14949 + Interview Questions in Maths in Class 11 Page 118 InterviewSolution

5851.	Express each of the following in the form b or bi, where b is a real number -i(-i)
Answer» ANSWER :`-1`

Discussion

5852.	For the distribution given in the following table, find the mean and the standard deviation by the step deviation method.
Answer» ANSWER :8 (to the NEAREST WHOLE NUMBER)

Discussion

5853.	The perpendicular from the origin to a line meets it at the point (-2, 9) find the equation of the line.
Answer» ANSWER :`2X - 9Y + 85 = 0 `

Discussion

5854.	Express each of the following in the form b or bi, where b is a real number i(-i)
Answer» ANSWER :1

Discussion

5855.	Find the sum to n term the series : (x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^(2)+y^(3))+…..
Answer» ANSWER :`=(1)/(X-y)[(x^(2)(x^(N)-1))/(x-1)-(y^(2)(y^(n)-1))/(y-1)]`

Discussion

5856.	Find the sum to n terms of each of the series in3 xx8 + 6 xx 11 + 9 xx 14 +.....
Answer» ANSWER :`3N(n+1) (n+3)`

Discussion

5857.	The value of sin^(3) 10^(0) + sin^(3) 50^(0) - sin^(3) 70^(0) is equal to
Answer» `-(3)/(2)` `(3)/(4)` `-(3)/(4)` `-(3)/(8)` ANSWER :D

Discussion

5858.	Next term of the sequence: 1/6,1/3,2/3,….. Is 4/3 (True/False)
Answer» ANSWER :TRUE

Discussion

5859.	Evaluate : lim_(xto0) (a^(x)-b^(x))/x
Answer» ANSWER :`log_(E) (a/b)`

Discussion

5860.	Find the value of the following: (a) (i) sin 48^(@)(ii) sin23^(@)26' (b)(i)cos20^(@) 10' (ii) cos16^(@) 11' ( c) (i) tan54^(@) 30' (ii) tan42^(@) 6' (d) (i) cot 131^(@) 20'(ii) cot46^(@) 26'.
Answer» ANSWER :(a) (i) 0.7431 (II)0.3976 (B)(i)0.9387(ii)0.9604 (i) 1.4019 (ii) 0.9036 (d) (i) -0.8795 (ii) 0.9512

Discussion

5861.	Parametric form of the equation of the line 3x - 6y - 2z - 15=0 = 2x + y- 2z - 5 is
Answer» `(X-5)/(-1) =y/2 = (z)/(15)` `(x-1)/(14) = (y-5)/(2) = (z-1)/(15)` `(x -3)/(14) = (y +1)/(2) = (z)/(15)` `(x +5)/( 14) = y/2 = (z)/(15)` ANSWER :C

Discussion

5862.	Two dice are thrown. The number on one die is multiple of 2 and the number on other die is multiple of 3. Its probability is ......
Answer» `(5)/(36)` `(11)/(36)` `(1)/(6)` `(1)/(3)` ANSWER :B

Discussion

5863.	Find the ratio in which the centroid of tetrahedron ABCD divides the line joining the vertex A to the centroid of triangle BCD.
Answer» ANSWER :`3 : 1`

Discussion

5864.	2x + y ge 4, x + y le 3, 2x - 3y le 6
Answer» SOLUTION :First INEQUATION : ` 2x + y le 4` Corresponding equation : ` 2x+ y = 4` This line passes through the points A(2, 0) and B (0, 4) . Join AB . At point (0, 0) , from the inequation `0 ge 4` (False) `:.` The solution of this inequation is that region of XY-place divided by line AB in which (0, 0) does not LIE. Second inequation : `x + y le 3` Corresponding equation : `x + y = 3` This line thorugh the points C(3, 0) and D (0, 3). Join CD. At point (0, 0), from the inequation, 0le3 (True) `:.` The solution of this inequation is that region of XY-plane divided by line CD in which (0, 0) lies. Third inequation : ` 2x - 3y le 6` Corresponding equation: ` 2x - 3y = 6` This line paaes through the points C (3, 0) and E (0, -2). Join CE At point (0, o), from the inequation, 0 le 6 (True) `:.` The solution of this inequation is that region of XY-plane divided by line CE in which (0, 0) lies . The solution of given inequations is shown by the SHADED region

Discussion

5865.	Identify the Quantifiers in the following statements: There exists a real number which is not a rational number.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

