43030 + Interview Questions in Mathematics Page 107 InterviewSolution

5301.	If [2−756][xy]=[139], then which of the following option is True
Answer» If $[\begin{matrix} 2 & - 7 5 & 6 \end{matrix}] [\begin{matrix} x y \end{matrix}] = [\begin{matrix} 139 \end{matrix}],$ then which of the following option is True

Discussion

5302.	23. Prove that nth terms of an ap cannot be n²+1.Give justification
Answer» 23. Prove that nth terms of an ap cannot be n²+1.Give justification

Discussion

5303.	Let n be a positive integer such that sin π2n + cos π2n = √n2. Then
Answer» Let n be a positive integer such that sin $\frac{π}{2^{n}}$ + cos $\frac{π}{2^{n}}$ = $\frac{\sqrt{n}}{2}$ . Then

Discussion

5304.	The random variabel Y is defined by Y=12(X+\|X\|) where ′X′ is another random variable. Then the density funciton of ′Y′ for y>0 is equal to
Answer» The random variabel Y is defined by $Y = \frac{1}{2} (X + \| X \|)$ where $^{'} X^{'}$ is another random variable. Then the density funciton of $^{'} Y^{'}$ for $y > 0$ is equal to

Discussion

5305.	The value of π/2∫0dx√cotx+1 is
Answer» The value of $π / 2 \int 0 \frac{d x}{\sqrt{cot x} + 1}$ is

Discussion

5306.	Find the modulus and argument of the complex number root 3 - i and converted into polar form
Answer» Find the modulus and argument of the complex number root 3 - i and converted into polar form

Discussion

5307.	Vector F also depends directly on vector r . When we split vector r into its magnitude and direction, r (magnitude) in the numerator cancels out one r (magnitude) in the denominator. Further, vector F is inversely proportional to r^2. Then, is it correct that vector F is inversely proportional to r^3 ?
Answer» Vector F also depends directly on vector r . When we split vector r into its magnitude and direction, r (magnitude) in the numerator cancels out one r (magnitude) in the denominator. Further, vector F is inversely proportional to r^2. Then, is it correct that vector F is inversely proportional to r^3 ?

Discussion

5308.	The maximum value of f(x)=[x(−1)+1]13,0≤x≤1 is\\ a) (13)13 b) 12 c) 1 d) zero
Answer» The maximum value of $f (x) = [x (- 1) + 1]^{\frac{1}{3}}, 0 \leq x \leq 1$ is\\ a) ${(\frac{1}{3})}^{\frac{1}{3}}$ b) $\frac{1}{2}$ c) 1 d) zero

Discussion

5309.	A plane passes through the points (2, 0, 0), (0, 3, 0) and (0, 0, 4). The equation of the plane is _______________.
Answer» A plane passes through the points (2, 0, 0), (0, 3, 0) and (0, 0, 4). The equation of the plane is _______________.

Discussion

5310.	In a ΔABC, If cotA2:cotB2:cotC2=1:4:15, then the greatest angle is:
Answer» In a $Δ A B C,$ If $cot \frac{A}{2} : cot \frac{B}{2} : cot \frac{C}{2} = 1 : 4 : 15,$ then the greatest angle is:

Discussion

5311.	43. tan[÷ 4-cos inverse 4÷ 5]
Answer» 43. tan[÷ 4-cos inverse 4÷ 5]

Discussion

5312.	logπ4(−1+√3i) can be expressed in cartesian form as
Answer» ${log}_{\frac{π}{4}} (- 1 + \sqrt{3} i)$ can be expressed in cartesian form as

Discussion

5313.	Find the values of x for which \|x−3\|+\|x−4\|=9.
Answer» Find the values of x for which $\| x - 3 \| + \| x - 4 \| = 9$ .

