14949 + Interview Questions in Maths in Class 11 Page 236 InterviewSolution

11751.	Let f(x) = {(x^(3) - x^(2) + 10x - 5",", x le 1),(-2x + log_(2)(b^(2) - 2)",",x gt 1):} find the values of b for which f(x) has the greatest valueat x = 1.
Answer» ANSWER :`b in [-SQRT(130), -sqrt(2)] CUP[sqrt(2), sqrt(130)]`

Discussion

11752.	(A) sin^(2)5+sin^(2)10+......+sin^(2)85=(17)/(2) (R) : If alpha+ beta=90^(@) then sin^(2)alpha+ sin ^(2) beta=1
Answer» A is TRUE, R is true and `R rArr A` A is true, R is true and `R CANCEL rArr A` A is true, R is false A is false, R is true Answer :A

Discussion

11753.	If x/a+y/b=1 " intersects " 5x^2+5y^2+5bx+5ay-9ab=0 at P and Q, anglePOQ=pi//2 then the relation between a and b is
Answer» a=B a=2b or b=2a a=3b or b=3a a+b=5 Answer :B

Discussion

11754.	In triangle ABC, a, b, c are the lengths of its sides and A, B C are the angles of triangle ABC. The correct relation is
Answer» `(B + c) SIN((B+C)/2) = a COS (A//2)` `(b - c) cos (A//2) = a sin((B-C)//2)` `(b - c) cos (A//2) = 2A sin (B+C)//2)` `(b-c)sin(B-C)//2)=a cos(A//2)` Answer :B

Discussion

11755.	6P_3 - 5P_2 = ......... .
Answer» ANSWER :100

Discussion

11756.	Find the slope of the line which makes an angle of 45^(@) with a line of slope -6/(5).
Answer» ANSWER : `11, 1/(11)`

Discussion

11757.	The ratio in which the line segmet joining the points (2,-4,3) and (-4,5,-6) is divided by the xy-plane is
Answer» " -1: 2" " 1:2" " -2 : 1 " " 2: 1 " ANSWER :B

Discussion

11758.	If f(0) = 0 ,f '(0)= 2, then the derivative of y = f(f(f(f(x)))) at x = 0 in
Answer» 2 8 16 1 Answer :C

Discussion

11759.	Which of the following sentences are statements ? Give reasons for your answer. (i) there are 35 days in a month. (ii) mathematics is difficult. (iii) the sum of 5 and 7 is greater than 10. (iv)the square of a number is an even number. (v) the sides of a quadrilateral have equal length. (vi) answer this question. (vii) the product of (-1) and 8 is 8. (viii) the sum of all interior angles of a triagle is 180^@. (ix) today is a windy day. (x) all real numbers are complex numbers.
Answer» SOLUTION :(i) it is always falase. `therefore` given sentence is a STATEMENT. (II) mathematics can be easy for someone and difficult for some other one. `therefore` given sentence is not a statement. (iii) this sentence is true. `therefore` given sentence is a statement. (iv) this sentence is sometimes true and sometimes false. `therefore` given sentence is not a statement. (v) this sentence is sometimes true and sometimes false . `therefore` given sentence is not a statement. (vi) it is a order. `therefore` given sentence is not a statement. (vii) this sentence is always false. `therefore` given sentence is a statement. (VIII) this sentence is always true. `therefore` given sentence is a statement. (ix) here, the word 'today' is used. `therefore` given sentence is not a statement. (x) all REAL numbers can be expressed in the form of complex numbers. `therefore` given sentence is a statement.

Discussion

11760.	The sum of two + ve numbers is 20 If the sum of their squares is minimum then one of the number is
Answer» 6 4 10 8 Answer :C

Discussion

11761.	Show that (secA+tanA)/("cosec A"+cot A)=("cosec A"-cotA)/(secA-tanA).
Answer» ANSWER :`("COSEC A"-COTA)/(secA-tanA)`.

