14949 + Interview Questions in Maths in Class 11 Page 33 InterviewSolution

1601.	Differentiate the following with respect to x.y = 4cosecx + 3sin^(-1)x
Answer» ANSWER :`-4cosecx COTX + 3/(SQRT(1-x^(2)))`

Discussion

1602.	Solution of 7 sin^(2) x + 3cos^(2) x = 4 is
Answer» `N PI PM pi//2` `n pi pm pi//4` `n pi pm pi//3` `n pi pm pi//6` ANSWER :D

Discussion

1603.	If U is same as in Example 50, then the value of {:[(3,2,0)]U[(3),(2),(0)]=:}
Answer» 5 `5//2` 4 `3//2` Solution :We have, `{:[(3,2,0)]U[(3),(2),(0)]=[(3,2,0)][(1,2,2),(-2,-1,-1),(1,-4,-3)][(3),(2),(0)]:}` `={:[(3,2,0)]:}[(7),(-8),(-5)]=21-16+0=5`

Discussion

1604.	Let z = (cosx)^5 and y = sinx. Then the value of (d^2z)/(dy^2) at x = (2pi)/9 is
Answer» `-1/2` `3/2` `5/2` `-3/2` ANSWER :C

Discussion

1605.	"If "5^(1+x)+5^(1-x),(a)/(2),25^(x)+25^(-x) are three consecutive terms of an A.P. then the minimum value of 'a' is :
Answer» 15 12 10 8 Solution :N/a

Discussion

1606.	If the d.c's of a line are proportional to (1,-2,1) find d.c's
Answer» Answer :`pm((1)/(SQRT(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))`

Discussion

1607.	Find the equation of the line passing through the point (-4,3) with slope1//2.
Answer» ANSWER :`X - 2Y + 10 = 0 `

Discussion

1608.	A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - C
Answer» ANSWER :`={4, 5}`

Discussion

1609.	Express each of the following complex number in the form a+ib: 4-sqrt(-5)
Answer» ANSWER :`4-sqrt(5)i`

Discussion

1610.	If a,b,c are in Hp. (a,b,c!=0 point of concurrence of family of lines x/a+y/b+1/c=0 is
Answer» (1,2) (1,-2) (-2,1) (2,1) ANSWER :B

Discussion

1611.	If cot theta + tan theta = x and sec theta - cos theta = y then
Answer» x sin THETA,COS theta = 1 `sin^(2) theta = y cos theta` `(x^(2)y)^(1//3)+(XY^(2))^(1//3)=1` `(x^(2)y)^(1//3)+(xy^(2))^(1//3)=1` Answer :A::B::D

Discussion

1612.	If n(A)=5, n(B)=8 andAsubB"then" n(AcupB)=…… .
Answer» ANSWER :8

Discussion

1613.	Assuming that straight lines work as the plane mirror for a point, find the image of the point (1,2) in the line x - 3y + 4 =0.
Answer» ANSWER :`((6)/(5) , (7)/(5))`

Discussion

1614.	What is theprobability that a numberselected from the numbers 1,2,3,…25 is a prime number ? You may assume that each of the 25 numbers is equally likely to be selected .
Answer» ANSWER :`(9)/(25)`

Discussion

1615.	Point (2, 1) has reflection as simple mirror (5, 2). Find equation of line.
Answer» ANSWER :`3X + y = 12`

Discussion

1616.	If f(x) , x^n , then the value of f(1) = (f'(1))/(1!) + (f''(1))/(2!) - (f'''(1))/(3!) +….+ (((-1)^n f^n (1))/(n!))
Answer» `2^N` `2^(n -1)` `0` `1` Answer :C

Discussion

1617.	Approximate value of (2.01)^(4) is
Answer» 16.32 16.01 16.032 16 Answer :A

Discussion

1618.	Find the ellipse if its foci are (pm2, 0) and the length of the latus rectum is 10/3.
Answer» ANSWER :`X^(2)/9+y^(2)/5=1`

Discussion

1619.	Draw the function f'(x) if f(x) = 2x^(2) - 5x + 3
Answer» ANSWER :`4x-5`

Discussion

1620.	Assertion (A) : The least value of sinx+(1)/(sinx) is 2 if x gt 0 Reason (R) : Least value of x+1//x is 2 if x gt 0 then correct statement is
Answer» A is TRUE R, is true ` R rArr A` A is true R is true but `R cancel rArr A` A is true, R is FALSE A is false, R is true Answer :D

Discussion

1621.	For any two sets A and B, prove that : (i) A cup(AcapB)=A (ii) A cap(A cupB)=A (iii) (A cupB)cap(A capB')=A (iv) A cap B = phi rArr A sube B' (v) A' cup B = U rArr A sube B where U = universal set.
Answer»

