43030 + Interview Questions in Mathematics

1.	x217·阿r2-1
Answer» x217·阿r2-1

Discussion

2.	equals
Answer» equals

2.

equals

Answer»

equals

Discussion

3.	21. The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto
Answer» 21. The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto

Discussion

4.	Help James find the value of "A" in the given equation:223÷23=A
Answer» $Help James find the value of " A " in the given equation:$ $2 \frac{2}{3} \div \frac{2}{3} = A$

Discussion

5.	Let f:R→R be a differentiable function such that f(x)=x2+x∫0e−tf(x−t)dt. Then, the value of 1∫0f(x)dx is
Answer» Let $f : R \to R$ be a differentiable function such that $f (x) = x^{2} + x \int 0 e^{- t} f (x - t) d t .$ Then, the value of $1 \int 0 f (x) d x$ is

Discussion

6.	Find the value of b ϵR such that x2+bx−1=0,x2+x+b=0 have a common root.
Answer» Find the value of b $ϵ R$ such that $x^{2} + b x - 1 = 0, x^{2} + x + b = 0$ have a common root.

Discussion

7.	Evaluate the following definete integrals as limit of sums. ∫14(x2−x)dx.
Answer» Evaluate the following definete integrals as limit of sums. $\int_{4}^{1} (x^{2} - x) d x .$

Discussion

8.	{\operatorname{sin}^{-1}(\operatorname{sin}8)>x^2-6x holds if }}{ (1) }(-\sqrt{1+3π},\sqrt{1+3π})}{ (2) }(3-\sqrt{1+3π},3+\sqrt{1+3π})}{ (3) }(3-\sqrt{1-3π},3+\sqrt{1-3π})}{ (4) }(0,3-\sqrt{1-3π})
Answer» {\operatorname{sin}^{-1}(\operatorname{sin}8)>x^2-6x holds if }}{ (1) }(-\sqrt{1+3π},\sqrt{1+3π})}{ (2) }(3-\sqrt{1+3π},3+\sqrt{1+3π})}{ (3) }(3-\sqrt{1-3π},3+\sqrt{1-3π})}{ (4) }(0,3-\sqrt{1-3π})

Discussion

9.	The coefficient of x12in(x3+x4+x5+x6.....)3 is
Answer» The coefficient of $x^{12} i n (x^{3} + x^{4} + x^{5} + x^{6} . . . . .)^{3}$ is

Discussion

10.	The number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes is
Answer» The number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes is

Discussion

11.	The equation of the hyperbola whose directrix is x+2y=1, focus (2,1) and eccentricity 2 is
Answer» The equation of the hyperbola whose directrix is $x + 2 y = 1$ , focus $(2, 1)$ and eccentricity $2$ is

Discussion

12.	Find the value of m such that roots of the quadratic equation x2−(m−3)x+m=0 (m∈R) are positive
Answer» Find the value of $m$ such that roots of the quadratic equation $x^{2} - (m - 3) x + m = 0$ $(m \in R)$ are positive

Discussion

13.	The area of the bounded by the curve y = sinx, x-axis and between x = 0 and x = 2π is _______________.
Answer» The area of the bounded by the curve y = sinx, x-axis and between x = 0 and x = 2π is _______________.

Discussion

14.	Range of rational expression y=x2−x+4x2+x+4, x∈R is
Answer» Range of rational expression $y = \frac{x^{2} - x + 4}{x^{2} + x + 4}, x \in R$ is

Discussion

15.	Examine the continuity of -- where -- is defined by f(x) {sin x−cos x, if x≠0−1, if x=0.
Answer» Examine the continuity of -- where -- is defined by f(x) ${\begin{matrix} s i n x - c o s x, i f x \neq 0 - 1, i f x = 0. \end{matrix}$

Discussion

16.	Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π=227)
Answer» Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use $π = \frac{22}{7}$ )

16.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π=227)

Answer»

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm

(Use $π = \frac{22}{7}$ )

