14949 + Interview Questions in Maths in Class 11 Page 254 InterviewSolution

12651.	(sin 12 A)/(sin 4A) - (cos 12 A)/(cos 4A)=
Answer» 6 4 2 1 Answer :C

Discussion

12652.	Which of the following statements are true and which are false? p:20 is the multiple of4 and 5.
Answer» ANSWER :1

Discussion

12653.	For x, y, z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)t+3pi The value of x+y+z is equal to
Answer» 1 0 2 -1 Answer :B

Discussion

12654.	If sin theta_(1) sin theta_(2) - cos theta_(1)cos theta_(2)+1=0, then the value of tan(theta_(1)//2)cot(theta_(1)//2) is equal to:
Answer» `-1` 1 2 `-2` ANSWER :A

Discussion

12655.	f: R rarr R, f(x) = sec^(2)x - tan^(2) x is constant function .
Answer» ANSWER :TRUE STATEMENT

Discussion

12656.	cos (alpha - beta ) = 1 and cos (alpha - beta ) = 1//e"where " alpha, beta in [-pi, pi] . Number of pairs of alpha , betawhich satisfy boththe equations is
Answer» 0 1 2 4 Answer :D

Discussion

12657.	Write down the converse of following statements: If a rectangle R is a square then R is a rhombus.
Answer» ANSWER :If the rectagle R is rhoumbus then it is SQUARE.

Discussion

12658.	Please go out side is statement .
Answer» ANSWER :FALSE STATEMENT

Discussion

12659.	Express (-sqrt(3) + sqrt(-2))(2sqrt(3)-i), in the form of a+ib.
Answer» ANSWER :`(6 + SQRT(2)) + sqrt(3)(1+2sqrt(2))i`

Discussion

12660.	If A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+bar(j)-bar(k)), C(bar(i)-3bar(j)+2bar(k)), D(bar(i)-bar(j)-2bar(k)) then the vector equation of the plane parallel to bar(ABC) and passing through the centroid of the tetra-hedron ABCD is
Answer» `bar(R)=(2BAR(i)-bar(J)-bar(k))+s(bar(i)+bar(j)+bar(k))+t(bar(i)+2bar(j)-5bar(k))` `bar(r)=(2bar(i)-bar(j)+bar(k))+s(bar(i)-bar(j)+bar(k))+t(bar(i)+2bar(j)+5bar(k))` `bar(r)=(2bar(i)+bar(j)-bar(k))+s(bar(i)+bar(j)-bar(k))+t(bar(i)-2bar(j)+5bar(k))` `bar(r)=(2bar(i)+bar(j)+bar(k))+s(bar(i)-bar(j)-bar(k))+t(bar(i)+2bar(j)-5bar(k))` Answer :A

Discussion

12661.	Evaluate the following limits in Exercises lim_(xto0)(ax+b)/(cx+1)
Answer» ANSWER :B

Discussion

12662.	Write the conjugate of (6+5i)^(2)
Answer» ANSWER :`11-60i`

Discussion

12663.	Two numbers are selected from first 40 natural numbers. The probability that the sum of two number is odd is:
Answer» `16/39` `19/39` `20/39` NONE of these Solution :N/a

Discussion

12664.	Find the mean, variance and standard deviation using short-cut method Calculate the standard deviation and mean diameter of the circles.
Answer» ANSWER :5.55, 43.5

Discussion

12665.	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 A – D
Answer» ANSWER :`{3, 6, 9, 12, 18, 21}`

Discussion

12666.	( cos 6 x +6 cos 4 x+ 15 cos 2 x+ 10)/( cos 5 x+ 5 cos 3 x + 10 cos x)=
Answer» `2 SIN x + cos x` `- 2 sin x` `cos 2x` `sin 2x` Answer :B

Discussion

12667.	Let E={1, 2, 3, 4} and F= {1, 2}. Then the number of onto functions from E to F is
Answer» 14 16 12 8 Answer :A

Discussion

12668.	How many triangles may be formed by joining any three of the nine points when no three of them are collinear ,
Answer» ANSWER :`84`

Discussion

12669.	Differentiate sqrt(x) with respect to x from definition.
Answer» Answer :`(d)/( DX) ( SQRT(x) ) = (1)/( 2 sqrt(x) )`

