14949 + Interview Questions in Maths in Class 11 Page 191 InterviewSolution

9501.	Write the following sets in roster form: D = {x : x is a prime number which is divisor of 60}
Answer» ANSWER :`D= 2, 3, 5`

Discussion

9502.	If the function f(x)=(1-cos^(3)ax)/(x sin x) for x ne 0f(0) =1/2 is continuous at x = 0, show that a=pm(1)/sqrt(3)
Answer» ANSWER :`PM(1)/SQRT(3)`

Discussion

9503.	Solve : cos 3x + cos 2x = sin ""(3)/(2) x + sin "" (1)/(2) x, 0 lt x le pi.
Answer» ANSWER :`X = (PI)/(7) or ( 5PI)/(7) or pi.`

Discussion

9504.	Let f(x)=\|x-2\|+\|x-3\|+\|x+4\| and g(x)=f(x+1). Then g(x) is
Answer» an EVEN function an ODD function neither even nor odd periodic Answer :C

Discussion

9505.	A point is moving along y^(3) = 27x. The interval in which the abscissa changes at slower rate than ordinate is
Answer» (-2,2) `(-OO,oo)` `(-1,1)` `(-oo,-3)CUP(3,oo)` ANSWER :C

Discussion

9506.	The probability that A speas truth is (4)/(5)whilethis porbability forB is (3)/(5). Theprobabilityof atleastoneof themis truewhenasked to speakon an event is
Answer» `(4)/(25)` `(2)/(25)` `(3)/(25)` `(23)/(25)` ANSWER :D

Discussion

9507.	If the xicoordinate of 'p' on the join of Q(2,2,1) and R(5,2,-2) is 4, then Z-coordinate of P is
Answer» -1 0 1 2 Answer :A

Discussion

9508.	The circumcentre of triangle formed by lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0 is
Answer» ANSWER :(-1, -1)

Discussion

9509.	A card is drawn from a well shuffled pack of 52 cards . Findthe probability of jack , queen or king
Answer» ANSWER :`(12)/(52),i.e.(3)/(13)`

Discussion

9510.	The x, y, z coordinates of each vertex of a triangle are in A.P. The x and y coordinates of the centroid of the triangle are 1 and 3 respectively. The distance of the centroid from the origin is
Answer» `SQRT2` `sqrt35` `SQRT32` `SQRT5` ANSWER :B

Discussion

9511.	In the following match each item given under the Column-I to its correct answer given under the Column-II.
Answer» ANSWER :d, a, B, C

Discussion

9512.	If cos theta =(a cos phi+b)/(a+bcosphi) then ("tan"(theta)/2)/("tan"(phi)/2)=
Answer» `(a-b)/(a+b)` `(a+b)/(a-b)` `SQRT((a+b)/(a-b))` `sqrt((a-b)/(a+b))` ANSWER :D

Discussion

9513.	If (a_(0))/(n+1) + ( a_(1))/( n ) + ( a_(2))/( n-1)+"......"+ (a_(n-1))/(2) + a_(n) =0then a_(0)x^(n) + a_(1) x^(n-1) + "..........." + a_(n-1)x + a_(n) =0 has
Answer» no SOLUTION in ( 0,1) at least ONE solution in ( 0,1) EXACTLY one solution in ( 0,1) at least one soluiotn in ( 2,3) Answer :B

Discussion

9514.	Evaluate Lt_(xto0)(27^(x)-9^(x)-3^(x)+1)/x^(2).
Answer»

Discussion

9515.	Let f(x) = x + sinx. Suppose g denotes the inverse function of f, then the value of g' (pi/4+1/sqrt2) has the value equal to
Answer» `SQRT2-1` `(sqrt2+1)/sqrt2` `2-sqrt2` `sqrt2+1` ANSWER :C

Discussion

9516.	Consider the compound statements ''35 is divisible by 5 or 6'' Write the component statement of the given statement.
Answer» SOLUTION : ''35 is DIVISIBLE by 5'', ''35 is divisible by 6''

Discussion

9517.	Let 0 ltx lt pi//4 then (sec2x-tan2x) equals
Answer» `TAN(x-(PI)/4)` `tan((pi)/4-x)` `tan(x+(pi)/4)` `tan^2(x+(pi)/4)` Answer :C