Discussion

17.	If a 6 digit number is made using all the digits 1,2,4,5,7,8, then the position of number ′′541782′′ when all numbers formed are arranged in ascending order is
Answer» If a $6$ digit number is made using all the digits $1, 2, 4, 5, 7, 8$ , then the position of number $^{''} 541782^{''}$ when all numbers formed are arranged in ascending order is

Discussion

18.	3. ax + bycos y
Answer» 3. ax + bycos y

Discussion

19.	If f(x)=x(x+1)/e^x on the closed interval [-1,0] . Then find the value of c using Rolle's Theorem:Options : (a) (1-√3)/2 (b) (1-√3)/4(c) (1-√5)/2(d) (1-√5)/4
Answer» If f(x)=x(x+1)/e^x on the closed interval [-1,0] . Then find the value of c using Rolle's Theorem: Options : (a) (1-√3)/2 (b) (1-√3)/4 (c) (1-√5)/2 (d) (1-√5)/4

Discussion

20.	5. J2cos 2x dix
Answer» 5. J2cos 2x dix

Discussion

21.	If cosθ−sinθ=15, where 0<θ<π2, then the value of 5(sinθ+cosθ) is
Answer» If $cos θ - sin θ = \frac{1}{5}$ , where $0 < θ < \frac{π}{2}$ , then the value of $5 (sin θ + cos θ)$ is

Discussion

22.	The medians of a right angles triangle are 3 and 4. Then, is area is?
Answer» The medians of a right angles triangle are 3 and 4. Then, is area is?

Discussion

23.	If F= 2/sin theta + cos theta, then the minimum value of F out of the following options is1. 12. 1/√23. 3/√24. √2
Answer» If F= 2/sin theta + cos theta, then the minimum value of F out of the following options is 1. 1 2. 1/√2 3. 3/√2 4. √2

Discussion

24.	If f(x)=∫2sin6x−5sin4x+10sin2x2cos5x−3cos3x+7cosxdx,f(0)=1, then which of the following option(s) is/are correct ?
Answer» If $f (x) = \int \frac{2 sin 6 x - 5 sin 4 x + 10 sin 2 x}{2 cos 5 x - 3 cos 3 x + 7 cos x} d x, f (0) = 1,$ then which of the following option(s) is/are correct ?

Discussion

25.	Find the roots of the quadratic equation 2x2+7x+52=0.
Answer» Find the roots of the quadratic equation $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$ .

Discussion

26.	Solve the equation x-7=-2 and check the result.
Answer» Solve the equation x-7=-2 and check the result.

Discussion

27.	If [.]denotes G.I F, ∫2π0[\|sin x\|−\|cos x\|]dx=
Answer» If $[.]$ denotes G.I F, $\int_{0}^{2 π} [\| s i n x \| - \| c o s x \|] d x =$

Discussion

28.	If , find the values of x and y .
Answer» If , find the values of x and y .

Discussion

29.	Let ¯¯bz+b¯¯¯z=c,b≠0 be a line in the complex plane. If a point z1 is the reflection of a point z2 through the line, then c is
Answer» Let $¯ ¯ b z + b ¯ ¯ ¯ z = c, b \neq 0$ be a line in the complex plane. If a point $z_{1}$ is the reflection of a point $z_{2}$ through the line, then $c$ is

Discussion

30.	limx→0(3x+\|x\|7x−5\|x\|)=___
Answer» $l i m_{x \to 0} (\frac{3 x + \| x \|}{7 x - 5 \| x \|})$ =___

Discussion

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

Discussion

32.	What is the rank of the word paris as in a dictionary. .?
Answer» What is the rank of the word paris as in a dictionary. .?