Discussion

1622.	Find the number of terms in the expansion of the following : (x^(2)+1-2x)^(8)
Answer» ANSWER :17

Discussion

1623.	If f(x) = x^(3) + bx^(2) +ax satisfies the conditions of Rolle's theorem on [1,3] with c = 2+(1)/(sqrt(3))then (a,b) =0
Answer» (11,6) (11,-6) (-6,11) (6,11) ANSWER :B

Discussion

1624.	A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=-1 and x=1//3andifint_(1)^(1)f(x)dx=(14)/(3)The value of c is
Answer» `-2` `-1` 0 2 Answer :B

Discussion

1625.	Find the derivative of f (x) w.r.t. g(x) for the f (x) = e ^(x), g (x) = sqrtx)
Answer» ANSWER :`2 SQRT (XE) ^(X)`

Discussion

1626.	Let g'(x)gt0andf'(x)lt0AA x inR . Thus .
Answer» `(F(x+1))gtg(f(x-1))` `f(G(x-1))gtf(g(x+1))` `g(f(x+1))ltg(f(x-1))` `g(g(x+1))ltg(g(x-1))` ANSWER :B::C

Discussion

1627.	Examine whether the following statements are true or false : {x : x is a letter in the word SCHOOL} sub {x : x is a letter of english alphabet}.
Answer» ANSWER :1

Discussion

1628.	Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z =5 Statement-1: The parametic equations of the line of intersection of the given planes are x =3+ 14t, y = 2t, z = 15 t Statement-2: The vector 14 hati + 2 hatj + 15 hatkis parallel to the line of intersection of the given planes.
Answer» Both the STATEMENT are true, Statement 2 is the correct EXPLANATION for Statemenet 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

1629.	If ((1-i)/(1+i))^(100)=a+ib then find (a,b)
Answer» ANSWER :(1,0)

Discussion

1630.	Let the function f: R to R be defined by f(x) = 2x + sinx for x in R, then f is
Answer» one-to-one and onto one-to-one but not onto onto but not-to-one neitherone-to-one nor onto Answer :A

Discussion

1631.	A running track 440 ft. is to be laid out enclosing foot ball field the shape of which a rectangle with a semi circle at each end .If the area of the rectangular position is to be maximum then the dimensions of the retangle are
Answer» 100,70 110 ,70 100 , 80 110 , 60 Answer :B

Discussion

1632.	For real number R out of the following, which is not correct?
Answer» `N sub R` `(a, b) sub R, a LT b` `PI sub R` `PHI sub R` Answer :C

Discussion

1633.	Evaluate the following limits : Lim_(x to 0) (e^(x^(2))-1)/(sin^2 x)
Answer» ANSWER :1

Discussion

1634.	Find the direction in which a straight line must be drawn through the point (-1,2). So that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.
Answer» ANSWER :The LINE is PARALLEL to X - AXIS or parallel to y- axis

Discussion

1635.	If tan^(2) A= 2 tan ^(2) B+1, "then " cos 2A + sin^(2)B =
Answer» `-1` 0 1 2 Answer :D

Discussion

1636.	Find dy/dx if x^(2)/a^(2)-y^(2)/b^(2) = 1:
Answer» `-(B^(2)X)/(a^(2)y)` `(b^(2)x)/(a^(2)y)` `(a^(2)y)/(b^(2)x)` `-(a^(2)y)/(b^(2)x)` ANSWER :B

Discussion

1637.	If 2 sin ^(3) x = cos xthen x =
Answer» `X = N pi + (pi)/(4), n in Z` `x = n pi + (pi)/( 3), n in Z` `x = n pi + (pi)/( 2), n in Z` ` x = n pi + (pi)/( 6) , n in Z` ANSWER :A

Discussion

1638.	f(x)= In (lnx) is increasing in
Answer» `(0,1)` `(1,OO)` `(0,2)` `(-oo,1)` ANSWER :B

Discussion

1639.	For an A.P. If S_(30)= 1635 and a_(30)= 98 then find A.P.
Answer» ANSWER :`11, 14, 17, 20`,…..

Discussion

1640.	Constant force barF_(1) = 4bari +barj -3bark and barF_(2) = 3bari +barj -bark act on a particle. If the work done where the particle is displaced from A to B, the position vectors of A and B being bari + 2barj +lambda bark and 5bari+4barj+bark respectively is 40 unit then find lambda.
Answer» ANSWER :3

Discussion

1641.	If f(x)=x^(3)-x^(2)+100x+2002, then
Answer» `f(1000)GTF(1001)` `f((1)/(2000))gtf((1)/(2001))` `f(x-1)gtf(x-2)` `f(2x-3)gtf(2x)` Answer :B::C

Discussion

1642.	For any statement 'p' prove that~(~p)-= p.
Answer» <P> Answer :Prepare the TRUTH table as shown . `(##SCH_OPM_ISC_MAT_XI_C27_E08_007_A01##)` SINCE the cloumns of p and ~(~p) COINCIDE, so ~(~p)-= p.