Discussion

9518.	Determine real values of x and y for which each statement is true (x-yi)(2+ 3i) = (x-2i)/(1-i)
Answer» ANSWER :`X= - (2)/(21), y= (8)/(21)`

Discussion

9519.	Simiplify :(3-7i)^(2)
Answer» ANSWER :`-40-42i`

Discussion

9520.	By shifting origin to (-1, 2), the equation y^(2) + 8x - 4y + 12 = 0 changes as y^(2) = 4axthen a =
Answer» 1 2 `-2` `-1` ANSWER :C

Discussion

9521.	(x^(2))/(25)-(y^(2))/(4)=1
Answer» Answer :(i) 10 UNITS , 4 units (ii) `A(-5,0),B(5,0)` (III) `F_(1)(-sqrt(29),0),F_(2)(sqrt(29),0)` (iv) `e=(sqrt(29))/(5)` `(v) 1(1)/(3) ` units

Discussion

9522.	The number of values of theta satisfying 4 cos theta + 3 sin theta = 5as well as 3 cos theta + 4 sin theta = 5is
Answer» one two zero three Answer :C

Discussion

9523.	sin x = 1/4 ,x in quadrant II
Answer» ANSWER :`(SQRT ( 8 + 2 sqrt15))/(4) , (sqrt ( 8- 2 sqrt15))/(4), 4 + sqrt15`

Discussion

9524.	Write the contrapositive and converse of the following statements: x is an even number implies that x is divisible by 4.
Answer» ANSWER :Contrapositive: if x is not divisible by 4 then x is not an even NUMBER. CONVERSE: Ifx is divisible by 4 then x is even number.

Discussion

9525.	A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will be B
Answer» ANSWER :`(2)/(11)`

Discussion

9526.	A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will beB or vowel ?
Answer» ANSWER :`(6)/(11)`

Discussion

9527.	A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will be a vowel
Answer» ANSWER :`(4)/(11)`

Discussion

9528.	Compute the derivative of f(x) = sin^(2) x.
Answer» ANSWER :SIN2X

Discussion

9529.	Solve sin ^(2) theta - 2 cos theta + (1)/(4) = 0 for the general solution.
Answer» ANSWER :`PI /3 , N in I`

Discussion

9530.	For what values of k the equation sin x + cos (k + x) + cos ( k - x) = 2has real solution ?
Answer» `N pi - (pi)/(6) le K le n pi + (pi)/(6), n in Z` `n pi + (pi)/(3) le k le n pi - (pi)/(3), n in Z` `n pi + (pi)/(2) le k le n pi - (pi)/(2), n in Z` `n pi + (pi)/(4) le k le n pi - (pi)/(4), n in Z` Answer :A

Discussion

9531.	Number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)Sin^(-1)(sinx)" where "-pi le x le pi
Answer» 0 1 2 4 Answer :C

Discussion

9532.	If 'f' is a polynomial such that f ((1-x)/(1+x))f((1+x)/(1-x))=f((1-x)/(1+x))+f((1+x)/(1-x)) ( where x != 0, pm 1 ) and f(3)=28 then the value of (1)/(605) ( sum_(n=1)^(10) (f(n)-1)) is
Answer»

Discussion

9533.	Let veca= 2 hati + 3hatj - 6hatk, vecb = 2hati - 3hatj + 6hatk and vecc = -2 hati + 3hatj + 6hatk. Let veca_(1) be the projection of veca on vecb and veca_(2) be the projection of veca_(1) on vecc . Thenveca_(1).vecb is equal to
Answer» `-41` `-41//7` 41 287 Solution :`veca_(1).VECB= (-41)/49 (2hati - 3hatj + 6hatk) . (2hati - 3hatj + 6hatk) =-41`

Discussion

9534.	\|{:(logx,logy,logz),(log2x,log2y,log2z),(log3x,log3y,log3z):}\|=
Answer» 0 `LOG(XYZ)` `log(6XYZ)` `6log(xyz)` ANSWER :A

Discussion

9535.	a = sec theta - tan theta and b=cosectheta+cottheta rArr a =
Answer» `(b+1)/(b-1)` `(1+b)/(1-b)` `(b-1)/(b+1)` `(1-b)/(1+b)` ANSWER :C

Discussion

9536.	Fill in the blanks of the following the value of sqrt(-25)xxsqrt(-9) is ...
Answer» ANSWER :`-15`

Discussion

9537.	Write the converse of the following statements: If a number n is even, then n^(2) is even.
Answer» ANSWER :If a NUMBER `N^(2)` is EVEN, then n is even.

