sqrt3)and it divides A into the angles 30^(@)" and " 45^(@) then length of side BC is
Answer» 1 2 3 4 Answer :B

Discussion

11612.	If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1,3,5 and 7, what is the probability of forming a number divisible by 5 when (i) the digits are repeated? (ii) the repetition of digits is not allowed?
Answer» ANSWER :`=(33)/(83)`

Discussion

11613.	x-3y-5=0 is the perpendicular bisector of the line segment joining the points A,B. If A=(-1,-3), find the co ordinates of B.
Answer» ANSWER :`(28/5,6/5)`

Discussion

11614.	Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0. When roots are x_(1),x_(2) and x_(3). The value of x_(1)^(2)+x_(2)^(2)+x_(3)^(2) equals
Answer» 1 2 ` 2 COS THETA ` ` sin theta ( sin theta + cos theta)` Answer :B

Discussion

11615.	Distance of point P on parabola y^(2) = 12x is SP = 6 then find co-ordinate of point P.
Answer» ANSWER :`(3, PM 6)`

Discussion

11616.	Which of the following pairs of sets are disjoint : {x : x in N, 1 lt x lt 5} {x : x in Z, -5 lt x lt 1}
Answer» ANSWER :it is not DISJOINT SET

Discussion

11617.	If the area of an isosceles triangle is sqrt2+1are vertical angle is 45^@ then the base of the triangle is
Answer» 1 2 `SQRT(2)` `sqrt(2)-1` ANSWER :B

Discussion

11618.	If f(x)=log_(e(x))((x^(2)+e)/(x^(2)+1)), then the range of f(x) is
Answer» (0, 1) [0, 1] [0, 1) (0, 1] ANSWER :D

Discussion

11619.	For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in Lagrange's mean value theorem is
Answer»

Discussion

11620.	If f ((x+ y)/( 3)) = (2 + f (x) + f (y))/(3) AA x, y in R and f'(2) =2 then determine y = f (x).
Answer» ANSWER :`2X +2`

Discussion

11621.	A rectangular vessel is of 2 mt long. 0.5 mt breadth and I mt deep. If water flows in at rate of 900 cubic cm per sec, then the rate of increase of water level when 25 cm deep is
Answer» 0.09 cm/sec 0.1 cm/sec 0.01 cm/sec 0.5 cm/sec Answer :A

Discussion

11622.	For inequality (x+2)/(x+3) gt 1 the numbers of positive integral solution is ...........
Answer» ANSWER :ZERO

Discussion

11623.	If f(theta)=\|(cos^(2) theta, cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2) theta, cos theta),(sin theta, -cos theta, 0)\| then f((pi)/12)=
Answer» ANSWER :1

Discussion

11624.	Observe the following statements I) If the radius of spherical ball is increased by 1/2% then approximate increase in volume is 1% II) In measuring the radius and height of a cone as 5cm,10cm there are errors 0.02 cm, 0.01cm ewspectively. Then error in volume approximately is 2.25pic.c Correct statement is
Answer» Only I Only II both I and II NEITHER I nor II Answer :D

Discussion

11625.	Three coins are tossed once. Let A denote the event 'three heads show", B denote the event "two heads and one tail show", C denote the event" three tails show and D denote the event 'a head shows on the first coin". Which events are (i) mutually exclusive? (ii) simple (iii) Compound?
Answer» ANSWER :(i) A and B; A and C; B and D; (II) A and C (III) B and D

Discussion

11626.	If (6,10,10),(1,0,-5), (6,-10,0) are vertices of a triangle, find the direciton ratios of its sides. Determine wherther it is right angled or isosceles.
Answer» Answer :`(-5,-`10,-10),(5,-10,5),(0,20,10) DELTA ABC` is RIGHT angled TRIANGLE.

Discussion

11627.	If \|x\| lt 1, then (1)/(2) log((1+x)/(1-x))=
Answer» TAN hx `sin h^(-1) (X)` `cot h^(-1) (x)` `tan h^(-1) (x)` Answer :D

Discussion

11628.	If f(x)=log_([x-1]) ((\|x\|)/(x)), where [.] is G.I.F then domain and range are
Answer» `(2, oo), (0,1)` `[3, oo) , {0}` `[3, oo), {0, 1}` `(-oo, oo),{0}` ANSWER :B

Discussion

11629.	Equation (s) of the straight line (s), inclinde at 30^@ to the x-axis such that the length of its (each of their) line segment (s) between the coordinate axes in 10 units, is (are)
Answer» `x+sqrt3y+5sqrt3=0` `x-sqrt3y+5sqrt3=0` `x+sqrt3y-5sqrt3=0` `x-sqrt3y-5sqrt3=0` ANSWER :B::D

Discussion

11630.	The periodof sin^(6) x +cos^(6)x is
Answer» `(PI)/(2)` `pi` `(3PI)/(2)` `2PI` ANSWER :A

Discussion

11631.	the coefficient of x^(7) in (ax - b^(-1) x^(-2))^(11) is
Answer» 0 2 3 4 Answer :A