Discussion

1643.	If 2x + y - 4= 0 is a bisector of angles between the lines a(x-1) + b(y-2) = 0, c(x-1) + d(y-2)=0 the other angular bisector is
Answer» `x-2y + 1 =0` `x-2y-3 = 0` ` x-2y + 3 =0` `x + 2y-5 = 0 ` ANSWER :C

Discussion

1644.	If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz + zx = 1
Answer» `xy+yz+zx=1` `X^(2)+y^(2)+Z^(2)+2xy=1` `x+y+z=xyz` `Sigmax+Sigmayz=1+xyz` ANSWER :A

Discussion

1645.	(a) If sin theta=(21)/(29) , prove that sectheta+"tan" theta=2(1)/(2) If lies betwwen 0 and pi/2 (b) What will be the value of the expression when theta lies: (i) between (pi)/(2) and pi(ii) between pi and (3pi)/(2) ?
Answer» Answer :(B) (i)`-2(1)/(2)`(ii)impossible.

Discussion

1646.	IF the sides ofa triangle ABC are 6,8,10 unit , then the radius of its circumcentre is
Answer» `4` `3` `6` `5` ANSWER :D

Discussion

1647.	Explain the types of equilibrium with suitable examples.
Answer» SOLUTION :Translational equilibrium (i) Linear momentum is constant. (ii) Net force is zero. ROTATIONAL equilibrium (i) Angular momentum is constant. (ii) Net torque is zero. Static equilibrium (i) Linear momentum and angular momentum are zero. (ii) Net force and net torque are zero. Dynamic equilibrium (i) Linear momentum and angular momentum are constant. (ii) Net force and net torque are zero. Stable equilibrium (i) Linear momentum and angular momentum are zero. (ii) The body tries to come back to equilibrium if slightly disturbed and released. (III) The center of mass of the body shifts slightly higher if disturbed from equilibrium. (iv) Potential energy of the body is minimum and it INCREASES if disturbed. Unstable equilibrium (i) Linear momentum and angular momentum are zero. (ii) The body cannot come back to equilibrium if slightly disturbed and released. (iii) The center of mass of the body shifts slightly lower if disturbed from equilibrium. (iv) Potential energy of the body is not minimum and it decreases if disturbed. Neutral equilibrium (i) Linear momentum and angular momentum are zero. (ii) The body remains at the same equilibrium if slightly disturbed and released. (iii) The center of mass of the body does not shift higher or lower if disturbed from equilibrium. (iv). Potential energy remains same EVEN if disturbed.

Discussion

1648.	Consider the expansion of (3x^3+2/x^2)^40 Find the general term in the expansion
Answer» SOLUTION :`T_(R+1)=(-1)^(R40)C_r(3x^3)^(40-r)(2/x^2)^r`

Discussion

1649.	If f(x)=coshx+sinhx and f(x)f(y)=f(k) then k =
Answer» XY `(X)/(y)` `x-y` `x+y` ANSWER :D

Discussion

1650.	Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))
Answer» Solution :We have `(5/4)^(1-X) gt (16/25)^(2(1+sqrt(x))` or `(4/5)^(x-1) gt (4/5)^(4(1+sqrt(x))` Since the base `0 gt 4/5 gt 1`, the inequality to the inequality `x-1 gt 4(1+sqrt(x))` `RARR (x-5)/4 gt sqrt(x)` Now, RHS is positive `rArr (x-5)/4 gtrArr x gt 5`.........(i) We have `(x-5)/4 gt sqrt(x)` both sides are positive, so squaring both SIDE `rArr (x-5)^(2)/16 gt x` or `(x-5)^(2)/16 -x gt 0` or `x^(2)-26x+25 gt 0` or `(x-25)(x-1) gt 0` `rArr x in (-infty,1) cup (25, infty)`.................(ii) intersection (i) and (ii) gives `x in (25,infty)`

Discussion

Explore topic-wise InterviewSolutions in .

Differentiate the following with respect to x.y = 4cosecx + 3sin^(-1)x

Solution of 7 sin^(2) x + 3cos^(2) x = 4 is

If U is same as in Example 50, then the value of {:[(3,2,0)]U[(3),(2),(0)]=:}

Let z = (cosx)^5 and y = sinx. Then the value of (d^2z)/(dy^2) at x = (2pi)/9 is

"If "5^(1+x)+5^(1-x),(a)/(2),25^(x)+25^(-x) are three consecutive terms of an A.P. then the minimum value of 'a' is :

If the d.c's of a line are proportional to (1,-2,1) find d.c's

Find the equation of the line passing through the point (-4,3) with slope1//2.