Discussion

9538.	Calculate the mean deviation about median age for the age distribution of 100 persons given below:
Answer» ANSWER :7.35

Discussion

9539.	Orthocentre of the triangle formed by lines 2x^(2)-3xy-2y^(2)=0 and 3x+4y-20=0 is
Answer» (2,3) (3,2) (0,0) (0,5) ANSWER :C

Discussion

9540.	Find the mean deviation about median for the following data:
Answer» ANSWER :10.34

Discussion

9541.	The time ‘t' of a complete oscillation of a simple pendulum of length 1 is given by t=2pisqrt((l)/(g)) where gis gravitational constant. Find the approximate percentage of error in t when the percentage of error in lis 1%
Answer» ANSWER :`(1)/(2)`

Discussion

9542.	A line with direction consines proportional to 1, -5 and -2 meets lines x = y + 5 =z + 1 and x + 5 = 3y = 2z. The coordinates of each of the points of the intersection are given by
Answer» `(2, -3, 1)` `(1,2,3)` `(0, 5//3, 5//2)` `(3, -2, 2)` ANSWER :A::B::C

Discussion

9543.	Find the derivative of cos x from first principle.
Answer» ANSWER :`-SINX`

Discussion

9544.	Find the constant term of (2x^(3)-(1)/(3x^(2)))^(5).
Answer» ANSWER :`=(-40)/(27)`

Discussion

9545.	Evaluate the following limits : Lim_(x to 0) (sin 3x - sin x )/(sin x)
Answer» ANSWER :2

Discussion

9546.	If p,q,r are in G.P then p/q=q/r (True/False)
Answer» ANSWER :TRUE

Discussion

9547.	The stationary points of f(x) =x^(3)-9x^(2)+24x-12are
Answer» `(2,4),(4,3)` `(2,8)(4,4)` `(0,-12)(1,4)` `(2,8)(1,4)` ANSWER :B

Discussion

9548.	Find the derivative of the function from first principle x ^(3)
Answer» ANSWER :`3X ^(2)`

Discussion

9549.	The solution set of equation cos^(5) x = 1 + sin^(4) xis
Answer» `{N PI , n in I}` `{2 n pi, n in I}` `{2 n pi, n in I}` `{n pi//2, n in I}` ANSWER :A

Discussion

9550.	If a line l passes through (k,2k)(3k,3k) and (3,1), k ne0, then the distance from the origin to the line l is
Answer» `4/sqrt5` `3/sqrt5` `2/sqrt5` `1/sqrt5` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

Write the following sets in roster form: D = {x : x is a prime number which is divisor of 60}

If the function f(x)=(1-cos^(3)ax)/(x sin x) for x ne 0f(0) =1/2 is continuous at x = 0, show that a=pm(1)/sqrt(3)

Solve : cos 3x + cos 2x = sin ""(3)/(2) x + sin "" (1)/(2) x, 0 lt x le pi.

Let f(x)=|x-2|+|x-3|+|x+4| and g(x)=f(x+1). Then g(x) is

A point is moving along y^(3) = 27x. The interval in which the abscissa changes at slower rate than ordinate is

The probability that A speas truth is (4)/(5)whilethis porbability forB is (3)/(5). Theprobabilityof atleastoneof themis truewhenasked to speakon an event is

If the xicoordinate of 'p' on the join of Q(2,2,1) and R(5,2,-2) is 4, then Z-coordinate of P is

The circumcentre of triangle formed by lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0 is

A card is drawn from a well shuffled pack of 52 cards . Findthe probability of jack , queen or king

The x, y, z coordinates of each vertex of a triangle are in A.P. The x and y coordinates of the centroid of the triangle are 1 and 3 respectively. The distance of the centroid from the origin is

In the following match each item given under the Column-I to its correct answer given under the Column-II.

