43030 + Interview Questions in Mathematics Page 151 InterviewSolution

7501.	Find the common solution of following inequalities, 1). (4x-1)(x-8)(x-20),(x-5)(x-7)(x-25)0,x4
Answer» Find the common solution of following inequalities, 1). (4x-1)(x-8)(x-20),(x-5)(x-7)(x-25)0,x4

Discussion

7502.	The locus of the point of intersection of the tangents at the extremities of the chord of the ellipse x2+2y2=6 which touches the ellipse x2+4y2=4, is
Answer» The locus of the point of intersection of the tangents at the extremities of the chord of the ellipse $x^{2} + 2 y^{2} = 6$ which touches the ellipse $x^{2} + 4 y^{2} = 4,$ is

Discussion

7503.	Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0} (ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Answer» Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = {x: x is solution of x² + 5x + 6 = 0} (ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

7503.

Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0} (ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

Answer»

Are the following pair of sets equal? Give reasons.

(i) A = {2, 3}; B = {x: x is solution of x² + 5x + 6 = 0}

(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

Discussion

7504.	Find the equation of the circle circumscribing the rectangle whose sides are x−3y=4,3x+y=22,x−3y=14 and 3x+y=62.
Answer» Find the equation of the circle circumscribing the rectangle whose sides are $x - 3 y = 4, 3 x + y = 22, x - 3 y = 14$ and $3 x + y = 62$ .

Discussion

7505.	sin x7.sin (x -a)
Answer» sin x7.sin (x -a)

Discussion

7506.	∫dx(x+1)√2x−3 equals to (where C is integration constant)
Answer» $\int \frac{d x}{(x + 1) \sqrt{2 x - 3}}$ equals to (where $C$ is integration constant)

Discussion

7507.	If In=∫tann x dx then which of the following relation is correct -
Answer» If $I_{n} = \int t a n^{n} x d x$ then which of the following relation is correct -

Discussion

7508.	In the equation Cos(wt+-)=sin(wt) How (-)= -/2
Answer» In the equation Cos(wt+-)=sin(wt) How (-)= -/2

Discussion

7509.	If A=⎡⎢⎣333333333⎤⎥⎦, then A3=
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 3 & 3 3 & 3 & 3 3 & 3 & 3 \end{matrix} ⎤ ⎥ ⎦$ , then $A^{3} =$

Discussion

7510.	If the sum of two consecutive odd natural numbers is 188,then the smallest of the two is equal to
Answer» If the sum of two consecutive odd natural numbers is 188,then the smallest of the two is equal to

Discussion

7511.	The vector equation of the line passing through the points (3, 4, –7) and (1, –1, 6) is _______________.
Answer» The vector equation of the line passing through the points (3, 4, –7) and (1, –1, 6) is _______________.

Discussion

7512.	A person wants to send a invitation card to seven friends and he can appoint one of three different persons to carry the invitation card. Then the number of ways in which he can send the card is
Answer» A person wants to send a invitation card to seven friends and he can appoint one of three different persons to carry the invitation card. Then the number of ways in which he can send the card is

Discussion

7513.	Find x , if
Answer» Find x , if

Discussion

7514.	If the equations x2+2x+3=0 and ax2+bx+c=0,a, b, c ϵ R have a common root, then a : b : c is
Answer» If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0$ ,a, b, c ϵ R have a common root, then a : b : c is

Discussion

7515.	∫-π2πsin-1sinxdx
Answer» $\int_{- \frac{π}{2}}^{π} \sin^{- 1} (\sin x) d x$

Discussion

7516.	Sin250sin550=?
Answer» Sin25⁰sin55⁰=?

Discussion

7517.	∫(x^{5^{}}×(2-x))^{1÷2}dx
Answer» ∫(x^{5^{}}×(2-x))^{1÷2}dx

Discussion

7518.	a+(a+d)+(a+2d)+....+(a+(n−1)d)=n2[2a+(n−1)d]
Answer» $a + (a + d) + (a + 2 d) + . . . . + (a + (n - 1) d) = \frac{n}{2} [2 a + (n - 1) d]$