Discussion

11762.	The r^(th) term t_(r) of a series is given by t_(r)=(r)/(r^(4)+r^(2)+1) then lim_(n to oo) overset(n) underset(r=1) sum t_(r)=
Answer» 1 `(1)/(2)` `(1)/(3)` does not exist Answer :B

Discussion

11763.	If the angles of a triangle are in the ratio 3:4:5, find the smallest angle in degrees and the greatest angle in radians.
Answer» ANSWER : `(##VVA_ISC_MAT_XI_MTP_03_E01_017_A01##)`

Discussion

11764.	Find the value ofsin ( - 405^(@))
Answer» ANSWER :`(-1)/(SQRT(2))`

Discussion

11765.	If 2,b,c, 23 are in G.P then (b-c)^(2)+ (c-2)^(2) + (23-b)^(2)= …….
Answer» 625 525 441 442 Answer :C

Discussion

11766.	sin^(-1) ( 12/13 ) + cos^(-1) (4/5) + tan^(-1) (63/16) =
Answer» ANSWER :A-q;B-s;C-p;D-r

Discussion

11767.	Find the value of k if the lines 2x+ky-10=0 and 5x+2y-7=0 are parallel.
Answer» ANSWER :`4/5`

Discussion

11768.	If sqrt(tan y) =e^(cos 2x) sin x,then (dy)/(dx) =
Answer» `sin2y.sin2x` `sin2y(Cotx-2sin2x)` `sin2x.sin2y` `cos2y.sin2x` ANSWER :B

Discussion

11769.	If sin (7 phi+9^(@))=cos2phi, find a value of phi.
Answer» ANSWER :`9^(@)`

Discussion

11770.	Two rods of lengths a and b slide along the axes in such a way that their ends are concyclic. The locus of the centre of the circle passing through these points is
Answer» `4(x^(2)+y^(2))=a^(2)+b^(2)` `x^(2)-y^(2)=a^(2)-b^(2)` `4(x^(2)-y^(2))=a^(2)-b^(2)` `x^(2)-y^(2)=a^(2)+b^(2)` Solution :Let `A_(1)A_(2) and B_(1)B_(2)` be two rods of length a and b which slide LONG OX and OY respectively. Let `x^(2) + y^(2) +2gx +2fy +c= 0` be the circle passing through `A_(1), A_(2), B_(1), B_(2)`.Then `A_(1)A_(2)`= Intercept of x-axis `=2 sqrt(g^(2)-c)` `rArr a=2 sqrt(g^(2)-c)`...(i) `B_(1)B_(2)`= intercept of y-axis `2sqrt(f^(2)-c)`...(ii) Squaring (i) and (ii), we get `a^(2)=4(g^(2)-c)` `b^(2)=4 (f^(2)-c)` Substracting `a^(2)-b^(2)=4(g^(2)-f^(2))` HENCE locus of CENTRE is `a^(2)-b^(2)=4(x^(2)-y^(2))`

Discussion

11771.	If the perimeter of a triangle is 12 unit and it in radius is 1 unit, then its area is
Answer» ANSWER : ` 6 SQ. `UNITS

Discussion

11772.	How many numbers are there between 100 and 1000 such that 7. is in the units places?
Answer» ANSWER :` 90 `

Discussion

11773.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of line which is of the equidistance from the line x = -2 and x = 6.
Answer» ANSWER :`X = 2`

Discussion

11774.	Find the mean deviation about the median for the data in 36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Answer» ANSWER :7

Discussion

11775.	Write the following sets in roster form: A = {x : x is an integer and –3 ≤ x < 7}
Answer» Answer :`A= {–3, –2, –1, 0, 1, 2, 3, 4, 5, 6 }`

Discussion

11776.	A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that All the three balls are white
Answer» ANSWER :`=(5)/(143)`

Discussion

11777.	A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that All the three balls are red
Answer» ANSWER :56

Discussion

11778.	Find the slope of a line perpendicular to the line which passes through each pair of the following points: (1, -11) and (5, 2)
Answer» ANSWER : `(-4)/(13)`

Discussion

11779.	Find the slope of a line perpendicular to the line which passes through each pair of the following points (-k, h) and (b, -f)
Answer» ANSWER : `(b+k)/(f+h)`