5866.	In triangle ABC if p_1, p_2, p_3 are the length of the altitudes from A, B, C then p_1,p_2,p_3
Answer» ` R ` ` ( 8 DELTA ^(3))/( abc ` ` (1)/(Delta) ` ` (1 )/(R ) ` ANSWER :B

Discussion

5867.	Sec h^(-1)((2)/(3))=log_(e)[((k+1)+sqrt(k^(2)+1))/(k)] then k=
Answer» 2 3 5 6 Answer :A

Discussion

5868.	The value of x in (0, (pi)/(2)) satisfying (sqrt(3) - 1)/(sin x) + (sqrt(3) + 1)/( cos x) = 4 sqrt(2) is
Answer» `(PI)/12` `(5PI)/12` `(7pi)/12` `(11pi)/36` ANSWER :A::D

Discussion

5869.	If 2sec 2alpha=tanbeta+cotbeta, then one of the values of alpha+beta is
Answer» `PI/4` `pi/3` `pi/2` `pi` ANSWER :A

Discussion

5870.	In each of the followingfind the equation fot the ellipse that satisfies the given conditions : Vertices (0,+-13), foci (0,+-5)
Answer» ANSWER :`(X^(2))/(144) + (y^(2))/(169) = 1`

Discussion

5871.	Evaluate the following limits : Lim_(x to 0) (sin^(2)5x)/(sin ^(2)bx)
Answer» ANSWER :`(a^(2))/(B^(2))`

Discussion

5872.	Three numbers a,b, c are between 2 and 18 such that a + b+ c= 25. If 2,a,b are in A.P and b,c 18 are in G.P then these numbers are…….
Answer» 5,8,12 4,8,13 3,9,13 5,9,11 Answer :A

Discussion

5873.	What is the rationalising factor of sqrt(1 + x) - sqrt(1 - x)?
Answer» SOLUTION :`SQRT(1+X) + sqrt(1 - x)`

Discussion

5874.	Evaluate Lt_(x to pi//2)(cos x)/((x - pi/2))
Answer» ANSWER :1

Discussion

5875.	What is meant by non-periodicmotion? Give any two examples .
Answer» Solution :Non-Periodic motion : Any motion which does not repeat itself after a REGULAR interval of TIME is known as non-periodic motion. Example : Occurance of EARTH quake, eruption of volcano, ETC

Discussion

5876.	Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find the length of the portion of the line interceptes between the axes.
Answer» ANSWER : `3/(2)SQRT(5)`

Discussion

5877.	Find the equation of the hyperbola with eccentricity (3)/(2) and foci at (pm 2, 0).
Answer» `(X^(2))/(4) - (y^(2))/(5) = (4)/(5)` `(x^(2))/(9) - (y^(2))/(9) = (4)/(9)` `(x^(2))/(4) - (y^(2))/(9) = 1` NONE of these Answer :A

Discussion

5878.	The plane passing through the points (1,1,1),(1,-1,1) and (-7,-3,-5) is parallel to
Answer» x-axis y-axis z-axis can not be DECIDED ANSWER :B

Discussion

5879.	Given that z=-1+isqrt(3)
Answer» ANSWER :`(2PI)/(3)`

Discussion

5880.	A = (1, 2, 2), B = (2, 3, 6), C = (3,4, 12). The d.c's of a line equally inclined with OA, OB and OC where O is the origin, are
Answer» `(1)/(SQRT(2)), (-1)/(sqrt(2)), 0` `(1)/(sqrt(2)), (1)/(sqrt(2)), 0` `(1)/(sqrt(3)), -(1)/(sqrt(3)),(1)/(sqrt(3))` `(1)/(sqrt(3)),-(1)/(sqrt(3)),-(1)/(sqrt(3))` Answer :D

Discussion

5881.	If sin h^(-1)x+cos h^(-1)x=y then sin hy=
Answer» `X^(2)+ SQRT(x^(4)-1)` `x^(2)- sqrt(x^(4)-1)` `x^(2)+ sqrt(x^(4)+1)` `x^(2)- sqrt(x^(4)+1)` Answer :A

Discussion

5882.	Express the following as functions of angles less than 45^(@) : sin(-1785^(@))
Answer» ANSWER :`SIN 15^(@)`

Discussion

5883.	If A is 3xx3 matrix and det A=-2 then \|"Adj A"\|=
Answer» `-4` 8 `-8` 4 Answer :D

Discussion

5884.	Three numbers are chosen at random from the first 20 natural numbers. The probability that their product is even is
Answer» `2/19` `4/19` `9/19` `17/19` ANSWER :A