Discussion

33.	Let P be the plane, which contains the line of intersection of the planes, x+y+z−6=0 and 2x+3y+z+5=0 and it is perpendicular to the xy-plane. Then the distance of the point (0,0,256) from P is equal to :
Answer» Let $P$ be the plane, which contains the line of intersection of the planes, $x + y + z - 6 = 0$ and $2 x + 3 y + z + 5 = 0$ and it is perpendicular to the $x y$ -plane. Then the distance of the point $(0, 0, 256)$ from $P$ is equal to :

Discussion

34.	Give examples of two functions f : N → Z and g : Z → Z such that g o f is injective but g is not injective. (Hint: Consider f ( x ) = x and g ( x ) = )
Answer» Give examples of two functions f : N → Z and g : Z → Z such that g o f is injective but g is not injective. (Hint: Consider f ( x ) = x and g ( x ) = )

Discussion

35.	If θ1 and θ2 be respectively the smallest and the largest values of θ in (0,2π)−{π} which satisfy the equation, 2cot2θ−5sinθ+4=0, then θ2∫θ1cos23θ dθ is equal to :
Answer» If $θ_{1}$ and $θ_{2}$ be respectively the smallest and the largest values of $θ$ in $(0, 2 π) - {π}$ which satisfy the equation, $2 {cot}^{2} θ - \frac{5}{sin θ} + 4 = 0$ , then $θ_{2} \int θ_{1} {cos}^{2} 3 θ d θ$ is equal to :

Discussion

36.	Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin2x−cosx,x ϵ(0,π)
Answer» Find the absolute maximum and absolute minimum values of the function f given by $f (x) = s i n^{2} x - c o s x, x ϵ (0, π)$

Discussion

37.	10 men and 6 women are to be seated in a row so that no two women sit together. the number of ways they can be seated is
Answer» 10 men and 6 women are to be seated in a row so that no two women sit together. the number of ways they can be seated is

Discussion

38.	A(α,β)=⎛⎜⎝cosαsinα0−sinαcosα000eβ⎞⎟⎠⇒[A(α,β)]−1=
Answer» $A (α, β) = ⎛ ⎜ ⎝ \begin{matrix} c o s α & s i n α & 0 - s i n α & c o s α & 0 0 & 0 & e^{β} \end{matrix} ⎞ ⎟ ⎠ \Rightarrow {[A (α, β)]}^{- 1} =$

Discussion

39.	Let h(x)=tan2{2sin−1(cos(sin−13x))+2cos−1(sin(cos−13x))3}; where x∈[−13,13], then the value of 10∑r=3h(1r2)=
Answer» Let $h (x) = {tan}^{2} {\frac{2 {sin}^{- 1} (cos ({sin}^{- 1} 3 x)) + 2 {cos}^{- 1} (sin ({cos}^{- 1} 3 x))}{3}};$ where $x \in [- \frac{1}{3}, \frac{1}{3}],$ then the value of $10 \sum r = 3 h (\frac{1}{r^{2}}) =$

Discussion

40.	∫2π0x In(3+cosx3−cosx)dx=___
Answer» $\int_{0}^{2 π} x I n (\frac{3 + c o s x}{3 - c o s x}) d x =$ ___

Discussion

41.	Let →a,→b,→c are units vectors satisfying →a×(→b×→c)=(→a×→b)×→c. If →a and →c are not collinear and →a⋅→c=12, then \|→a+→b+→c\| equals
Answer» Let $\to a, \to b, \to c$ are units vectors satisfying $\to a \times (\to b \times \to c) = (\to a \times \to b) \times \to c .$ If $\to a$ and $\to c$ are not collinear and $\to a \cdot \to c = \frac{1}{2},$ then $\| \to a + \to b + \to c \|$ equals

Discussion

42.	The number of solution of the pair of equations 2sin$-cos2$=0 , 2cos$-3sin$=0 in the interval [0,360] is _______ 1) 0 2) 1 3) 2 4) 4
Answer» The number of solution of the pair of equations 2sin$-cos2$=0 , 2cos$-3sin$=0 in the interval [0,360] is _______ 1) 0 2) 1 3) 2 4) 4

Discussion

43.	If the cartesian form of a line is 3−x5=y+47=2z−64, write the vector equation for the line.
Answer» If the cartesian form of a line is $\frac{3 - x}{5} = \frac{y + 4}{7} = \frac{2 z - 6}{4}$ , write the vector equation for the line.