Discussion

11780.	f:R rarr [-1, oo) and f(x)= ln([\|sin 2 x \| + \| cos 2 x \| ])( where [.] is the greatest integer function ) Then,
Answer» `f(x)` has range Z `f(x)` is PERIODIC with FUNDAMENTAL PERIOD `pi/4` `f(x)` is invertible in `[0, pi/4]` `f(x)` is into function Answer :B::D

Discussion

11781.	Find the slope of a line perpendicular to the line which passes through each pair of the following points: (0, 8) and (-5, 2)
Answer» ANSWER : `(-5)/(6)`

Discussion

11782.	Evaluate the following limits : lim_(x to 0) (sin 3x)/(sin 2x)
Answer» ANSWER :`3/2`

Discussion

11783.	Find the slope of a line perpendicular to the line which passes through each pair of the following points: \[{\text{(}}{{\text{x}}_1}{\text{,}}{{\text{y}}_1}{\text{) and (}}{{\text{x}}_2}{\text{,}}{{\text{y}}_2}{\text{)}}{\text{.}}\]
Answer» ANSWER :`-((x_(2)-x_(1))/(y_(2)-y_(1)))`

Discussion

11784.	If theta is the angle between the vectors bar(i) + bar(j) , bar(j) + bar(k) then find sin theta.
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

11785.	Check the validity of the statements given below by the method given against it: q: If n is a real number with ngt3, then n^(2)gt9. (by contradiction method)
Answer» ANSWER :STATEMENT Q is TRUE

Discussion

11786.	The verticles of a triangle are (0,0) , (x cosx) and (sin^(3)x,0) , where 0ltxlt(pi)/(2). The maximum area for such a triangle in sq units is
Answer» `(3sqrt(3))/(32)` `(3sqrt(3))/(32)` `(4)/(32)` `(6sqrt(3))/(32)` ANSWER :A

Discussion

11787.	Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(2, 4, -8), C(-2, 2, 4). Find the coordinates of the fourth vertex.
Answer» ANSWER :D(X, y, Z) = (4, 7, 6)

Discussion

11788.	For what value of a is the function is continues at x=2 f(x)={(x^4 -16)/(x-2) ,if xne2a,if x=2
Answer» ANSWER :32

Discussion

11789.	If cos 2x gt \|sinx\|, x in (-(pi)/2,pi) then x in
Answer» `(-(pi)/6, (pi)/6)uu((5PI)/6, pi)` `(-(pi)/6, (pi)/6)uu(pi,((pi)/2)` `(-pi,(pi)/2)uu((5pi)/6,pi)` `(-pi,(pi)/2)uu((5pi)/6,2pi)` Answer :A

Discussion

11790.	Consider three planes P _(1) = x-y + z=1 , P_(2) = x + y -z = -1 and P _(3) , x - 3y + 3z =2. LetL_(1), L_(2) and L_(3) be the lines of intersection of the planes P _(2) and P _(3) , P _(3) and P _(1), and P _(2), respectively Statement -1: At least two of the lines L _(1),_(2) and L _(3) are non-parallel . Statement -1: the three planes fo not have a common point
Answer» Both the STATEMENT are true, and Statement 2 is the correct explanation for Statement 1 Both the statement are true, but Statement 2 is not the correct explanation for Statement 1 Statement 1 is true and Statement 2 is FALSE Statement 1 is false and Statement 2 is true. Answer :D

Discussion

11791.	If 180^(@)lt thetalt270^(@) and Sintheta=(-4)/5 calculate "Sin"theta/2 and "Cos"theta/2
Answer» ANSWER :`2/SQRT5, (-1)/sqrt5`

Discussion

11792.	PQR is an isosceles triangle whose equal sides PQ and PR are at right angles S and T are points on PQ such that QS = 6 (SP) " and " QT = 2 (TP) " and if" angle PRS = theta , angle PRT = phithen
Answer» `sin 2 PHI = 3//5` `2 phi + theta = pi//4` `SIN2 theta = 3//5` ` sin phi + cos phi = 4/sqrt10` Answer :A::B::D

Discussion

11793.	Let Aand B be two symmetrices of same order. Then which one of the following statement is not true ?
Answer» A+B is a symmetric matrix AB is a symmetric matrix AB = `(BA)^(T)` `A^(T)B = AB^(T)` Answer :A::B::C