Discussion

5314.	If I=∫π0xsin2x⋅sin(π2cosx)(2x−π)dx, then the value of π2I=
Answer» If $I = \int_{0}^{π} \frac{x sin 2 x \cdot sin (\frac{π}{2} cos x)}{(2 x - π)} d x,$ then the value of $π^{2} I =$

Discussion

5315.	If Cr denotes coefficient of xr in (1+x)99 then the value of C0−2C1+3C2−4C3+…100C99=
Answer» If $C_{r}$ denotes coefficient of $x^{r}$ in $(1 + x)^{99}$ then the value of $C_{0} - 2 C_{1} + 3 C_{2} - 4 C_{3} + \dots 100 C_{99} =$

Discussion

5316.	Write the following functions in the simplest form : tan−1(3a2x−x3a3−3ax2),a>0;−a√3<x<a√3
Answer» Write the following functions in the simplest form : ${tan}^{- 1} (\frac{3 a^{2} x - x^{3}}{a^{3} - 3 a x^{2}}), a > 0; \frac{- a}{\sqrt{3}} < x < \frac{a}{\sqrt{3}}$

Discussion

5317.	If (P2−1)x2+(P−1)x+(P2−4P+3)=0 is an identity in x, then the value of P is
Answer» If $(P^{2} - 1) x^{2} + (P - 1) x + (P^{2} - 4 P + 3) = 0$ is an identity in $x$ , then the value of $P$ is

Discussion

5318.	Let S be the set of values of x for which the tangent to the curve y=f(x)=x3−x2−2x at (x,y) is parallel to the line segment joining the points (1,f(1)) and (−1,f(−1)), then S is equal to:
Answer» Let S be the set of values of $x$ for which the tangent to the curve $y = f (x) = x^{3} - x^{2} - 2 x$ at $(x, y)$ is parallel to the line segment joining the points $(1, f (1)) and (- 1, f (- 1))$ , then S is equal to:

Discussion

5319.	Find the linear inequations for which the solution set is the shaded region given in figure.
Answer» Find the linear inequations for which the solution set is the shaded region given in figure.

5319.

Find the linear inequations for which the solution set is the shaded region given in figure.

Answer»

Find the linear inequations for which the solution set is the shaded region given in figure.

Discussion

5320.	[[5(x+1)]^(ln5)]=(2y)^(ln2) and (x+1)^(ln2)=[5^(lny)], then x is ,[[ (A) (1)/(5), (B) -(1)/(5)],[ (C) (4)/(5), (D) -(4)/(5)]]
Answer» [[5(x+1)]^(ln5)]=(2y)^(ln2) and (x+1)^(ln2)=[5^(lny)], then x is ,[[ (A) (1)/(5), (B) -(1)/(5)],[ (C) (4)/(5), (D) -(4)/(5)]]

Discussion

5321.	Compute the derivative of sinx.
Answer» Compute the derivative of $sin x$ .

Discussion

5322.	The value of sin(25π3)+sec(41π4)+tan(−16π3)−cosec(−33π4) is
Answer» The value of $sin (\frac{25 π}{3}) + sec (\frac{41 π}{4}) + tan (- \frac{16 π}{3}) - cosec (- \frac{33 π}{4})$ is

Discussion

5323.	A die is rolled, then the probability that a number 1 or 6 may appear is
Answer» A die is rolled, then the probability that a number 1 or 6 may appear is

Discussion

5324.	On the ellipse 4x2+9y2=1, the points at which the tangents are parallel to the line 8x=9y are
Answer» On the ellipse $4 x^{2} + 9 y^{2} = 1$ , the points at which the tangents are parallel to the line $8 x = 9 y$ are

Discussion

5325.	The general solution of the differential equation of the type dxdy+Rx=S, Where R and S are function of y, is _________________.
Answer» The general solution of the differential equation of the type $\frac{d x}{d y} + R x = S,$ Where R and S are function of y, is _________________.

Discussion

5326.	The equation of the normal at the point (6,4) on the hyperbola x29−y216=3 is
Answer» The equation of the normal at the point (6,4) on the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 3$ is

5326.