Discussion

12670.	A parabolic path is with focus (-6,-6) and vetex (-2,-2).Find the equation of the parabolic path.
Answer» SOLUTION :`x^2 +y^2-2xy+32x+32y+128=0`

Discussion

12671.	If a+b + c=0 then line 3ax+by+c=0 passes from ….....of the following point.
Answer» ANSWER :`(3/4,1/2)`

Discussion

12672.	Reduce the lines 3x - 4y + 4 = 0 and 4x - 3y + 12 = 0 to the normal form and hence find which line is nearer to the origin.
Answer» Answer :`3X - 4t + 4 = 0 is NEARER to ORIGIN

Discussion

12673.	Check whether the statement is true or not:"Every square is a rectangle."
Answer» ANSWER :T

Discussion

12674.	If the area os an isosceles triangle is sqrt2 + 1 and vertical angle is 45^(@) then the base of the triangle is
Answer» 1 2 `SQRT2` `sqrt2 - 1` ANSWER :B

Discussion

12675.	If the function 'f' defined by f(x)={{:(kx+1,if,-1lex le1),(x^(2)-1,if, 1le x le2):} is continuous functo on [-1,2] then the find th value of K.
Answer» ANSWER :`k=-1`

Discussion

12676.	The probability that a student will pass the final examinatin in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?
Answer» ANSWER :0.65

Discussion

12677.	Find the stationary points and stationary values for the following functions. (x-1)(x-2)(x-3)
Answer» ANSWER :`(2+(1)/(SQRT(3)), (-2)/(3sqrt(3))), (2-(1)/(sqrt(3)), (2)/(3sqrt(3)))`

Discussion

12678.	The following questions consist of two statements, one labelled as 'Statement I' and the other 'Statement II'. You have to examine these two statements carefully and decide if the Statement I and the Statement II, are individually true and if so, whether the Statement II is the correct explanation for the given Statement I. Select your answer to these items using the codes given below and then select the correct option. Statement-1 : sin^(-1)(1/sqrt(e)) gt tan^(-1)(1/sqrt(pi)) Statement-2 : sin^(-1)x gt tan^(-1)y" for "x gt y, forallx, y in (0,1)
Answer» Both I and II are INDIVIDUALLY trueand II is the CORRECT explanation of I Both I and II are individually TRUE but II is not the correct explanation of I I is true but II is false I is false but II is true Answer :A

Discussion

12679.	Prove by direct method that for any integer n, n^(3)-n is always even.
Answer» ANSWER :HENCE the GIVEN STATEMENT is PROVED.

Discussion

12680.	A, B and C are mutually exclusive and exhaustive events. If 1/3P(C)=1/2P(A)=P(B),then p(B) = …..
Answer» ANSWER :`1/6`

Discussion

12681.	If(n!)/( 2!( n-2) !)and (eta !)/( 4!(n-4)!)are in the ratio 2: 1 , find the value of n.
Answer» ANSWER :` 5`

Discussion

12682.	The orthocentre of the triangle whose sides are given by 4x-7y+10=0,x+y-5=0 and 7x+4y-15=0
Answer» `(-1,2)` `(1,0)` `(-1,2)` `(1,2)` ANSWER :D

Discussion

12683.	Which is larger (1.01)^1000000 or 10,000?
Answer» ANSWER :`(1..01)^1000000` 10000

Discussion

12684.	Period of sinx cos ( x + (pi)/(4) ) is
Answer» `(PI)/(2)` `pi` `(3PI)/(2)` `2PI` ANSWER :B

Discussion

12685.	Iftan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the equation 8x ^(2) -26x + 15 =0, then find the value of cos (alpha + beta).
Answer» ANSWER :`- (627)/(725)`

Discussion

12686.	Let f(x) and g(x) be two continous functions defined from Rrarr R, such that f(x_(1)) gt f(x_(2)) and g(x_(1)) lt g(x_(2)) AA x_(1) gt x_(2), then find the solution set of f(g(alpha^(2) - 2 alpha) gt f(g(3 alpha - 4).
Answer» ANSWER :`(ALPHA - 1)(alpha - 4) lt 0`