Discussion

11794.	Find the area of a DeltaABC in which angleA=30^(0), b=6cm, c=2cm.
Answer» ANSWER :3 `CM^(2)`

Discussion

11795.	for any real number 't' [t] denotes the G.I.F. Let W be the set of all non- negative integers andf: W to Wis a gunctions defined byf (x)=(x- 10 [(x)/( 10 )] ) 10 ^([log _e x])+ f ([( x)/( 10)]), x gt 0if x= 0 , f( 7752)is a four digit number abcd then(c+d)- ( a+b)=
Answer» 5 7 3 2 Answer :B

Discussion

11796.	Identify the quantifers used in the following statements and write the negation of the statements : (i) there exists a number which is equal to its cube. (ii) for all states in india, there is a capital in india. (iii) there exists a man whose age is 150 years. (iv) all students are of 25 years or more.
Answer» Solution :(i) there exists : negation : there dones not exist a number which is equal to its cube. (II) for all : negation : there is a STATE in india which has no capital. (iii) There exists: Negation : There does not exist a man whose AGE is 150 YEARS. (iv) for all : negation: no student is of 25 years or more.

Discussion

11797.	Assertion (A): All chords of the curve 4x^(2)+y^(2)-x+4y=0, which subtends right angle at the origin passes through the point ((1)/(5), -(4)/(5)) Reason (R ) : Chords of any curve, substending right angle at origin passes through a fixed point.
Answer» Both A&R are TRUE R is CORRECT explanation of A Both A&R are true R is not correct explanation of A A is true R is false A is false R is true Answer :C

Discussion

11798.	Consider the points A (4,3), B (8,-3) and C (0,9).Find the slopes of AB and BC
Answer» SOLUTION :`[-3/2, -3/2]`

Discussion

11799.	Using the polar form and x + iy form of (1+i)/sqrt3+i, prove that cospi/12 = (sqrt3+1)/2sqrt2 and sinpi/12 = (sqrt3-1)/2sqrt2
Answer» ANSWER :`sqrt3+i=2abs(cospi/6+isinpi/6`

Discussion

11800.	Prove thatcos ^(2) x + cos ^(2) (x + (pi)/(3)) + cos ^(2) (x - (pi)/(3)) = 3/2.
Answer» ANSWER :`3/2=R.H.S.`

Discussion

Explore topic-wise InterviewSolutions in .

Let f(x) = {(x^(3) - x^(2) + 10x - 5",", x le 1),(-2x + log_(2)(b^(2) - 2)",",x gt 1):} find the values of b for which f(x) has the greatest valueat x = 1.

(A) sin^(2)5+sin^(2)10+......+sin^(2)85=(17)/(2) (R) : If alpha+ beta=90^(@) then sin^(2)alpha+ sin ^(2) beta=1

If x/a+y/b=1 " intersects " 5x^2+5y^2+5bx+5ay-9ab=0 at P and Q, anglePOQ=pi//2 then the relation between a and b is

In triangle ABC, a, b, c are the lengths of its sides and A, B C are the angles of triangle ABC. The correct relation is

6P_3 - 5P_2 = ......... .

Find the slope of the line which makes an angle of 45^(@) with a line of slope -6/(5).

The ratio in which the line segmet joining the points (2,-4,3) and (-4,5,-6) is divided by the xy-plane is

If f(0) = 0 ,f '(0)= 2, then the derivative of y = f(f(f(f(x)))) at x = 0 in

The sum of two + ve numbers is 20 If the sum of their squares is minimum then one of the number is

Show that (secA+tanA)/("cosec A"+cot A)=("cosec A"-cotA)/(secA-tanA).

The r^(th) term t_(r) of a series is given by t_(r)=(r)/(r^(4)+r^(2)+1) then lim_(n to oo) overset(n) underset(r=1) sum t_(r)=

If the angles of a triangle are in the ratio 3:4:5, find the smallest angle in degrees and the greatest angle in radians.