The equation of the normal at the point (6,4) on the hyperbola x29−y216=3 is

Answer»

The equation of the normal at the point (6,4) on the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 3$ is

Discussion

5327.	If sinA=34, then what is the value of cosA?
Answer» If $sin A = \frac{3}{4}$ , then what is the value of $cos A$ ?

Discussion

5328.	The latitude and departure of a line AB are + 78 m and - 45.1 m respectively , The whole circle bearing of the line AB is
Answer» The latitude and departure of a line AB are + 78 m and - 45.1 m respectively , The whole circle bearing of the line AB is

Discussion

5329.	If \|t\|=3, then the possible value(s) of \|2t−1\| is/are
Answer» If $\| t \| = 3,$ then the possible value(s) of $\| 2 t - 1 \|$ is/are

Discussion

5330.	Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Answer» Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12

Discussion

5331.	If u, v and w are functions of x, then show that ddx(u.v.w)=dudxv.w+u.dvdxw+u.vdwdxIn two ways-first by repeated application of product rule, second by logarithmic differentiation.
Answer» If u, v and w are functions of x, then show that $\frac{d}{d x} (u . v . w) = \frac{d u}{d x} v . w + u . \frac{d v}{d x} w + u . v \frac{d w}{d x}$ In two ways-first by repeated application of product rule, second by logarithmic differentiation.

Discussion

5332.	A real valued function f(x) satisfies the functional equation f(x-y)=f (x)f (y)-f (a-x)f (a+y), where a is given constant and f(0)=1, then find f(2a-x)
Answer» A real valued function f(x) satisfies the functional equation f(x-y)=f (x)f (y)-f (a-x)f (a+y), where a is given constant and f(0)=1, then find f(2a-x)

Discussion

5333.	If the system of linear equations2x+y−z=3x−y−z=α3x+3y+βz=3has infinitely many solutions, then (α+β−αβ) is equal to
Answer» If the system of linear equations $2 x + y - z = 3$ $x - y - z = α$ $3 x + 3 y + β z = 3$ has infinitely many solutions, then $(α + β - α β)$ is equal to

Discussion

5334.	If 5,3,2 are the direction ratios of a normal to the plane passing through the point (2,3,1), then the sum of the intercepts made by the plane on the x−axis and y−axis is
Answer» If $5, 3, 2$ are the direction ratios of a normal to the plane passing through the point $(2, 3, 1)$ , then the sum of the intercepts made by the plane on the $x -$ axis and $y -$ axis is

Discussion

5335.	The length of common chord of two intersecting circles is 30cm. If the diameters of these two circles be 50 cm and 34 cm, then the distance between their centres is
Answer» The length of common chord of two intersecting circles is $30$ cm. If the diameters of these two circles be $50$ cm and $34$ cm, then the distance between their centres is

Discussion

5336.	If ∫0a14+x2dx=π8, find the value of a. [CBSE 2014]
Answer» If $\int_{0}^{a} \frac{1}{4 + x^{2}} d x = \frac{π}{8}$ , find the value of a. [CBSE 2014]

Discussion

5337.	59.If A and B are 2 matrices such that AB=B and BA=A then A2 + B2 is equal to
Answer» 59.If A and B are 2 matrices such that AB=B and BA=A then A2 + B2 is equal to

Discussion

5338.	{ 5. In }△ ABC, the coordinates of the vertex }A are }(4,-1) and lines }x-y-1=0 and }2x-y=3 are the intermal }} bisecters of angles }B and }C . Then, the radius of the incircle of triangle }ABC is
Answer» { 5. In }△ ABC, the coordinates of the vertex }A are }(4,-1) and lines }x-y-1=0 and }2x-y=3 are the intermal }} bisecters of angles }B and }C . Then, the radius of the incircle of triangle }ABC is

Discussion

5339.	If ∫dxx3(1+x6)2/3=xf(x)(1+x6)1/3+C where C is a constant of integration, then the function f(x) is equal to :
Answer» If $\int \frac{d x}{x^{3} (1 + x^{6})^{2 / 3}} = x f (x) (1 + x^{6})^{1 / 3} + C$ where $C$ is a constant of integration, then the function $f (x)$ is equal to :

Discussion

5340.	Derive : I= neVdA
Answer» Derive : I= neVdA

Discussion

5341.	Find the domain of following:-f(x)=√log0.5(-x^2+x+6) + 1/(x^2+2x)
Answer» Find the domain of following:- f(x)=√log0.5(-x^2+x+6) + 1/(x^2+2x)

Discussion

5342.	find the equation of the ellipse whose centre is (-2,3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.
Answer» find the equation of the ellipse whose centre is (-2,3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.