Discussion

7519.	The integral value of λ for which vectors λ2^i−2^j,2λ2^j+64^k,−λ2^k−^i are linearly dependent, is equal to
Answer» The integral value of $λ$ for which vectors $λ^{2}^i - 2^j, 2 λ^{2}^j + 64^k, - λ^{2}^k -^i$ are linearly dependent, is equal to

Discussion

7520.	If a=bcos2π3=ccos4π3, then write the value of ab+bc+ca.
Answer» If $a = b c o s \frac{2 π}{3} = c c o s \frac{4 π}{3}$ , then write the value of ab+bc+ca.

Discussion

7521.	If in a ΔABC, tan A + tan B + tan C = 0, then cot A cot B cot C =
Answer» If in a $Δ A B C$ , tan A + tan B + tan C = 0, then cot A cot B cot C =

Discussion

7522.	The general solution of sec theta + tan theta = root3 is
Answer» The general solution of sec theta + tan theta = root3 is

Discussion

7523.	If →a,→b,→c are non-coplanar vectors, then the number of real value(s) of λ for which [λ(→a+→b) λ2→b λ→c]=[→a →b+→c →b], is
Answer» If $\to a, \to b, \to c$ are non-coplanar vectors, then the number of real value(s) of $λ$ for which $[λ (\to a + \to b) λ^{2} \to b λ \to c] = [\to a \to b + \to c \to b],$ is

Discussion

7524.	What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
Answer» What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Discussion

7525.	Differentiate the function (5x)3cos2x w.r.t.x.
Answer» Differentiate the function $(5 x)^{3 cos 2 x}$ w.r.t. $x$ .

Discussion

7526.	Find the principal value of sin−1(−12).
Answer» Find the principal value of ${sin}^{- 1} (- \frac{1}{2}) .$

Discussion

7527.	find the solutions of the equations x=0 ; y=0
Answer» find the solutions of the equations x=0 ; y=0

Discussion

7528.	If the function f:B→[−5,∞) defined by f(x)=x2−4x+5 is one-one function, then B is
Answer» If the function $f : B \to [- 5, \infty)$ defined by $f (x) = x^{2} - 4 x + 5$ is one-one function, then $B$ is

Discussion

7529.	If cos(A+B)sin(C−D)=cos(A−B)sin(C+D), then the value of tanAtanBtanC+tanD is
Answer» If $cos (A + B) sin (C - D) = cos (A - B) sin (C + D),$ then the value of $tan A tan B tan C + tan D$ is

Discussion

7530.	27. Find the equation of the diameter of the circle x squaredm plus y square minus 2 X + 4 Y = 0 which passes through the origin
Answer» 27. Find the equation of the diameter of the circle x squaredm plus y square minus 2 X + 4 Y = 0 which passes through the origin

Discussion

7531.	The sum of all integral values of k (k≠0) for which the equation 2x−1−1x−2=2k in x has no real roots, is
Answer» The sum of all integral values of $k (k \neq 0)$ for which the equation $\frac{2}{x - 1} - \frac{1}{x - 2} = \frac{2}{k}$ in $x$ has no real roots, is

Discussion

7532.	If x=cosec θ−sinθ,y=cosecnθ−sinnθ,n∈R then (x2+4)(dydx)2−n2y2=
Answer» If $x = cosec θ - sin θ, y = {cosec}^{n} θ - {sin}^{n} θ, n \in R$ then $(x^{2} + 4) {(\frac{d y}{d x})}^{2} - n^{2} y^{2} =$

Discussion

7533.	14. The Fibonacci sequence is defined by1 - a, a, and aa 1+a 2, n> 2n-2n+1forn-1,2, 3, 4,5
Answer» 14. The Fibonacci sequence is defined by1 - a, a, and aa 1+a 2, n> 2n-2n+1forn-1,2, 3, 4,5

Discussion

7534.	38.Draw a graph of x=a, where 'a' is equal to 15 upon 2 plus 2.
Answer» 38.Draw a graph of x=a, where 'a' is equal to 15 upon 2 plus 2.

