14949 + Interview Questions in Maths in Class 11 Page 168 InterviewSolution

8351.	An aeroplane is moving one kilometer high from west to east horizontally. From a point on the ground due south, the angle of elevation of the aaeroplane is 60^(@), and after 10 second, the angle ofelevtion of the aeroplane is observed as 30^(@),then the speed (in m//s) of the aeroplane is
Answer» `240sqrt3km//hr` `485km//hr` `364km//hr` `523 km//hr` ANSWER :A

Discussion

8352.	The set of points satisfying ax+by+cz=0 when a^(2)+b^(2)+c^(2)=0 is the
Answer» XY-co ORDINATE PLANE YZ-coordinate plane X-axis Every POINT of the SPACE ANSWER :D

Discussion

8353.	Simplify the following (5)/(i^(3))
Answer» ANSWER :5I

Discussion

8354.	Ifx= tan A - tan B , y= cot B- cot A " then " (1)/(x)+(1)/(y)=
Answer» COT (A - B) Cot (B - A) TAN (A - B) Tan (B - A) ANSWER :A

Discussion

8355.	2"tan"^(-1)1/5+"tan"^(-1)1/7+2"tan"^(-1)1/8=
Answer» `3/5` `5/3` `4/5` `SQRT(2)` ANSWER :B

Discussion

8356.	If cosA=-3/5 and pi/2 lt A lt pi, find the values of the following: i) sin2A, ii) cos2A, iii) tan2A
Answer» SOLUTION :i) `-24/25`, II) `-7/25`, III) `24/7`

Discussion

8357.	Find the sum of the sequence 7, 77, 777, 7777, ... to n terms.
Answer» ANSWER :`7/9[(10(10^(n-1)))/9-n]`

Discussion

8358.	Write down the contrapositive of the following statements.:if x is a real number such that 0ltxlt1, then x^(2)lt1
Answer» ANSWER :not REAL NUMBER.

Discussion

8359.	The ratio of the roots of the equation x^(2)+alphax+alpha+2=0 is 2. find the values of the parameter alpha.
Answer» ANSWER :`a=6,(-3)/(2)`.

Discussion

8360.	Let f and g be real-valued functions such that f(x+y)+f(x-y)=2f(x).g(y)AA x, y in R. Statements 1: If f(x) is not identically zero and \|f(x)\|le 1 AA x in R, then \|g(y)\|le 1AA y in R. Statement 2 : For any two real numbers x and y.\|x+y\| le \|x\|+\|y\|
Answer» Statement 1 is TRUE, statement 2 is true, statement 2 iscorrect explanation for statement 1. Statement 1 is true, statement 2 is true, statement 2 is notcorrect explanation for statement 1. Statement 1 is FALSE, but statement 2 is ture Statement 1 is true, but statement 2 is false Answer :A

Discussion

8361.	Find the equation of the set of the points P such that its distance from the points A(3, 4, -5) and B(-2, 1, 4) are equal.
Answer» ANSWER :10X + 6Y - 18z - 29 = 0

Discussion

8362.	Intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.
Answer» ANSWER :`2X + y + 6 = 0 `

Discussion

8363.	Find the mean deviation about the mean for the data in Question:
Answer» SOLUTION : MEAN `BARX=(sumf_(i)x_(i))/(sumf_(i))=17900/50=358` and mean DEVIATION `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))=7896/50` `=157.92`

Discussion

8364.	Letf(x)= (1)/(2)[f( xy ) + f((x)/(y)) ]AA x, y in R ^(+)such thatf(1)= 0, f^(1)(1) =2Now answer the following f^(1) (3) =
Answer» `1/3` `2/3` `1/2` `1/4` ANSWER :B

Discussion

8365.	Find the mean deviation about the mean for the data in Question:
Answer» SOLUTION : MEAN `BARX=(sumf_(i)x_(i))/(sumf_(i))=12530/100=125.3` `:.` Mean DEVIATION `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))=1128.8/100` `=11.28`

Discussion

8366.	Let f(x) be a polynomical function in x satisfyingthe conditionf(x) f(1//x)=f(x) +f(x) and f(3) = 28x ne 0The ratio in which xy plane divides the line joining the points A(f(2), f(1) f(0)) and B(f(0), f(-1), f(2)) is
Answer» `-1:9` `2:3` `1:9` `-2:9` ANSWER :a

Discussion

8367.	If the point A is symmetric to the point B(4,-1) with respect to the bisector of the first Quadrant then AB=
Answer» `5` `5sqrt(2)` `3sqrt(2)` `3` ANSWER :B