Discussion

11632.	Evaluate : lim_(xto0) (e^(x) -e^(-x))/x
Answer» ANSWER :1

Discussion

11633.	If y=x^(cosx) then (dy)/(dx)=
Answer» `X^(COSX)((cosx)/(x)+sinx.logx)` `x^(cosx)((cosx)/(x)-sinx.logx)` `-x^(cosx)((cosx)/(x)-sinx.logx)` `-x^(cosx)((cosx)/(x)+sinx.logx)` ANSWER :B

Discussion

11634.	The quantity (in mg) of a drug in the blood at time t(sec) is given by q=3 (0.4)^t. Find the instantaneous rate of change at t=2sec.
Answer» ANSWER :`3(0.4)^(2)log_(E) (0.4)`

Discussion

11635.	Find the equation of pair of bisectors of the angles between the pair of lines. 6x^(2)+5xy-6y=0
Answer» ANSWER :`5X^(2)-24xy-5y^(2)=0`

Discussion

11636.	If3 tan ^(2) theta -2 sin theta = 0" then " theta =
Answer» `N PI, n pi+(-1)^(n)(pi)/3, n in Z` `n pi , n pi +(-1)^(n)(pi)/6, n in Z` `n pi ,n pi +(-1)^(n)(pi)/2, n in Z` `n pi , n pi +(-1)^(n)(pi)/4, n in Z` Answer :B

Discussion

11637.	The periodof \|sin x + cos x\| is
Answer» `2PI` `2pi` `(PI)/(4 )` `(pi)/(2)` ANSWER :2

Discussion

11638.	If the equation of the plane pasing through the points (1,2,3). (-1,2,0) and perpendicular to the ZX - plane is ax + by + cz + d=0 (a gt0) then
Answer» `a =0 and c =0` `a + d =0` `c + d - 5 =0` `a + B + c + d - 4 =0` Answer :D

Discussion

11639.	For any nxxn matrix A, prove that A can be uniquely expressed as a sum of a symmetric matrix and a skew symmetric matrix.
Answer» ANSWER :`1/2(A-A^(T))`

Discussion

11640.	Three numbers are chosen at random from the first 20 natural numbers. The probability that they are not consecutive is
Answer» `187/190` `93/95` `94/95` `3/190` ANSWER :A

Discussion

11641.	Find the equation of pair of lines through origin and forming an equilateral triangle with the line and also find its area. 3x-4y+5=0
Answer» ANSWER :`39x^(2)+96xy+11y^(2)=0,(1)/(SQRT(3))`

Discussion

11642.	Find the slope of a line whose inclination is 15^(@)
Answer» ANSWER : `2-sqrt(3)`

Discussion

11643.	Find the equation of pair of lines through origin and forming an equilateral triangle with the line and also find its area. 2x+y+1=0
Answer» Answer :`x^(2)+16xy-11y^(2)=0,(1)/(5sqrt(3))`

Discussion

11644.	x^(2) + 3x + 5=0
Answer» ANSWER :`(-3+-sqrt(11)i)/2`

Discussion

11645.	If the diagonals of a parallelogram are bar(i)+5bar(j)-2bar(k) and -2bar(i)+bar(j)+3bar(k) then the lengths of its sides are
Answer» `sqrt(8), sqrt(10)` `sqrt(6), sqrt(14)` `sqrt(5), sqrt(12)` `sqrt(3), sqrt(12)` Answer :B

Discussion

11646.	p_(1),p_(2),p_(3) be the product of perpendicular from (0,0) to xy+x+y+1=0, x^(2)-x^(2)+2x+1=0, 2x^(2)+3xy-2y^(2)+3x+y+1=0 respectively then :
Answer» <P>`p_(1) lt p_(2) lt p_(3)` `p_(3) lt p_(2) lt p_(1)` `p_(2) lt p_(3) lt p_(1)` `p_(1) lt p_(3) lt p_(2)` Answer :B

Discussion

11647.	AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by
Answer» 50 25 2425 2550 Answer :B

Discussion

11648.	Find the roots of -x^(2) + x-2=0
Answer» ANSWER :`(-1+-sqrt(7)i)/(-2)`

Discussion

11649.	A coin is tossed twice, what is the probability that atleast one tail occurs?
Answer» ANSWER :`3/4`

Discussion

11650.	(b)Translate the following compound statement into symbolic form:"The sky is blue and grass is green".
Answer» SOLUTION :The SKY is BLUE, the GRASS is GREEN

Discussion

Explore topic-wise InterviewSolutions in .

Write the negation of the following statements.Ashok reads news paper daily

There are 12 true - false questions in an examination .How many seqences of answer are possible?

The quadratic equations x^(2)-6x+a=0 and x^(2)-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3. then the common root is

If A={x|x is the multiple of 4} and B = {x|x is the multiple of 6} then A cap B= {………}

A andB are mutually exclusive events and P(A)=3/5,P(B)=1/5then P(A OR B ) = …..