Discussion

5885.	(I) A Refrigerator is a reverse of carnot engine. (II) Carnot engine has lowest efficiency. Which one is correct statement?
Answer» I only II only Both are correct None Solution :I only

Discussion

5886.	Find the coefficient of (iii) (1)/(x^(17) ) in the expansion of (x^(4) - (1)/(x^3) )^(15).
Answer» ANSWER :`-1365`

Discussion

5887.	(i) Find tan(- (2pi)/(3)), cos 315^(@), sec210^(@), cosec225^(@), Tan(- (23pi)/(3)), cot(-300^(@)) and sin. (-(17pi)/(4)).
Answer» ANSWER :` -SIN. Pi/4 = -(1)/(SQRT(2))`

Discussion

5888.	What loci do the equation represent in space? z =0
Answer» ANSWER :y = 0 , Z = 0 is the EQUATION of X - axisin SPACE .

Discussion

5889.	Ifalpha in Q_(4) and sin""(alpha)/2 + cos""(alpha)/2 = (-1)/2then sin 2 alpha=
Answer» `(3sqrt7)/8` `(3sqrt7)/16` `(-3sqrt7)/4` `(-3sqrt7)/8` ANSWER :D

Discussion

5890.	Evaluate the following limits in lim_(xrarr0)(ax+b)/(cx+1)
Answer» ANSWER :B

Discussion

5891.	If f(x+k) + f(x) = 0 AA x in R and k in R^(+), then the period of f(x) is
Answer» 0 `(PI)/(2)` 2K Does not exist Answer :C

Discussion

5892.	Find the parametic equation of the circle : x^(2)+y^(2)+px+qy=0.
Answer» ANSWER :`(-p/2+1/2sqrt(p^(2)+Q^(2))COSTHETA,-q/2+1/2sqrt(p^(2)+q^(2))sin THETA)`

Discussion

5893.	If (sintheta,costheta,0 in[0,2theta] and (1,4) " lie on the same side or on the line " sqrt3x-y+1=0 then the maximum value of sintheta will be
Answer» 1 0 `1/2` `1-sqrt3/2` ANSWER :B

Discussion

5894.	If x+ y = sin(x+y) then (dy)/(dx) =
Answer» `1/2` 0 `-1` `1/3` ANSWER :C

Discussion

5895.	Cot^(-1)(sqrt(Cos alpha))-Tan^(-1)( sqrt(Cos alpha))=x then Sinx=
Answer» `"TAN"^(2)(ALPHA)/2` `COT^(2)((alpha)/2)` `tan alpha` `"cot"(alpha)/2` ANSWER :A

Discussion

5896.	An experiment consists of rolling a die until a 2 appears. (ii) How many elements of the sample space correspond to the event that the 2 appears not later than the kth roll of the die ?
Answer» ANSWER :`=(5^(K)-1)/(5-1)`

Discussion

5897.	Represent to solution set of each of the following inequationgraphically in two dimensional plane: \ -3x+2ylt=6
Answer» ANSWER :`-2/5`

Discussion

5898.	Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^("th") " to " (2n)^("th")term is 1/r^n .
Answer» ANSWER :`(1)/(R^(N))`

Discussion

5899.	Find from first principles the differential coefficient of 2x^(2) + 3x.
Answer» ANSWER :`4X +3`

Discussion

5900.	Number of solutions of equation cosx+cosy+cosz=-3
Answer» ONE solution if `x,y,ZIN[0,pi]` one solution if `x,y,Z in [0,2pi]` TWO solution if `x,y,z in [0,2pi]` No solution if `x,y,z in [0,pi]` Answer :A::B::D

Discussion

Explore topic-wise InterviewSolutions in .

Express each of the following in the form b or bi, where b is a real number -i(-i)

For the distribution given in the following table, find the mean and the standard deviation by the step deviation method.

The perpendicular from the origin to a line meets it at the point (-2, 9) find the equation of the line.

Express each of the following in the form b or bi, where b is a real number i(-i)

Find the sum to n term the series : (x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^(2)+y^(3))+…..

Find the sum to n terms of each of the series in3 xx8 + 6 xx 11 + 9 xx 14 +.....

The value of sin^(3) 10^(0) + sin^(3) 50^(0) - sin^(3) 70^(0) is equal to

Next term of the sequence: 1/6,1/3,2/3,….. Is 4/3 (True/False)

Evaluate : lim_(xto0) (a^(x)-b^(x))/x

Find the value of the following: (a) (i) sin 48^(@)(ii) sin23^(@)26' (b)(i)cos20^(@) 10' (ii) cos16^(@) 11' ( c) (i) tan54^(@) 30' (ii) tan42^(@) 6' (d) (i) cot 131^(@) 20'(ii) cot46^(@) 26'.

