43030 + Interview Questions in Mathematics Page 144 InterviewSolution

7151.	Solve the following system of equations in R. \|x+1\|+\|x\|>3
Answer» Solve the following system of equations in R. \|x+1\|+\|x\|>3

7151.

Solve the following system of equations in R. |x+1|+|x|>3

Answer»

Solve the following system of equations in R.

|x+1|+|x|>3

7152.	If 22x+2−a⋅2x+2+5−4a≥0 has atleast one real solution, Then a ϵ
Answer» If $2^{2 x + 2} - a \cdot 2^{x + 2} + 5 - 4 a \geq 0$ has atleast one real solution, Then a $ϵ$

Discussion

7153.	If f(x)=x\|x\|, then the value of f′(x)−2\|x\| at x=2021 is
Answer» If $f (x) = x \| x \|$ , then the value of $f^{'} (x) - 2 \| x \|$ at $x = 2021$ is

Discussion

7154.	What will be the number of significant figures in 100• and why?
Answer» What will be the number of significant figures in 100• and why?

Discussion

7155.	If sin-12a1-a2+cos-11-a21+a2=tan-12x1-x2, where a, x∈0, 1, then, the value of x is(a) 0(b) a2(c) a(d) 2a1-a2
Answer» If $\sin^{- 1} (\frac{2 a}{1 - a^{2}}) + \cos^{- 1} (\frac{1 - a^{2}}{1 + a^{2}}) = \tan^{- 1} (\frac{2 x}{1 - x^{2}}), where a, x \in (0, 1)$ , then, the value of x is (a) 0 (b) $\frac{a}{2}$ (c) a (d) $\frac{2 a}{1 - a^{2}}$

Discussion

7156.	Number of value(s) of x for which sin−1(x2−x43+x69...)+cos−1(x4−x83+x129...)=π2, where 0≤\|x\|<31/4, is
Answer» Number of value(s) of $x$ for which ${sin}^{- 1} (x^{2} - \frac{x^{4}}{3} + \frac{x^{6}}{9} . . .) + {cos}^{- 1} (x^{4} - \frac{x^{8}}{3} + \frac{x^{12}}{9} . . .) = \frac{π}{2}$ , where $0 \leq \| x \| < 3^{1 / 4}$ , is

Discussion

7157.	4x +5sin x3x + 7cosx26.
Answer» 4x +5sin x3x + 7cosx26.

Discussion

7158.	limx→0sinxx is(a) 1 (b) −1 (c) 0 (d) does not exist
Answer» $\lim_{x \to 0} \frac{\|\sin x\|}{x}$ is (a) 1 (b) −1 (c) 0 (d) does not exist

Discussion

7159.	Prove that cos x cos π3-x cos π3+x≤14 for all values of x
Answer» Prove that $\|\cos x \cos (\frac{π}{3} - x) \cos (\frac{π}{3} + x)\| \leq \frac{1}{4}$ for all values of x

Discussion

7160.	Using properties of determinants, prove that:
Answer» Using properties of determinants, prove that:

Discussion

7161.

The weight of coffee in 70 jars is shown in the following table: Weight (in grams): 200–201 201–202 202–203 203–204 204–205 205–206 Frequency: 13 27 18 10 1 1 Determine the variance and standard deviation of the above distribution. [NCERT EXEMPLAR]

Answer» The weight of coffee in 70 jars is shown in the following table:

Weight (in grams):	200–201	201–202	202–203	203–204	204–205	205–206
Frequency:	13	27	18	10	1	1

Determine the variance and standard deviation of the above distribution. [NCERT EXEMPLAR]

Discussion

7162.	How many significant figures are there in 126000?
Answer» How many significant figures are there in 126000?

Discussion

7163.	Expand the expression (2x – 3)6
Answer» Expand the expression (2x – 3)⁶

Discussion

7164.	Integerate x.dx/(x+2)sqrt(x+1)
Answer» Integerate x.dx/(x+2)sqrt(x+1)

Discussion

7165.	IfA=⎡⎢⎣123456710⎤⎥⎦,B=⎡⎢⎣100030045⎤⎥⎦ and Tr(AB)=λTr(A)⋅Tr(B), then λ is equal to
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 3 & 0 0 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦$ and $T r (A B) = λ T r (A) \cdot T r (B)$ , then $λ$ is equal to

Discussion

7166.	134secx lies in fourth quadrant.
Answer» 134secx lies in fourth quadrant.