Let f(x)=(1-tan x)/(4x-pi), x ne pi/4, x in [0,pi/2]." If f(x) is continuous in "[0,pi/4]," then "f(pi/4)is

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find B – D

............are the numbers of words using the letters of word ROSE with its meaning or without its meaning.

Expand (1+ax)^n upto the third term if n is a positive integer

The P.V.'s of the vertices of a triangle are 2bar(i)+3bar(j)+4bar(k), 4bar(i)+6bar(j)+3bar(k), 3bar(i)+2bar(j)+3bar(k) P.V. of its orthocentre is

In a triangle ABC, the median to the side BC is of length 1/sqrt(11 - 6 sqrt3)and it divides A into the angles 30^(@)" and " 45^(@) then length of side BC is

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1,3,5 and 7, what is the probability of forming a number divisible by 5 when (i) the digits are repeated? (ii) the repetition of digits is not allowed?

x-3y-5=0 is the perpendicular bisector of the line segment joining the points A,B. If A=(-1,-3), find the co ordinates of B.

Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0. When roots are x_(1),x_(2) and x_(3). The value of x_(1)^(2)+x_(2)^(2)+x_(3)^(2) equals

Distance of point P on parabola y^(2) = 12x is SP = 6 then find co-ordinate of point P.

Which of the following pairs of sets are disjoint : {x : x in N, 1 lt x lt 5} {x : x in Z, -5 lt x lt 1}

If the area of an isosceles triangle is sqrt2+1are vertical angle is 45^@ then the base of the triangle is

If f(x)=log_(e(x))((x^(2)+e)/(x^(2)+1)), then the range of f(x) is

For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in Lagrange's mean value theorem is

If f ((x+ y)/( 3)) = (2 + f (x) + f (y))/(3) AA x, y in R and f'(2) =2 then determine y = f (x).

A rectangular vessel is of 2 mt long. 0.5 mt breadth and I mt deep. If water flows in at rate of 900 cubic cm per sec, then the rate of increase of water level when 25 cm deep is

For inequality (x+2)/(x+3) gt 1 the numbers of positive integral solution is ...........

If f(theta)=|(cos^(2) theta, cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2) theta, cos theta),(sin theta, -cos theta, 0)| then f((pi)/12)=

Three coins are tossed once. Let A denote the event 'three heads show", B denote the event "two heads and one tail show", C denote the event" three tails show and D denote the event 'a head shows on the first coin". Which events are (i) mutually exclusive? (ii) simple (iii) Compound?

If (6,10,10),(1,0,-5), (6,-10,0) are vertices of a triangle, find the direciton ratios of its sides. Determine wherther it is right angled or isosceles.

If |x| lt 1, then (1)/(2) log((1+x)/(1-x))=

If f(x)=log_([x-1]) ((|x|)/(x)), where [.] is G.I.F then domain and range are

Equation (s) of the straight line (s), inclinde at 30^@ to the x-axis such that the length of its (each of their) line segment (s) between the coordinate axes in 10 units, is (are)

The periodof sin^(6) x +cos^(6)x is

the coefficient of x^(7) in (ax - b^(-1) x^(-2))^(11) is

Evaluate : lim_(xto0) (e^(x) -e^(-x))/x

If y=x^(cosx) then (dy)/(dx)=

The quantity (in mg) of a drug in the blood at time t(sec) is given by q=3 (0.4)^t. Find the instantaneous rate of change at t=2sec.

Find the equation of pair of bisectors of the angles between the pair of lines. 6x^(2)+5xy-6y=0

If3 tan ^(2) theta -2 sin theta = 0" then " theta =

The periodof |sin x + cos x| is

If the equation of the plane pasing through the points (1,2,3). (-1,2,0) and perpendicular to the ZX - plane is ax + by + cz + d=0 (a gt0) then

For any nxxn matrix A, prove that A can be uniquely expressed as a sum of a symmetric matrix and a skew symmetric matrix.

Three numbers are chosen at random from the first 20 natural numbers. The probability that they are not consecutive is

Find the equation of pair of lines through origin and forming an equilateral triangle with the line and also find its area. 3x-4y+5=0

Find the slope of a line whose inclination is 15^(@)

Find the equation of pair of lines through origin and forming an equilateral triangle with the line and also find its area. 2x+y+1=0

x^(2) + 3x + 5=0

If the diagonals of a parallelogram are bar(i)+5bar(j)-2bar(k) and -2bar(i)+bar(j)+3bar(k) then the lengths of its sides are

p_(1),p_(2),p_(3) be the product of perpendicular from (0,0) to xy+x+y+1=0, x^(2)-x^(2)+2x+1=0, 2x^(2)+3xy-2y^(2)+3x+y+1=0 respectively then :

AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

Find the roots of -x^(2) + x-2=0

A coin is tossed twice, what is the probability that atleast one tail occurs?

(b)Translate the following compound statement into symbolic form:"The sky is blue and grass is green".