Discussion

44.	The sum of digits of the result of the subtraction 1099 – 99 is 872 . 873. 874. 876
Answer» The sum of digits of the result of the subtraction 10^{99 – 99 is 872 . 873. 874. 876}

Discussion

45.	5 countries president and prime minister went for summit. If all 5 prime minister shake hand to president at random, in how many ways they can shake hand if none of the same country PM shake hand to that country president.
Answer» 5 countries president and prime minister went for summit. If all 5 prime minister shake hand to president at random, in how many ways they can shake hand if none of the same country PM shake hand to that country president.

Discussion

46.	35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R ,then h(x) is symmetric about
Answer» 35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R ,then h(x) is symmetric about

Discussion

47.	limx→0atanx−asinxtanx−sinx is equal to (a>0)
Answer» $l i m x \to 0 \frac{a^{t a n x} - a^{s i n x}}{t a n x - s i n x}$ is equal to (a>0)

Discussion

48.	If fn(θ)=cosθ2+cos2θ+cos7θ2+⋯+cos(3n−2)θ2sinθ2+sin2θ+sin7θ2+⋯+sin(3n−2)θ2, then which among the following is (are) CORRECT?
Answer» If $f_{n} (θ) = \frac{cos \frac{θ}{2} + cos 2 θ + cos \frac{7 θ}{2} + \dots + cos \frac{(3 n - 2) θ}{2}}{sin \frac{θ}{2} + sin 2 θ + sin \frac{7 θ}{2} + \dots + sin \frac{(3 n - 2) θ}{2}},$ then which among the following is (are) CORRECT?

Discussion

49.	The solution of the differential equation dydx=sec x (sec x+tan x) is
Answer» The solution of the differential equation $\frac{d y}{d x} = s e c x (s e c x + t a n x)$ is

49.

The solution of the differential equation dydx=sec x (sec x+tan x) is

Answer»

The solution of the differential equation $\frac{d y}{d x} = s e c x (s e c x + t a n x)$ is

Discussion

50.	Solve 1≤x-2≤3 [NCERT EXEMPLAR]
Answer» Solve $1 \leq \|x - 2\| \leq 3$ [NCERT EXEMPLAR]

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

x217·阿r2-1

equals

21. The function f:R-R which is defined as f(X) = (x-1)(x-2)(x-3) is 1) One-one but not onto 2) Onto but not one-one 3)Both one-one and onto 4) Neither one-one nor onto

Help James find the value of "A" in the given equation:223÷23=A

Let f:R→R be a differentiable function such that f(x)=x2+x∫0e−tf(x−t)dt. Then, the value of 1∫0f(x)dx is

Find the value of b ϵR such that x2+bx−1=0,x2+x+b=0 have a common root.

Evaluate the following definete integrals as limit of sums. ∫14(x2−x)dx.

{\operatorname{sin}^{-1}(\operatorname{sin}8)>x^2-6x holds if }}{ (1) }(-\sqrt{1+3π},\sqrt{1+3π})}{ (2) }(3-\sqrt{1+3π},3+\sqrt{1+3π})}{ (3) }(3-\sqrt{1-3π},3+\sqrt{1-3π})}{ (4) }(0,3-\sqrt{1-3π})

The coefficient of x12in(x3+x4+x5+x6.....)3 is

The number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes is

The equation of the hyperbola whose directrix is x+2y=1, focus (2,1) and eccentricity 2 is

Find the value of m such that roots of the quadratic equation x2−(m−3)x+m=0 (m∈R) are positive

The area of the bounded by the curve y = sinx, x-axis and between x = 0 and x = 2π is _______________.