Discussion

7167.	The value of ∫1x2√1+x2dx is
Answer» The value of $\int \frac{1}{x^{2} \sqrt{1 + x^{2}}} d x$ is

Discussion

7168.	find value of n, for which (-1)^n+(-1) ^4 =0
Answer» find value of n, for which (-1)^n+(-1) ^4 =0

Discussion

7169.	If 4560 is equivalent to 3x, then the value of x is(a) 3(b) 6(c) 4(d) 9
Answer» If $\frac{45}{60}$ is equivalent to $\frac{3}{x}$ , then the value of x is (a) 3 (b) 6 (c) 4 (d) 9

Discussion

7170.	The conjugate of (2+i)23+i , in the form of a+ib, is
Answer» The conjugate of $\frac{(2 + i)^{2}}{3 + i}$ , in the form of a+ib, is

Discussion

7171.	The value of cos-1 sincos-112is ________________________.
Answer» The value of cos^-1 $\{\sin (\cos^{- 1} \frac{1}{2})\}$ is ________________________.

Discussion

7172.	If sin21∘=xy, then sec21∘−sin69∘ is equal to
Answer» If $sin 21^{\circ} = \frac{x}{y}$ , then $sec 21^{\circ} - sin 69^{\circ}$ is equal to

Discussion

7173.	Compute the mean deviation from the median of the following distribution : Class0−1010−2020−3030−4040−50Frequency51020510
Answer» Compute the mean deviation from the median of the following distribution : $\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequency & 5 & 10 & 20 & 5 & 10 \end{matrix}$

7173.

Compute the mean deviation from the median of the following distribution : Class0−1010−2020−3030−4040−50Frequency51020510

Answer»

Compute the mean deviation from the median of the following distribution :

$\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequency & 5 & 10 & 20 & 5 & 10 \end{matrix}$

Discussion

7174.	If 1+∑18r=0(r(r+2)+1)r!=n!, then n is not divisible by
Answer» If $1 + \sum_{r = 0}^{18} (r (r + 2) + 1) r! = n!$ , then n is not divisible by

Discussion

7175.	limx→0sinx cosx3x
Answer» ${lim}_{x \to 0} \frac{s i n x c o s x}{3 x}$

Discussion

7176.	The least positive value of x satisfying tanx=x+1 lies in the interval
Answer» The least positive value of $x$ satisfying $tan x = x + 1$ lies in the interval

Discussion

7177.	Suppose that 5% of men and 0.25% of women have grey hair. A haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Answer» Suppose that 5% of men and 0.25% of women have grey hair. A haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

Discussion

7178.	If all the letters of the word AGAIN are arranged in dictionary order, find the 43rd and 54th words.
Answer» If all the letters of the word AGAIN are arranged in dictionary order, find the 43rd and 54th words.

Discussion

7179.	The equation of the tangent to the curve y=x+4x2, which is parallel to the x− axis, is
Answer» The equation of the tangent to the curve $y = x + \frac{4}{x^{2}},$ which is parallel to the $x -$ axis, is

Discussion

7180.	If two sets A and B are such that (A−B)=A, then A∩B=
Answer» If two sets $A$ and $B$ are such that $(A - B) = A$ , then $A \cap B =$

Discussion

7181.	Evaluate limx→2f(x) (if it exists), where f(x) =⎧⎪⎨⎪⎩x−[x],x<24,x=23x−5,x>2
Answer» Evaluate ${lim}_{x \to 2} f (x)$ (if it exists), where f(x) $= ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - [x], & x < 2 4, & x = 2 3 x - 5, & x > 2 \end{matrix}$

7181.

Evaluate limx→2f(x) (if it exists), where f(x) =⎧⎪⎨⎪⎩x−[x],x<24,x=23x−5,x>2

Answer»

Evaluate ${lim}_{x \to 2} f (x)$ (if it exists), where f(x)

$= ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - [x], & x < 2 4, & x = 2 3 x - 5, & x > 2 \end{matrix}$

Discussion

7182.	Why do symmetrical ethers possess dipole moment even if the arrows cancel the effect of each other?
Answer» Why do symmetrical ethers possess dipole moment even if the arrows cancel the effect of each other?