Discussion

5343.	The value of the integral 1∫−1{x2015e\|x\|(x2+cosx)+1e\|x\|}dx is equal to
Answer» The value of the integral $1 \int - 1 {\frac{x^{2015}}{e^{\| x \|} (x^{2} + cos x)} + \frac{1}{e^{\| x \|}}} d x$ is equal to

Discussion

5344.	A chord of the circle x2+y2−4x−6y=0 passing through the origin subtends an angle tan−1(74) at the point where the circle meets positive y-axis. Equation of the chord is
Answer» A chord of the circle $x^{2} + y^{2} - 4 x - 6 y = 0$ passing through the origin subtends an angle $t a n^{- 1} (\frac{7}{4})$ at the point where the circle meets positive y-axis. Equation of the chord is

Discussion

5345.	7-(3x+11)6,2
Answer» 7-(3x+11)6,2

Discussion

5346.	If the angle between the pair of straight lines represented by the equation x2−3xy+λy2+3x−5y+2=0 is tan−1(13), where λ is a non- negative real number, then λ is
Answer» If the angle between the pair of straight lines represented by the equation $x^{2} - 3 x y + λ y^{2} + 3 x - 5 y + 2 = 0$ is ${tan}^{- 1} (\frac{1}{3})$ , where $λ$ is a non- negative real number, then $λ$ is

Discussion

5347.	Which of the following is parallel to plane 3x - 3y +4z = 7 ?
Answer» Which of the following is parallel to plane 3x - 3y +4z = 7 ?

Discussion

5348.	Let ∗ be a binary operation on the set Q of rational number as follows: (vi)a∗b=ab2 Show that none of the operations has an identity.
Answer» Let $$ be a binary operation on the set Q of rational number as follows: $(v i) a b = a b^{2}$ Show that none of the operations has an identity.

Discussion

5349.	25.The longest side of a triangle is 3 times the shortest side and the third side is 2 cmshorter than the longest side. If the perimeter of the triangle is at least 61 cm, findthe minimum length of the shortest side.
Answer» 25.The longest side of a triangle is 3 times the shortest side and the third side is 2 cmshorter than the longest side. If the perimeter of the triangle is at least 61 cm, findthe minimum length of the shortest side.

Discussion

5350.	A partical projected from origin moves in x-y plane with a velocity v=3i+6xj, where I and j are the unit vectors along x and y axis. Find equation of path followed by the partical
Answer» A partical projected from origin moves in x-y plane with a velocity v=3i+6xj, where I and j are the unit vectors along x and y axis. Find equation of path followed by the partical

Discussion

Explore topic-wise InterviewSolutions in .

If [2−756][xy]=[139], then which of the following option is True

23. Prove that nth terms of an ap cannot be n²+1.Give justification

Let n be a positive integer such that sin π2n + cos π2n = √n2. Then

The random variabel Y is defined by Y=12(X+|X|) where ′X′ is another random variable. Then the density funciton of ′Y′ for y&gt;0 is equal to

The value of π/2∫0dx√cotx+1 is

Find the modulus and argument of the complex number root 3 - i and converted into polar form

The maximum value of f(x)=[x(−1)+1]13,0≤x≤1 is\\ a) (13)13 b) 12 c) 1 d) zero

A plane passes through the points (2, 0, 0), (0, 3, 0) and (0, 0, 4). The equation of the plane is _______________.

In a ΔABC, If cotA2:cotB2:cotC2=1:4:15, then the greatest angle is:

43. tan[÷ 4-cos inverse 4÷ 5]

logπ4(−1+√3i) can be expressed in cartesian form as

Find the values of x for which |x−3|+|x−4|=9.

If I=∫π0xsin2x⋅sin(π2cosx)(2x−π)dx, then the value of π2I=

If Cr denotes coefficient of xr in (1+x)99 then the value of C0−2C1+3C2−4C3+…100C99=

Write the following functions in the simplest form : tan−1(3a2x−x3a3−3ax2),a&gt;0;−a√3&lt;x&lt;a√3

If (P2−1)x2+(P−1)x+(P2−4P+3)=0 is an identity in x, then the value of P is

Let S be the set of values of x for which the tangent to the curve y=f(x)=x3−x2−2x at (x,y) is parallel to the line segment joining the points (1,f(1)) and (−1,f(−1)), then S is equal to:

Find the linear inequations for which the solution set is the shaded region given in figure.