Discussion

12687.	How many terms of G.P. 3, 3^2, 3^3,… are needed to give the sum 120?
Answer» ANSWER :4

Discussion

12688.	Which of the following sets are finite or infinite : {x : x in N, x lt 200}
Answer» ANSWER :it is an FINITE SET

Discussion

12689.	If f''(x)lt0AAx inRandg(x)=f(x^(2)-2)+f(6-x^(2))then
Answer» G(X)is an INCREASING in [0,2] g(x) is an increasing in `[2,oo)` g(x) has a local minima at x=-2 g(x) has a local maxima at x=2 Answer :A::D

Discussion

12690.	sec^(2)(tan^(-1)(2))+cosec^(2)(cot^(-1)(2))=
Answer» `5` 10 15 50 Answer :B

Discussion

12691.	The distance between the circumcentre and the orthocentre of the triangle formed by the points (2, 1, 5), (3, 2, 3) and (4, 0, 4) is
Answer» (2,1,5) (3,2,3) (4,0,4) (3,1,4) ANSWER :D

Discussion

12692.	Determine the domain and range of the relation R defined by R={(x,x+5) : x in [0,1,2,3,4,5}}.
Answer» ANSWER :DOMAIN of R={0,1,2,3,4,5} RANGE of R={5,6,7,8,9,10}

Discussion

12693.	Find the mean, variance and standard deviation using short-cut method
Answer» ANSWER :93, 105.58, 10.27

Discussion

12694.	If the equations x^(2) + 2x + 3 lambda =0 and 2x^(2) + 3x + 5 lambda= 0 have a non- zero common roots. then lambda =(a)1(b)-1(c)3(d)None of these
Answer» 1 `-1` 3 None of these ANSWER :B

Discussion

12695.	Find the derivative of w.r.to x log (cot ( 1 - x ^(2)))
Answer» ANSWER :`4X COSEC (2-2x ^(2))`

Discussion

12696.	If the pair of lines 6x^(2)+7xy+2y^(2)=0,6x^(2)+7xy+2y^(2)-5x-3y+1=0 form a parallelogram then its area
Answer» 1 2 3 4 Answer :A

Discussion

12697.	Consider the system of equations sin x cos 2 y = (a^(2) - 1) ^(2) + 1, cos x sin 2 y = a + 1 The number of values of a for which the system has a solution is
Answer» 1 2 3 4 Answer :B

Discussion

12698.	If f(x)=sin^(-1)(sqrt(3)/2x-1/2sqrt(1-x^(2))), -1/2 le x le 1, then f(x) is equal to
Answer» `SIN^(-1)(1/2)-sin^(-1)(X)` `sin^(-1)x-pi/6` `sin^(-1)x+pi/6` NONE of these Answer :B

Discussion

12699.	For every integer n ge 1, (3^(2n) -1) is divisible by
Answer» `2^(N+2)` `2^(n+1)` `2^(n+3)` `2^(n)` ANSWER :A

Discussion

12700.	""^(35)C_(8)+sum_(r=1)^(1)""^(42-r)C_(7)+sum_(s=1)^(5)""^(47-s)C_(40-s) , is
Answer» `""^(46)C_(7)` `""46C_(8)` `""^(47)C_(7)` `""^(47)C_(8)` Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

(sin 12 A)/(sin 4A) - (cos 12 A)/(cos 4A)=

Which of the following statements are true and which are false? p:20 is the multiple of4 and 5.

For x, y, z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)t+3pi The value of x+y+z is equal to

If sin theta_(1) sin theta_(2) - cos theta_(1)cos theta_(2)+1=0, then the value of tan(theta_(1)//2)cot(theta_(1)//2) is equal to:

f: R rarr R, f(x) = sec^(2)x - tan^(2) x is constant function .

cos (alpha - beta ) = 1 and cos (alpha - beta ) = 1//e"where " alpha, beta in [-pi, pi] . Number of pairs of alpha , betawhich satisfy boththe equations is

Write down the converse of following statements: If a rectangle R is a square then R is a rhombus.

Please go out side is statement .

Express (-sqrt(3) + sqrt(-2))(2sqrt(3)-i), in the form of a+ib.