Discussion

7183.	A rectangle with side lengths as 2m−1 and 2n−1 units is divided into squares of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is
Answer» A rectangle with side lengths as $2 m - 1$ and $2 n - 1$ units is divided into squares of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is

Discussion

7184.	Equation of the ellipse with focus (3,−2),eccentricity 34 and directrix 2x−y+3=0 is
Answer» Equation of the ellipse with focus $(3, - 2)$ , eccentricity $\frac{3}{4}$ and directrix $2 x - y + 3 = 0$ is

Discussion

7185.	the ratio in which the sphere x^2+y^2+z^2=504 divides the line joining (12,-4,8) and (27,-9,8) internally i
Answer» the ratio in which the sphere x^2+y^2+z^2=504 divides the line joining (12,-4,8) and (27,-9,8) internally i

Discussion

7186.	If xdydx=x2+y−2, y(1)=1, and x>0 then y(2) equals
Answer» If $x \frac{d y}{d x} = x^{2} + y - 2, y (1) = 1,$ and $x > 0$ then $y (2)$ equals

Discussion

7187.	The value of the expression 2(1+1ω)(1+1ω2)+3(2+1ω)(2+1ω2)+4(3+1ω)(3+1ω2)+⋯+(n+1)(n+1ω)(n+1ω2), where ω is an imaginary cube root of unity, is
Answer» The value of the expression $2 (1 + \frac{1}{ω}) (1 + \frac{1}{ω^{2}}) + 3 (2 + \frac{1}{ω}) (2 + \frac{1}{ω^{2}}) + 4 (3 + \frac{1}{ω}) (3 + \frac{1}{ω^{2}}) + \dots + (n + 1) (n + \frac{1}{ω}) (n + \frac{1}{ω^{2}}),$ where $ω$ is an imaginary cube root of unity, is

Discussion

7188.	If cosαcosβ+sinαsinβ=−1, then the value of cos3βcosα+sin3βsinα is
Answer» If $\frac{cos α}{cos β} + \frac{sin α}{sin β} = - 1,$ then the value of $\frac{{cos}^{3} β}{cos α} + \frac{{sin}^{3} β}{sin α}$ is

Discussion

7189.	∫cosx+√31+4sin(x+π3)+4sin2(x+π3) dx is where c is constant of integration
Answer» $\int \frac{cos x + \sqrt{3}}{1 + 4 sin (x + \frac{π}{3}) + 4 {sin}^{2} (x + \frac{π}{3})} d x$ is where $c$ is constant of integration

Discussion

7190.	The value of the integral ∫02πcos7x sin4x dx is ________________.
Answer» The value of the integral $\int_{0}^{2 π} \cos^{7} x \sin^{4} x d x$ is ________________.

Discussion

7191.	The number of arbitrary constants in the general solution of a differential equation of fourth order is (a) zero (b) 2 (c) 3 (d) 4
Answer» The number of arbitrary constants in the general solution of a differential equation of fourth order is (a) zero (b) 2 (c) 3 (d) 4

Discussion

7192.	5. sin' x cos'x
Answer» 5. sin' x cos'x

Discussion

7193.	if x€(-infinity ,-1)then find the value of 4 tan^-1x+sin^-1(2x/1+x^2)+cos^-1(1-x^2/1+x^2)
Answer» if x€(-infinity ,-1)then find the value of 4 tan^-1x+sin^-1(2x/1+x^2)+cos^-1(1-x^2/1+x^2)

Discussion

7194.	\lim_{x→0} (5x + 3)(6x + 2)
Answer» \lim_{x→0} (5x + 3)(6x + 2)

Discussion

7195.	The eccentric angle of a point on the ellipse x26+y22=1 whose distance from the center of the ellipse is √5 is:
Answer» The eccentric angle of a point on the ellipse $\frac{x^{2}}{6} + \frac{y^{2}}{2} = 1$ whose distance from the center of the ellipse is $\sqrt{5}$ is:

Discussion

7196.	If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
Answer» If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.

Discussion

7197.	If two ordered pairs are related as (4a−3,a+2b)=(3a,2a−b), then a−b=
Answer» If two ordered pairs are related as $(4 a - 3, a + 2 b) = (3 a, 2 a - b)$ , then $a - b =$

Discussion

7198.	Which of the following represents the number of elements that can be sorted in Θ(n) times using merge sort?
Answer» Which of the following represents the number of elements that can be sorted in $Θ (n)$ times using merge sort?

Discussion

7199.	If the vertices of triangle are (1,2,3), (2,3,1), (3,1,2), then the co-ordinates of centroid of triangle is
Answer» If the vertices of triangle are (1,2,3), (2,3,1), (3,1,2), then the co-ordinates of centroid of triangle is

Discussion

7200.	What is the condition for a function y = f(x) to be a strictly increasing function.
Answer» What is the condition for a function y = f(x) to be a strictly increasing function.

Discussion

Explore topic-wise InterviewSolutions in .

Solve the following system of equations in R. |x+1|+|x|&gt;3

If 22x+2−a⋅2x+2+5−4a≥0 has atleast one real solution, Then a ϵ

If f(x)=x|x|, then the value of f′(x)−2|x| at x=2021 is

What will be the number of significant figures in 100• and why?