[[5(x+1)]^(ln5)]=(2y)^(ln2) and (x+1)^(ln2)=[5^(lny)], then x is ,[[ (A) (1)/(5), (B) -(1)/(5)],[ (C) (4)/(5), (D) -(4)/(5)]]

Compute the derivative of sinx.

The value of sin(25π3)+sec(41π4)+tan(−16π3)−cosec(−33π4) is

A die is rolled, then the probability that a number 1 or 6 may appear is

On the ellipse 4x2+9y2=1, the points at which the tangents are parallel to the line 8x=9y are

The general solution of the differential equation of the type dxdy+Rx=S, Where R and S are function of y, is _________________.

The equation of the normal at the point (6,4) on the hyperbola x29−y216=3 is

If sinA=34, then what is the value of cosA?

The latitude and departure of a line AB are + 78 m and - 45.1 m respectively , The whole circle bearing of the line AB is

If |t|=3, then the possible value(s) of |2t−1| is/are

Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12

If u, v and w are functions of x, then show that ddx(u.v.w)=dudxv.w+u.dvdxw+u.vdwdxIn two ways-first by repeated application of product rule, second by logarithmic differentiation.

A real valued function f(x) satisfies the functional equation f(x-y)=f (x)f (y)-f (a-x)f (a+y), where a is given constant and f(0)=1, then find f(2a-x)

If the system of linear equations2x+y−z=3x−y−z=α3x+3y+βz=3has infinitely many solutions, then (α+β−αβ) is equal to

If 5,3,2 are the direction ratios of a normal to the plane passing through the point (2,3,1), then the sum of the intercepts made by the plane on the x−axis and y−axis is

The length of common chord of two intersecting circles is 30cm. If the diameters of these two circles be 50 cm and 34 cm, then the distance between their centres is

If ∫0a14+x2dx=π8, find the value of a. [CBSE 2014]

59.If A and B are 2 matrices such that AB=B and BA=A then A2 + B2 is equal to

{ 5. In }△ ABC, the coordinates of the vertex }A are }(4,-1) and lines }x-y-1=0 and }2x-y=3 are the intermal }} bisecters of angles }B and }C . Then, the radius of the incircle of triangle }ABC is

If ∫dxx3(1+x6)2/3=xf(x)(1+x6)1/3+C where C is a constant of integration, then the function f(x) is equal to :

Derive : I= neVdA

Find the domain of following:-f(x)=√log0.5(-x^2+x+6) + 1/(x^2+2x)

find the equation of the ellipse whose centre is (-2,3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.

The value of the integral 1∫−1{x2015e|x|(x2+cosx)+1e|x|}dx is equal to

A chord of the circle x2+y2−4x−6y=0 passing through the origin subtends an angle tan−1(74) at the point where the circle meets positive y-axis. Equation of the chord is

7-(3x+11)6,2

If the angle between the pair of straight lines represented by the equation x2−3xy+λy2+3x−5y+2=0 is tan−1(13), where λ is a non- negative real number, then λ is

Which of the following is parallel to plane 3x - 3y +4z = 7 ?

Let ∗ be a binary operation on the set Q of rational number as follows: (vi)a∗b=ab2 Show that none of the operations has an identity.

25.The longest side of a triangle is 3 times the shortest side and the third side is 2 cmshorter than the longest side. If the perimeter of the triangle is at least 61 cm, findthe minimum length of the shortest side.

A partical projected from origin moves in x-y plane with a velocity v=3i+6xj, where I and j are the unit vectors along x and y axis. Find equation of path followed by the partical

The random variabel Y is defined by Y=12(X+|X|) where ′X′ is another random variable. Then the density funciton of ′Y′ for y>0 is equal to

Write the following functions in the simplest form : tan−1(3a2x−x3a3−3ax2),a>0;−a√3<x<a√3