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - C

Express each of the following complex number in the form a+ib: 4-sqrt(-5)

If a,b,c are in Hp. (a,b,c!=0 point of concurrence of family of lines x/a+y/b+1/c=0 is

If cot theta + tan theta = x and sec theta - cos theta = y then

If n(A)=5, n(B)=8 andAsubB"then" n(AcupB)=…… .

Assuming that straight lines work as the plane mirror for a point, find the image of the point (1,2) in the line x - 3y + 4 =0.

What is theprobability that a numberselected from the numbers 1,2,3,…25 is a prime number ? You may assume that each of the 25 numbers is equally likely to be selected .

Point (2, 1) has reflection as simple mirror (5, 2). Find equation of line.

If f(x) , x^n , then the value of f(1) = (f'(1))/(1!) + (f''(1))/(2!) - (f'''(1))/(3!) +….+ (((-1)^n f^n (1))/(n!))

Approximate value of (2.01)^(4) is

Find the ellipse if its foci are (pm2, 0) and the length of the latus rectum is 10/3.

Draw the function f'(x) if f(x) = 2x^(2) - 5x + 3

Assertion (A) : The least value of sinx+(1)/(sinx) is 2 if x gt 0 Reason (R) : Least value of x+1//x is 2 if x gt 0 then correct statement is

For any two sets A and B, prove that : (i) A cup(AcapB)=A (ii) A cap(A cupB)=A (iii) (A cupB)cap(A capB')=A (iv) A cap B = phi rArr A sube B' (v) A' cup B = U rArr A sube B where U = universal set.

Find the number of terms in the expansion of the following : (x^(2)+1-2x)^(8)

If f(x) = x^(3) + bx^(2) +ax satisfies the conditions of Rolle's theorem on [1,3] with c = 2+(1)/(sqrt(3))then (a,b) =0

A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=-1 and x=1//3andifint_(1)^(1)f(x)dx=(14)/(3)The value of c is

Find the derivative of f (x) w.r.t. g(x) for the f (x) = e ^(x), g (x) = sqrtx)

Let g'(x)gt0andf'(x)lt0AA x inR . Thus .

Examine whether the following statements are true or false : {x : x is a letter in the word SCHOOL} sub {x : x is a letter of english alphabet}.

Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z =5 Statement-1: The parametic equations of the line of intersection of the given planes are x =3+ 14t, y = 2t, z = 15 t Statement-2: The vector 14 hati + 2 hatj + 15 hatkis parallel to the line of intersection of the given planes.

If ((1-i)/(1+i))^(100)=a+ib then find (a,b)

Let the function f: R to R be defined by f(x) = 2x + sinx for x in R, then f is

A running track 440 ft. is to be laid out enclosing foot ball field the shape of which a rectangle with a semi circle at each end .If the area of the rectangular position is to be maximum then the dimensions of the retangle are

For real number R out of the following, which is not correct?

Evaluate the following limits : Lim_(x to 0) (e^(x^(2))-1)/(sin^2 x)

Find the direction in which a straight line must be drawn through the point (-1,2). So that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.

If tan^(2) A= 2 tan ^(2) B+1, "then " cos 2A + sin^(2)B =

Find dy/dx if x^(2)/a^(2)-y^(2)/b^(2) = 1:

If 2 sin ^(3) x = cos xthen x =

f(x)= In (lnx) is increasing in

For an A.P. If S_(30)= 1635 and a_(30)= 98 then find A.P.

Constant force barF_(1) = 4bari +barj -3bark and barF_(2) = 3bari +barj -bark act on a particle. If the work done where the particle is displaced from A to B, the position vectors of A and B being bari + 2barj +lambda bark and 5bari+4barj+bark respectively is 40 unit then find lambda.

If f(x)=x^(3)-x^(2)+100x+2002, then

For any statement 'p' prove that~(~p)-= p.

If 2x + y - 4= 0 is a bisector of angles between the lines a(x-1) + b(y-2) = 0, c(x-1) + d(y-2)=0 the other angular bisector is

If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz + zx = 1

(a) If sin theta=(21)/(29) , prove that sectheta+"tan" theta=2(1)/(2) If lies betwwen 0 and pi/2 (b) What will be the value of the expression when theta lies: (i) between (pi)/(2) and pi(ii) between pi and (3pi)/(2) ?

IF the sides ofa triangle ABC are 6,8,10 unit , then the radius of its circumcentre is

Explain the types of equilibrium with suitable examples.

Consider the expansion of (3x^3+2/x^2)^40 Find the general term in the expansion

If f(x)=coshx+sinhx and f(x)f(y)=f(k) then k =

Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))