If sin-12a1-a2+cos-11-a21+a2=tan-12x1-x2, where a, x∈0, 1, then, the value of x is(a) 0(b) a2(c) a(d) 2a1-a2

Number of value(s) of x for which sin−1(x2−x43+x69...)+cos−1(x4−x83+x129...)=π2, where 0≤|x|&lt;31/4, is

4x +5sin x3x + 7cosx26.

limx→0sinxx is(a) 1 (b) −1 (c) 0 (d) does not exist

Prove that cos x cos π3-x cos π3+x≤14 for all values of x

Using properties of determinants, prove that:

The weight of coffee in 70 jars is shown in the following table: Weight (in grams): 200–201 201–202 202–203 203–204 204–205 205–206 Frequency: 13 27 18 10 1 1 Determine the variance and standard deviation of the above distribution. [NCERT EXEMPLAR]

How many significant figures are there in 126000?

Expand the expression (2x – 3)6

Integerate x.dx/(x+2)sqrt(x+1)

IfA=⎡⎢⎣123456710⎤⎥⎦,B=⎡⎢⎣100030045⎤⎥⎦ and Tr(AB)=λTr(A)⋅Tr(B), then λ is equal to

134secx lies in fourth quadrant.

The value of ∫1x2√1+x2dx is

find value of n, for which (-1)^n+(-1) ^4 =0

If 4560 is equivalent to 3x, then the value of x is(a) 3(b) 6(c) 4(d) 9

The conjugate of (2+i)23+i , in the form of a+ib, is

The value of cos-1 sincos-112is ________________________.

If sin21∘=xy, then sec21∘−sin69∘ is equal to

Compute the mean deviation from the median of the following distribution : Class0−1010−2020−3030−4040−50Frequency51020510

If 1+∑18r=0(r(r+2)+1)r!=n!, then n is not divisible by

limx→0sinx cosx3x

The least positive value of x satisfying tanx=x+1 lies in the interval

Suppose that 5% of men and 0.25% of women have grey hair. A haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

If all the letters of the word AGAIN are arranged in dictionary order, find the 43rd and 54th words.

The equation of the tangent to the curve y=x+4x2, which is parallel to the x− axis, is

If two sets A and B are such that (A−B)=A, then A∩B=

Evaluate limx→2f(x) (if it exists), where f(x) =⎧⎪⎨⎪⎩x−[x],x&lt;24,x=23x−5,x&gt;2

Why do symmetrical ethers possess dipole moment even if the arrows cancel the effect of each other?

A rectangle with side lengths as 2m−1 and 2n−1 units is divided into squares of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is

Equation of the ellipse with focus (3,−2),eccentricity 34 and directrix 2x−y+3=0 is

the ratio in which the sphere x^2+y^2+z^2=504 divides the line joining (12,-4,8) and (27,-9,8) internally i

If xdydx=x2+y−2, y(1)=1, and x&gt;0 then y(2) equals

The value of the expression 2(1+1ω)(1+1ω2)+3(2+1ω)(2+1ω2)+4(3+1ω)(3+1ω2)+⋯+(n+1)(n+1ω)(n+1ω2), where ω is an imaginary cube root of unity, is

If cosαcosβ+sinαsinβ=−1, then the value of cos3βcosα+sin3βsinα is

∫cosx+√31+4sin(x+π3)+4sin2(x+π3) dx is where c is constant of integration

The value of the integral ∫02πcos7x sin4x dx is ________________.

The number of arbitrary constants in the general solution of a differential equation of fourth order is (a) zero (b) 2 (c) 3 (d) 4

5. sin' x cos'x

if x€(-infinity ,-1)then find the value of 4 tan^-1x+sin^-1(2x/1+x^2)+cos^-1(1-x^2/1+x^2)

\lim_{x→0} (5x + 3)(6x + 2)

The eccentric angle of a point on the ellipse x26+y22=1 whose distance from the center of the ellipse is √5 is:

If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.

If two ordered pairs are related as (4a−3,a+2b)=(3a,2a−b), then a−b=

Which of the following represents the number of elements that can be sorted in Θ(n) times using merge sort?

If the vertices of triangle are (1,2,3), (2,3,1), (3,1,2), then the co-ordinates of centroid of triangle is

What is the condition for a function y = f(x) to be a strictly increasing function.

Solve the following system of equations in R. |x+1|+|x|>3

Number of value(s) of x for which sin−1(x2−x43+x69...)+cos−1(x4−x83+x129...)=π2, where 0≤|x|<31/4, is

Evaluate limx→2f(x) (if it exists), where f(x) =⎧⎪⎨⎪⎩x−[x],x<24,x=23x−5,x>2

If xdydx=x2+y−2, y(1)=1, and x>0 then y(2) equals