Find the value ofsin ( - 405^(@))

If 2,b,c, 23 are in G.P then (b-c)^(2)+ (c-2)^(2) + (23-b)^(2)= …….

sin^(-1) ( 12/13 ) + cos^(-1) (4/5) + tan^(-1) (63/16) =

Find the value of k if the lines 2x+ky-10=0 and 5x+2y-7=0 are parallel.

If sqrt(tan y) =e^(cos 2x) sin x,then (dy)/(dx) =

If sin (7 phi+9^(@))=cos2phi, find a value of phi.

Two rods of lengths a and b slide along the axes in such a way that their ends are concyclic. The locus of the centre of the circle passing through these points is

If the perimeter of a triangle is 12 unit and it in radius is 1 unit, then its area is

How many numbers are there between 100 and 1000 such that 7. is in the units places?

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of line which is of the equidistance from the line x = -2 and x = 6.

Find the mean deviation about the median for the data in 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Write the following sets in roster form: A = {x : x is an integer and –3 ≤ x < 7}

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that All the three balls are white

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that All the three balls are red

Find the slope of a line perpendicular to the line which passes through each pair of the following points: (1, -11) and (5, 2)

Find the slope of a line perpendicular to the line which passes through each pair of the following points (-k, h) and (b, -f)

f:R rarr [-1, oo) and f(x)= ln([|sin 2 x | + | cos 2 x | ])( where [.] is the greatest integer function ) Then,

Find the slope of a line perpendicular to the line which passes through each pair of the following points: (0, 8) and (-5, 2)

Evaluate the following limits : lim_(x to 0) (sin 3x)/(sin 2x)

Find the slope of a line perpendicular to the line which passes through each pair of the following points: \[{\text{(}}{{\text{x}}_1}{\text{,}}{{\text{y}}_1}{\text{) and (}}{{\text{x}}_2}{\text{,}}{{\text{y}}_2}{\text{)}}{\text{.}}\]

If theta is the angle between the vectors bar(i) + bar(j) , bar(j) + bar(k) then find sin theta.

Check the validity of the statements given below by the method given against it: q: If n is a real number with ngt3, then n^(2)gt9. (by contradiction method)

The verticles of a triangle are (0,0) , (x cosx) and (sin^(3)x,0) , where 0ltxlt(pi)/(2). The maximum area for such a triangle in sq units is

Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(2, 4, -8), C(-2, 2, 4). Find the coordinates of the fourth vertex.

For what value of a is the function is continues at x=2 f(x)={(x^4 -16)/(x-2) ,if xne2a,if x=2

If cos 2x gt |sinx|, x in (-(pi)/2,pi) then x in

If 180^(@)lt thetalt270^(@) and Sintheta=(-4)/5 calculate "Sin"theta/2 and "Cos"theta/2

PQR is an isosceles triangle whose equal sides PQ and PR are at right angles S and T are points on PQ such that QS = 6 (SP) " and " QT = 2 (TP) " and if" angle PRS = theta , angle PRT = phithen

Let Aand B be two symmetrices of same order. Then which one of the following statement is not true ?

Find the area of a DeltaABC in which angleA=30^(0), b=6cm, c=2cm.

for any real number 't' [t] denotes the G.I.F. Let W be the set of all non- negative integers andf: W to Wis a gunctions defined byf (x)=(x- 10 [(x)/( 10 )] ) 10 ^([log _e x])+ f ([( x)/( 10)]), x gt 0if x= 0 , f( 7752)is a four digit number abcd then(c+d)- ( a+b)=

Assertion (A): All chords of the curve 4x^(2)+y^(2)-x+4y=0, which subtends right angle at the origin passes through the point ((1)/(5), -(4)/(5)) Reason (R ) : Chords of any curve, substending right angle at origin passes through a fixed point.

Consider the points A (4,3), B (8,-3) and C (0,9).Find the slopes of AB and BC

Using the polar form and x + iy form of (1+i)/sqrt3+i, prove that cospi/12 = (sqrt3+1)/2sqrt2 and sinpi/12 = (sqrt3-1)/2sqrt2

Prove thatcos ^(2) x + cos ^(2) (x + (pi)/(3)) + cos ^(2) (x - (pi)/(3)) = 3/2.