Discussion

8368.	Given that \|z+2\|=\|z-2\|
Answer» ANSWER :(-2,0) (2,0)

Discussion

8369.	If theta is eliminated from the equations x=a cos(theta-alpha) and y=b cos(theta-beta), then x^(2)/a^(2) + y^(2)/b^(2) -(2xy)/(ab) cos(alpha-beta) is equal to:
Answer» `sec^(2)(ALPHA - beta)` `"cosec"^(2)(alpha - beta)` `cos^(2)(-beta)` `SIN^(2)(alpha - beta)` ANSWER :D

Discussion

8370.	Find the derivative of the function from first principle cos ^(2) x
Answer» ANSWER :`SIN 2X`

Discussion

8371.	How many different words can be formed by using all the letters of the word ALLAHABAD ? In how many of them, vowels occupy the even position ? In how many of them has two L's are not together ?
Answer» ANSWER :7560, 60, 5880

Discussion

8372.	Find the equation of lines passing through origin and perpendicular to the pair of lines. x^(2)+xy-2y^(2)+4x-y+3=0
Answer» ANSWER :`2X^(2)+xy-y^(2)=0`

Discussion

8373.	The product of all values of x satisfying the equation sin^(-1)cos((2x^(2)+10abs(x)+4)/(x^(2)+5abs(x)+3))=cot(cot^(-1)((2-18abs(x))/(9abs(x))))+pi/2 is
Answer» 9 -9 -3 -1 Answer :A

Discussion

8374.	Find the number of popstive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
Answer» ANSWER :112

Discussion

8375.	Solve the inequalities graphically, x+2y le 8, 2x+y le 8, x ge 0,y ge 0.
Answer» ANSWER :`(##SPH_KSK_MAT_QB_XI_MAR_15_E09_004_A01##)`

Discussion

8376.	A plane passes through (2, 3, -1) and is perpendicular to the line having direction ratios 3, -4,7. The perpendicular distance from the origin to this plane is
Answer» `(3)/(SQRT(74))` `(5)/(sqrt(74))` `(6)/(sqrt(74))` `(13)/(sqrt(74))` Answer :D

Discussion

8377.	If A and B are two events such that A sub B and P(B)!=0, then which of the followingis correct ?
Answer» <P>` P(A//B) = (P (A))/(P(B)) ` `P(A//B) lt P (A) ` `P(A//B) GE P(A) ` `P(A//B) gt P(B) ` ANSWER :` P(A//B) ge P(A) `

Discussion

8378.	Fill in the blanks to make each of the following a true statement : A= {x : x in R, x ge 4}" and "{x : x in R, x lt 5} then A cap B = "………."
Answer» ANSWER :`= {4, 5}`

Discussion

8379.	If tan beta=2 sin alpha sin gamma "cosec" (alpha+ gamma) then cot alpha, cot beta, cot gamma are in
Answer» A.P G.P H.P A.G.P Answer :A

Discussion

8380.	A man 6ft. Walks at a uniform rate of 4 miles per hour away from a lamp post of 20 ft. high. Find the rate at which (i) the length of his shadow increases and (ii) the tip of his shadow moves.
Answer» ANSWER :`(40)/7` miles/hour

Discussion

8381.	Sketch the graphof cos 4x.
Answer» ANSWER :` (##VVA_ISC_MAT_XI_MTP_14_E01_018_A01##)`

Discussion

8382.	Write the following interval in set builder form. (-23, 5)
Answer» ANSWER :`={x : x in R, -23 le x LT 5}`

Discussion

8383.	Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms"= (n(n+1)^(2)(n+2))/(12), AA n in N.
Answer» `(N(n+1)^(2) (n+2)^(2) )/( 12)` `(n(n+1)^(2) ( n+2))/( 12)` `(n^(2) (n+1) (n+2) )/(12)` `((n+1))/(2)` ANSWER :B

Discussion

8384.	Examine the consistency of the following systems of equationsx+y+z=6,x+2y+3z=10,x+2y+4z=1 and if consistent find the complete solutions.
Answer» ANSWER :CONSISTANT UNIQUE SOLTUION `x=-7,y=22,z=-9`

Discussion

8385.	Examine the consistency of the following systems of equations2x+3y+z=9,x+2y+3z=6,3x+y+2z=8 and if consistent find the complete solutions.
Answer» ANSWER :Consistent ; `x=(35)/(18),y=(29)/(18),z=(5)/(18)`,

Discussion

8386.	Find the value of (a^2 + sqrta^2 - 1)^4 + (a^2 - sqrt'a^2 - 1')^4 .
Answer» ANSWER :`2a^8` + `12a^6` - `10a^4` -`4a^2` + 2

Discussion

8387.	Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. 2x-y+3z=8 -x+2y+z=4 3x+y-4z=0
Answer» ANSWER :CONSISTENT ; `x=y=z=2`