If A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+bar(j)-bar(k)), C(bar(i)-3bar(j)+2bar(k)), D(bar(i)-bar(j)-2bar(k)) then the vector equation of the plane parallel to bar(ABC) and passing through the centroid of the tetra-hedron ABCD is

Evaluate the following limits in Exercises lim_(xto0)(ax+b)/(cx+1)

Write the conjugate of (6+5i)^(2)

Two numbers are selected from first 40 natural numbers. The probability that the sum of two number is odd is:

Find the mean, variance and standard deviation using short-cut method Calculate the standard deviation and mean diameter of the circles.

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 A – D

( cos 6 x +6 cos 4 x+ 15 cos 2 x+ 10)/( cos 5 x+ 5 cos 3 x + 10 cos x)=

Let E={1, 2, 3, 4} and F= {1, 2}. Then the number of onto functions from E to F is

How many triangles may be formed by joining any three of the nine points when no three of them are collinear ,

Differentiate sqrt(x) with respect to x from definition.

A parabolic path is with focus (-6,-6) and vetex (-2,-2).Find the equation of the parabolic path.

If a+b + c=0 then line 3ax+by+c=0 passes from ….....of the following point.

Reduce the lines 3x - 4y + 4 = 0 and 4x - 3y + 12 = 0 to the normal form and hence find which line is nearer to the origin.

Check whether the statement is true or not:"Every square is a rectangle."

If the area os an isosceles triangle is sqrt2 + 1 and vertical angle is 45^(@) then the base of the triangle is

If the function 'f' defined by f(x)={{:(kx+1,if,-1lex le1),(x^(2)-1,if, 1le x le2):} is continuous functo on [-1,2] then the find th value of K.

The probability that a student will pass the final examinatin in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?

Find the stationary points and stationary values for the following functions. (x-1)(x-2)(x-3)

Prove by direct method that for any integer n, n^(3)-n is always even.

A, B and C are mutually exclusive and exhaustive events. If 1/3P(C)=1/2P(A)=P(B),then p(B) = …..

If(n!)/( 2!( n-2) !)and (eta !)/( 4!(n-4)!)are in the ratio 2: 1 , find the value of n.

The orthocentre of the triangle whose sides are given by 4x-7y+10=0,x+y-5=0 and 7x+4y-15=0

Which is larger (1.01)^1000000 or 10,000?

Period of sinx cos ( x + (pi)/(4) ) is

Iftan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the equation 8x ^(2) -26x + 15 =0, then find the value of cos (alpha + beta).

Let f(x) and g(x) be two continous functions defined from Rrarr R, such that f(x_(1)) gt f(x_(2)) and g(x_(1)) lt g(x_(2)) AA x_(1) gt x_(2), then find the solution set of f(g(alpha^(2) - 2 alpha) gt f(g(3 alpha - 4).

How many terms of G.P. 3, 3^2, 3^3,… are needed to give the sum 120?

Which of the following sets are finite or infinite : {x : x in N, x lt 200}

If f''(x)lt0AAx inRandg(x)=f(x^(2)-2)+f(6-x^(2))then

sec^(2)(tan^(-1)(2))+cosec^(2)(cot^(-1)(2))=

The distance between the circumcentre and the orthocentre of the triangle formed by the points (2, 1, 5), (3, 2, 3) and (4, 0, 4) is

Determine the domain and range of the relation R defined by R={(x,x+5) : x in [0,1,2,3,4,5}}.

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

If the equations x^(2) + 2x + 3 lambda =0 and 2x^(2) + 3x + 5 lambda= 0 have a non- zero common roots. then lambda =(a)1(b)-1(c)3(d)None of these

Find the derivative of w.r.to x log (cot ( 1 - x ^(2)))

If the pair of lines 6x^(2)+7xy+2y^(2)=0,6x^(2)+7xy+2y^(2)-5x-3y+1=0 form a parallelogram then its area

Consider the system of equations sin x cos 2 y = (a^(2) - 1) ^(2) + 1, cos x sin 2 y = a + 1 The number of values of a for which the system has a solution is

If f(x)=sin^(-1)(sqrt(3)/2x-1/2sqrt(1-x^(2))), -1/2 le x le 1, then f(x) is equal to

For every integer n ge 1, (3^(2n) -1) is divisible by

""^(35)C_(8)+sum_(r=1)^(1)""^(42-r)C_(7)+sum_(s=1)^(5)""^(47-s)C_(40-s) , is