Discussion

7535.	A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be
Answer» A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be

7535.

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be

Answer»

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure.

The new magnetic dipole moment will be

Discussion

7536.	If a+b+c+d = 1 , then the maximum value of 16 abcd is
Answer» If a+b+c+d = 1 , then the maximum value of 16 abcd is

Discussion

7537.	Find the second order derivative of the function y=log x
Answer» Find the second order derivative of the function $y = log x$

Discussion

7538.	(1.) \|3x-2\| + x = 11 ; values of x will be?(2) x^2 -5\|x\| + 6 < 0 ; values of x are?(3)\|x-2\|
Answer» (1.) \|3x-2\| + x = 11 ; values of x will be? (2) x^2 -5\|x\| + 6 < 0 ; values of x are? (3)\|x-2\| <= \|x+4\|

Discussion

7539.	how to find integral of sin^3 dx?
Answer» how to find integral of sin^3 dx?

Discussion

7540.	7. For what value of k does the equation x² + 2x+ k²+1 =0 has real and equaal roots?
Answer» 7. For what value of k does the equation x² + 2x+ k²+1 =0 has real and equaal roots?

Discussion

7541.	Solve 8−3x3≤2x3−4
Answer» Solve $\frac{8 - 3 x}{3} \leq \frac{2 x}{3} - 4$

Discussion

7542.	18. Graph of {sinx
Answer» 18. Graph of {sinx

Discussion

7543.	Identify the function which is formed when the following transformations are made on the graph of the function y=sinx1) Flipped over the y-axis2) Shifted vertically upwards by 2 units3) Stretched by a factor of 3 along the x-axis
Answer» Identify the function which is formed when the following transformations are made on the graph of the function $y = sin x$ 1) Flipped over the y-axis 2) Shifted vertically upwards by 2 units 3) Stretched by a factor of 3 along the x-axis

Discussion

7544.	A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.
Answer» A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$ . Find the number of blue marbles in the jar.

Discussion

7545.	The value of 2(nC0)+32(nC1)+43(nC2)+54(nC3)+⋯ is
Answer» The value of $2 (^{n} C_{0}) + \frac{3}{2} (^{n} C_{1}) + \frac{4}{3} (^{n} C_{2}) + \frac{5}{4} (^{n} C_{3}) + \dots$ is

Discussion

7546.	If tan x+y+tan x-y=1, find dydx
Answer» If $\tan (x + y) + \tan (x - y) = 1, find \frac{d y}{d x}$

Discussion

7547.	If S 1 , S 2 , S 3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that
Answer» If S 1 , S 2 , S 3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that

Discussion

7548.	9. 4x9y2 36
Answer» 9. 4x9y2 36

Discussion

7549.	If cos(x−y),cosx,cos(x+y) are in H.P., where y≠2nπ,n∈Z, then the value of [cosxsecy2] is/are (where [.] denotes greatest integer function)
Answer» If $cos (x - y), cos x, cos (x + y)$ are in H.P., where $y \neq 2 n π, n \in Z$ , then the value of $[cos x sec \frac{y}{2}]$ is/are (where [.] denotes greatest integer function)

Discussion

7550.	THE VALUE OF 2^3MULTIPLIED BY 3^3 MULTIPLIED BY 4^-5 MULTTIPLIED BY 6^2
Answer» THE VALUE OF 2^3MULTIPLIED BY 3^3 MULTIPLIED BY 4^-5 MULTTIPLIED BY 6^2

Discussion

Explore topic-wise InterviewSolutions in .