Parametric form of the equation of the line 3x - 6y - 2z - 15=0 = 2x + y- 2z - 5 is

Two dice are thrown. The number on one die is multiple of 2 and the number on other die is multiple of 3. Its probability is ......

Find the ratio in which the centroid of tetrahedron ABCD divides the line joining the vertex A to the centroid of triangle BCD.

2x + y ge 4, x + y le 3, 2x - 3y le 6

Identify the Quantifiers in the following statements: There exists a real number which is not a rational number.

In triangle ABC if p_1, p_2, p_3 are the length of the altitudes from A, B, C then p_1,p_2,p_3

Sec h^(-1)((2)/(3))=log_(e)[((k+1)+sqrt(k^(2)+1))/(k)] then k=

The value of x in (0, (pi)/(2)) satisfying (sqrt(3) - 1)/(sin x) + (sqrt(3) + 1)/( cos x) = 4 sqrt(2) is

If 2sec 2alpha=tanbeta+cotbeta, then one of the values of alpha+beta is

In each of the followingfind the equation fot the ellipse that satisfies the given conditions : Vertices (0,+-13), foci (0,+-5)

Evaluate the following limits : Lim_(x to 0) (sin^(2)5x)/(sin ^(2)bx)

Three numbers a,b, c are between 2 and 18 such that a + b+ c= 25. If 2,a,b are in A.P and b,c 18 are in G.P then these numbers are…….

What is the rationalising factor of sqrt(1 + x) - sqrt(1 - x)?

Evaluate Lt_(x to pi//2)(cos x)/((x - pi/2))

What is meant by non-periodicmotion? Give any two examples .

Show that the three points (5, 1), (1, -1) and (11, 4) lie on a straight line. Further find the length of the portion of the line interceptes between the axes.

Find the equation of the hyperbola with eccentricity (3)/(2) and foci at (pm 2, 0).

The plane passing through the points (1,1,1),(1,-1,1) and (-7,-3,-5) is parallel to

Given that z=-1+isqrt(3)

A = (1, 2, 2), B = (2, 3, 6), C = (3,4, 12). The d.c's of a line equally inclined with OA, OB and OC where O is the origin, are

If sin h^(-1)x+cos h^(-1)x=y then sin hy=

Express the following as functions of angles less than 45^(@) : sin(-1785^(@))

If A is 3xx3 matrix and det A=-2 then |"Adj A"|=

Three numbers are chosen at random from the first 20 natural numbers. The probability that their product is even is

(I) A Refrigerator is a reverse of carnot engine. (II) Carnot engine has lowest efficiency. Which one is correct statement?

Find the coefficient of (iii) (1)/(x^(17) ) in the expansion of (x^(4) - (1)/(x^3) )^(15).

(i) Find tan(- (2pi)/(3)), cos 315^(@), sec210^(@), cosec225^(@), Tan(- (23pi)/(3)), cot(-300^(@)) and sin. (-(17pi)/(4)).

What loci do the equation represent in space? z =0

Ifalpha in Q_(4) and sin""(alpha)/2 + cos""(alpha)/2 = (-1)/2then sin 2 alpha=

Evaluate the following limits in lim_(xrarr0)(ax+b)/(cx+1)

If f(x+k) + f(x) = 0 AA x in R and k in R^(+), then the period of f(x) is

Find the parametic equation of the circle : x^(2)+y^(2)+px+qy=0.

If (sintheta,costheta,0 in[0,2theta] and (1,4) " lie on the same side or on the line " sqrt3x-y+1=0 then the maximum value of sintheta will be

If x+ y = sin(x+y) then (dy)/(dx) =

Cot^(-1)(sqrt(Cos alpha))-Tan^(-1)( sqrt(Cos alpha))=x then Sinx=

An experiment consists of rolling a die until a 2 appears. (ii) How many elements of the sample space correspond to the event that the 2 appears not later than the kth roll of the die ?

Represent to solution set of each of the following inequationgraphically in two dimensional plane: \ -3x+2ylt=6

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^("th") " to " (2n)^("th")term is 1/r^n .

Find from first principles the differential coefficient of 2x^(2) + 3x.

Number of solutions of equation cosx+cosy+cosz=-3