Range of rational expression y=x2−x+4x2+x+4, x∈R is

Examine the continuity of -- where -- is defined by f(x) {sin x−cos x, if x≠0−1, if x=0.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π=227)

If a 6 digit number is made using all the digits 1,2,4,5,7,8, then the position of number ′′541782′′ when all numbers formed are arranged in ascending order is

3. ax + bycos y

If f(x)=x(x+1)/e^x on the closed interval [-1,0] . Then find the value of c using Rolle's Theorem:Options : (a) (1-√3)/2 (b) (1-√3)/4(c) (1-√5)/2(d) (1-√5)/4

5. J2cos 2x dix

If cosθ−sinθ=15, where 0&lt;θ&lt;π2, then the value of 5(sinθ+cosθ) is

The medians of a right angles triangle are 3 and 4. Then, is area is?

If F= 2/sin theta + cos theta, then the minimum value of F out of the following options is1. 12. 1/√23. 3/√24. √2

If f(x)=∫2sin6x−5sin4x+10sin2x2cos5x−3cos3x+7cosxdx,f(0)=1, then which of the following option(s) is/are correct ?

Find the roots of the quadratic equation 2x2+7x+52=0.

Solve the equation x-7=-2 and check the result.

If [.]denotes G.I F, ∫2π0[|sin x|−|cos x|]dx=

If , find the values of x and y .

Let ¯¯bz+b¯¯¯z=c,b≠0 be a line in the complex plane. If a point z1 is the reflection of a point z2 through the line, then c is

limx→0(3x+|x|7x−5|x|)=___

If A=⎡⎢⎣123456710⎤⎥⎦,B=⎡⎢⎣100030045⎤⎥⎦, then Tr(AB) is

What is the rank of the word paris as in a dictionary. .?

Let P be the plane, which contains the line of intersection of the planes, x+y+z−6=0 and 2x+3y+z+5=0 and it is perpendicular to the xy-plane. Then the distance of the point (0,0,256) from P is equal to :

Give examples of two functions f : N → Z and g : Z → Z such that g o f is injective but g is not injective. (Hint: Consider f ( x ) = x and g ( x ) = )

If θ1 and θ2 be respectively the smallest and the largest values of θ in (0,2π)−{π} which satisfy the equation, 2cot2θ−5sinθ+4=0, then θ2∫θ1cos23θ dθ is equal to :

Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin2x−cosx,x ϵ(0,π)

10 men and 6 women are to be seated in a row so that no two women sit together. the number of ways they can be seated is

A(α,β)=⎛⎜⎝cosαsinα0−sinαcosα000eβ⎞⎟⎠⇒[A(α,β)]−1=

Let h(x)=tan2{2sin−1(cos(sin−13x))+2cos−1(sin(cos−13x))3}; where x∈[−13,13], then the value of 10∑r=3h(1r2)=

∫2π0x In(3+cosx3−cosx)dx=___

Let →a,→b,→c are units vectors satisfying →a×(→b×→c)=(→a×→b)×→c. If →a and →c are not collinear and →a⋅→c=12, then |→a+→b+→c| equals

The number of solution of the pair of equations 2sin$-cos2$=0 , 2cos$-3sin$=0 in the interval [0,360] is _______ 1) 0 2) 1 3) 2 4) 4

If the cartesian form of a line is 3−x5=y+47=2z−64, write the vector equation for the line.

The sum of digits of the result of the subtraction 1099 – 99 is 872 . 873. 874. 876 ​​

5 countries president and prime minister went for summit. If all 5 prime minister shake hand to president at random, in how many ways they can shake hand if none of the same country PM shake hand to that country president.

35. Let h(x) = f(x)-1 . If f(x)+f(1-x) =2 for all x benlongs to R ,then h(x) is symmetric about

limx→0atanx−asinxtanx−sinx is equal to (a>0)

If fn(θ)=cosθ2+cos2θ+cos7θ2+⋯+cos(3n−2)θ2sinθ2+sin2θ+sin7θ2+⋯+sin(3n−2)θ2, then which among the following is (are) CORRECT?

The solution of the differential equation dydx=sec x (sec x+tan x) is

Solve 1≤x-2≤3 [NCERT EXEMPLAR]

If cosθ−sinθ=15, where 0<θ<π2, then the value of 5(sinθ+cosθ) is

The sum of digits of the result of the subtraction 1099 – 99 is 872 . 873. 874. 876