Find the common solution of following inequalities, 1). (4x-1)(x-8)(x-20),(x-5)(x-7)(x-25)0,x4

The locus of the point of intersection of the tangents at the extremities of the chord of the ellipse x2+2y2=6 which touches the ellipse x2+4y2=4, is

Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0} (ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

Find the equation of the circle circumscribing the rectangle whose sides are x−3y=4,3x+y=22,x−3y=14 and 3x+y=62.

sin x7.sin (x -a)

∫dx(x+1)√2x−3 equals to (where C is integration constant)

If In=∫tann x dx then which of the following relation is correct -

In the equation Cos(wt+-)=sin(wt) How (-)= -/2

If A=⎡⎢⎣333333333⎤⎥⎦, then A3=

If the sum of two consecutive odd natural numbers is 188,then the smallest of the two is equal to

The vector equation of the line passing through the points (3, 4, –7) and (1, –1, 6) is _______________.

A person wants to send a invitation card to seven friends and he can appoint one of three different persons to carry the invitation card. Then the number of ways in which he can send the card is

Find x , if

If the equations x2+2x+3=0 and ax2+bx+c=0,a, b, c ϵ R have a common root, then a : b : c is

∫-π2πsin-1sinxdx

Sin250sin550=?

∫(x^{5^{}}×(2-x))^{1÷2}dx

a+(a+d)+(a+2d)+....+(a+(n−1)d)=n2[2a+(n−1)d]

The integral value of λ for which vectors λ2^i−2^j,2λ2^j+64^k,−λ2^k−^i are linearly dependent, is equal to

If a=bcos2π3=ccos4π3, then write the value of ab+bc+ca.

If in a ΔABC, tan A + tan B + tan C = 0, then cot A cot B cot C =

The general solution of sec theta + tan theta = root3 is

If →a,→b,→c are non-coplanar vectors, then the number of real value(s) of λ for which [λ(→a+→b) λ2→b λ→c]=[→a →b+→c →b], is

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

Differentiate the function (5x)3cos2x w.r.t.x.

Find the principal value of sin−1(−12).

find the solutions of the equations x=0 ; y=0

If the function f:B→[−5,∞) defined by f(x)=x2−4x+5 is one-one function, then B is

If cos(A+B)sin(C−D)=cos(A−B)sin(C+D), then the value of tanAtanBtanC+tanD is

27. Find the equation of the diameter of the circle x squaredm plus y square minus 2 X + 4 Y = 0 which passes through the origin

The sum of all integral values of k (k≠0) for which the equation 2x−1−1x−2=2k in x has no real roots, is

If x=cosec θ−sinθ,y=cosecnθ−sinnθ,n∈R then (x2+4)(dydx)2−n2y2=

14. The Fibonacci sequence is defined by1 - a, a, and aa 1+a 2, n> 2n-2n+1forn-1,2, 3, 4,5

38.Draw a graph of x=a, where 'a' is equal to 15 upon 2 plus 2.

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be

If a+b+c+d = 1 , then the maximum value of 16 abcd is

Find the second order derivative of the function y=log x

(1.) |3x-2| + x = 11 ; values of x will be?(2) x^2 -5|x| + 6 < 0 ; values of x are?(3)|x-2|

how to find integral of sin^3 dx?

7. For what value of k does the equation x² + 2x+ k²+1 =0 has real and equaal roots?

Solve 8−3x3≤2x3−4

18. Graph of {sinx

Identify the function which is formed when the following transformations are made on the graph of the function y=sinx1) Flipped over the y-axis2) Shifted vertically upwards by 2 units3) Stretched by a factor of 3 along the x-axis

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 23. Find the number of blue marbles in the jar.

The value of 2(nC0)+32(nC1)+43(nC2)+54(nC3)+⋯ is

If tan x+y+tan x-y=1, find dydx

If S 1 , S 2 , S 3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that

9. 4x9y2 36

If cos(x−y),cosx,cos(x+y) are in H.P., where y≠2nπ,n∈Z, then the value of [cosxsecy2] is/are (where [.] denotes greatest integer function)

THE VALUE OF 2^3MULTIPLIED BY 3^3 MULTIPLIED BY 4^-5 MULTTIPLIED BY 6^2