Discussion

8388.	Simplify: (3-7i)^(2)
Answer» ANSWER :`-40-42i`

Discussion

8389.	Examine the consistency of the following systems of equationsx+y+z=9,2x+5y+7z=52,2x+y-z=0and if consistent find the complete solutions.
Answer» ANSWER :CONSISTENT ; `x=1,y=3,z=5`

Discussion

8390.	Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. x-4y+7z=8 3x+8y-2z=6 7x-8y+26z=31
Answer» ANSWER :INCONSISTENT

Discussion

8391.	Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. x-3y-8z=-10 3x+y-4z=0 2x+5y+6z=13
Answer» ANSWER :`x=2k-1,y=3-2k,z=K` where k is a REAL NUMBER

Discussion

8392.	If tan^(-1)""(a+x)/a+tan^(-1)""(a-x)/a=pi/6 , then x^(2)=
Answer» `2sqrt(3A)` `sqrt(3a)` `2sqrt(3a^(2))` NONE of these Answer :C

Discussion

8393.	The value of the expression(1+sin2alpha)/(cos(2alpha-2pi)tan(alpha-(3pi)/4))-1/4sin2alpha(cot""(alpha)/2+cot((3pi)/2+(alpha)/2)) is
Answer» 0 1 `"SIN"^(2)ALPHA/2` `Sin^(2)alpha` ANSWER :D

Discussion

8394.	At x=0,f(x)=(3-x)e^(2x)-4xe^(x)-x
Answer» Has a minimum Has a maximum Has no extremum Is not defined Answer :C

Discussion

8395.	If the d.c's (l,m,n) of two lines are connected by the relations 3l+m+5n=0, 6mn - 2nl + 5lm=0 then the angle between the lines is
Answer» `COS^(-1)((1)/(6))orpi-cos^(-1)((1)/(6))` `45^(@)` `60^(@) or 120^(@)` `cos^(-1)""(19)/(SQRT(364))` Answer :A

Discussion

8396.	If f(x)= (x-a)^(2) (x-b)^(2) then find f(a+b)
Answer» ANSWER :`a^(2)B^(2)`

Discussion

8397.	Evaluate: int(2x+1)/((x-1)(x^(2)+1))dx.
Answer» ANSWER :`(3)/(2)log\|x-1\|+(7)/(4)log\|x^(2)+1\|+(1)/(2)TAN^(-1)x+c`

Discussion

8398.	The sum of the coefficients of the first three terms in the expansion of (x-3/(x^2))^m, x != 0. m being a natural number, is 559. Find the term of the expansion containing x^3.
Answer» ANSWER :`-5940`

Discussion

8399.	If the function f(x)=(log(1+ax)-log(1-bx))/(x) is continuous at x=0, then f(0)=
Answer» ANSWER :a+b

Discussion

8400.	Observe the following statements : A : If sin h^(-1)sqrt(3) = log_(e)(sec theta + tan theta), then theta = (pi)/(3) R : If tan theta sqrt(3), sec theta = 2 rArr theta = (pi)/(3). The the true statement among the following is :
Answer» A is TRUE, R is FALSE A is true, R is true, `R rArr A` A is false, R is true A is false, R is false Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

An aeroplane is moving one kilometer high from west to east horizontally. From a point on the ground due south, the angle of elevation of the aaeroplane is 60^(@), and after 10 second, the angle ofelevtion of the aeroplane is observed as 30^(@),then the speed (in m//s) of the aeroplane is

The set of points satisfying ax+by+cz=0 when a^(2)+b^(2)+c^(2)=0 is the

Simplify the following (5)/(i^(3))

Ifx= tan A - tan B , y= cot B- cot A " then " (1)/(x)+(1)/(y)=

2"tan"^(-1)1/5+"tan"^(-1)1/7+2"tan"^(-1)1/8=

If cosA=-3/5 and pi/2 lt A lt pi, find the values of the following: i) sin2A, ii) cos2A, iii) tan2A

Find the sum of the sequence 7, 77, 777, 7777, ... to n terms.

Write down the contrapositive of the following statements.:if x is a real number such that 0ltxlt1, then x^(2)lt1

The ratio of the roots of the equation x^(2)+alphax+alpha+2=0 is 2. find the values of the parameter alpha.

Let f and g be real-valued functions such that f(x+y)+f(x-y)=2f(x).g(y)AA x, y in R. Statements 1: If f(x) is not identically zero and |f(x)|le 1 AA x in R, then |g(y)|le 1AA y in R. Statement 2 : For any two real numbers x and y.|x+y| le |x|+|y|

Find the equation of the set of the points P such that its distance from the points A(3, 4, -5) and B(-2, 1, 4) are equal.

Intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.