If cos theta =(a cos phi+b)/(a+bcosphi) then ("tan"(theta)/2)/("tan"(phi)/2)=

If (a_(0))/(n+1) + ( a_(1))/( n ) + ( a_(2))/( n-1)+"......"+ (a_(n-1))/(2) + a_(n) =0then a_(0)x^(n) + a_(1) x^(n-1) + "..........." + a_(n-1)x + a_(n) =0 has

Evaluate Lt_(xto0)(27^(x)-9^(x)-3^(x)+1)/x^(2).

Let f(x) = x + sinx. Suppose g denotes the inverse function of f, then the value of g' (pi/4+1/sqrt2) has the value equal to

Consider the compound statements ''35 is divisible by 5 or 6'' Write the component statement of the given statement.

Let 0 ltx lt pi//4 then (sec2x-tan2x) equals

Determine real values of x and y for which each statement is true (x-yi)(2+ 3i) = (x-2i)/(1-i)

Simiplify :(3-7i)^(2)

By shifting origin to (-1, 2), the equation y^(2) + 8x - 4y + 12 = 0 changes as y^(2) = 4axthen a =

(x^(2))/(25)-(y^(2))/(4)=1

The number of values of theta satisfying 4 cos theta + 3 sin theta = 5as well as 3 cos theta + 4 sin theta = 5is

sin x = 1/4 ,x in quadrant II

Write the contrapositive and converse of the following statements: x is an even number implies that x is divisible by 4.

A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will be B

A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will beB or vowel ?

A letter is chosen at random from the letters in the word PROBABILITY . Whatis the probability that tha letter will be a vowel

Compute the derivative of f(x) = sin^(2) x.

Solve sin ^(2) theta - 2 cos theta + (1)/(4) = 0 for the general solution.

For what values of k the equation sin x + cos (k + x) + cos ( k - x) = 2has real solution ?

Number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)Sin^(-1)(sinx)" where "-pi le x le pi

If 'f' is a polynomial such that f ((1-x)/(1+x))f((1+x)/(1-x))=f((1-x)/(1+x))+f((1+x)/(1-x)) ( where x != 0, pm 1 ) and f(3)=28 then the value of (1)/(605) ( sum_(n=1)^(10) (f(n)-1)) is

Let veca= 2 hati + 3hatj - 6hatk, vecb = 2hati - 3hatj + 6hatk and vecc = -2 hati + 3hatj + 6hatk. Let veca_(1) be the projection of veca on vecb and veca_(2) be the projection of veca_(1) on vecc . Thenveca_(1).vecb is equal to

|{:(logx,logy,logz),(log2x,log2y,log2z),(log3x,log3y,log3z):}|=

a = sec theta - tan theta and b=cosectheta+cottheta rArr a =

Fill in the blanks of the following the value of sqrt(-25)xxsqrt(-9) is ...

Write the converse of the following statements: If a number n is even, then n^(2) is even.

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Orthocentre of the triangle formed by lines 2x^(2)-3xy-2y^(2)=0 and 3x+4y-20=0 is

Find the mean deviation about median for the following data:

The time ‘t' of a complete oscillation of a simple pendulum of length 1 is given by t=2pisqrt((l)/(g)) where gis gravitational constant. Find the approximate percentage of error in t when the percentage of error in lis 1%

A line with direction consines proportional to 1, -5 and -2 meets lines x = y + 5 =z + 1 and x + 5 = 3y = 2z. The coordinates of each of the points of the intersection are given by

Find the derivative of cos x from first principle.

Find the constant term of (2x^(3)-(1)/(3x^(2)))^(5).

Evaluate the following limits : Lim_(x to 0) (sin 3x - sin x )/(sin x)

If p,q,r are in G.P then p/q=q/r (True/False)

The stationary points of f(x) =x^(3)-9x^(2)+24x-12are

Find the derivative of the function from first principle x ^(3)

The solution set of equation cos^(5) x = 1 + sin^(4) xis

If a line l passes through (k,2k)(3k,3k) and (3,1), k ne0, then the distance from the origin to the line l is