Find the mean deviation about the mean for the data in Question:

Letf(x)= (1)/(2)[f( xy ) + f((x)/(y)) ]AA x, y in R ^(+)such thatf(1)= 0, f^(1)(1) =2Now answer the following f^(1) (3) =

Find the mean deviation about the mean for the data in Question:

Let f(x) be a polynomical function in x satisfyingthe conditionf(x) f(1//x)=f(x) +f(x) and f(3) = 28x ne 0The ratio in which xy plane divides the line joining the points A(f(2), f(1) f(0)) and B(f(0), f(-1), f(2)) is

If the point A is symmetric to the point B(4,-1) with respect to the bisector of the first Quadrant then AB=

Given that |z+2|=|z-2|

If theta is eliminated from the equations x=a cos(theta-alpha) and y=b cos(theta-beta), then x^(2)/a^(2) + y^(2)/b^(2) -(2xy)/(ab) cos(alpha-beta) is equal to:

Find the derivative of the function from first principle cos ^(2) x

How many different words can be formed by using all the letters of the word ALLAHABAD ? In how many of them, vowels occupy the even position ? In how many of them has two L's are not together ?

Find the equation of lines passing through origin and perpendicular to the pair of lines. x^(2)+xy-2y^(2)+4x-y+3=0

The product of all values of x satisfying the equation sin^(-1)cos((2x^(2)+10abs(x)+4)/(x^(2)+5abs(x)+3))=cot(cot^(-1)((2-18abs(x))/(9abs(x))))+pi/2 is

Find the number of popstive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.

Solve the inequalities graphically, x+2y le 8, 2x+y le 8, x ge 0,y ge 0.

A plane passes through (2, 3, -1) and is perpendicular to the line having direction ratios 3, -4,7. The perpendicular distance from the origin to this plane is

If A and B are two events such that A sub B and P(B)!=0, then which of the followingis correct ?

Fill in the blanks to make each of the following a true statement : A= {x : x in R, x ge 4}" and "{x : x in R, x lt 5} then A cap B = "………."

If tan beta=2 sin alpha sin gamma "cosec" (alpha+ gamma) then cot alpha, cot beta, cot gamma are in

A man 6ft. Walks at a uniform rate of 4 miles per hour away from a lamp post of 20 ft. high. Find the rate at which (i) the length of his shadow increases and (ii) the tip of his shadow moves.

Sketch the graphof cos 4x.

Write the following interval in set builder form. (-23, 5)

Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms"= (n(n+1)^(2)(n+2))/(12), AA n in N.

Examine the consistency of the following systems of equationsx+y+z=6,x+2y+3z=10,x+2y+4z=1 and if consistent find the complete solutions.

Examine the consistency of the following systems of equations2x+3y+z=9,x+2y+3z=6,3x+y+2z=8 and if consistent find the complete solutions.

Find the value of (a^2 + sqrta^2 - 1)^4 + (a^2 - sqrt'a^2 - 1')^4 .

Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. 2x-y+3z=8 -x+2y+z=4 3x+y-4z=0

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

Examine the consistency of the following systems of equationsx+y+z=9,2x+5y+7z=52,2x+y-z=0and if consistent find the complete solutions.

Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. x-4y+7z=8 3x+8y-2z=6 7x-8y+26z=31

Examine whether the systems of equations given are consistent or inconsistent and if consistent find the complete solution. x-3y-8z=-10 3x+y-4z=0 2x+5y+6z=13

If tan^(-1)""(a+x)/a+tan^(-1)""(a-x)/a=pi/6 , then x^(2)=

The value of the expression(1+sin2alpha)/(cos(2alpha-2pi)tan(alpha-(3pi)/4))-1/4sin2alpha(cot""(alpha)/2+cot((3pi)/2+(alpha)/2)) is

At x=0,f(x)=(3-x)e^(2x)-4xe^(x)-x

If the d.c's (l,m,n) of two lines are connected by the relations 3l+m+5n=0, 6mn - 2nl + 5lm=0 then the angle between the lines is

If f(x)= (x-a)^(2) (x-b)^(2) then find f(a+b)

Evaluate: int(2x+1)/((x-1)(x^(2)+1))dx.

The sum of the coefficients of the first three terms in the expansion of (x-3/(x^2))^m, x != 0. m being a natural number, is 559. Find the term of the expansion containing x^3.

If the function f(x)=(log(1+ax)-log(1-bx))/(x) is continuous at x=0, then f(0)=

Observe the following statements : A : If sin h^(-1)sqrt(3) = log_(e)(sec theta + tan theta), then theta = (pi)/(3) R : If tan theta sqrt(3), sec theta = 2 rArr theta = (pi)/(3). The the true statement among the following is :