43030 + Interview Questions in Mathematics

1.	Let f : R → R be defined by fx=1x. Then, f is(a) one-one(b) onto(e) bijective(d) not defined
Answer» Let f : R → R be defined by $f (x) = \frac{1}{x} .$ Then, f is (a) one-one (b) onto (e) bijective (d) not defined

Discussion

2.	Find the following integrals. ∫(4e3x+1)dx.
Answer» Find the following integrals. $\int (4 e^{3 x} + 1) d x .$

Discussion

3.	The value of C20+3C21+5C22+⋯ up to 51 terms is equal to( where Cr= 50Cr)
Answer» The value of $C_{0}^{2} + 3 C_{1}^{2} + 5 C_{2}^{2} + \dots$ up to $51$ terms is equal to ( where $C_{r} =^{50} C_{r}$ )

Discussion

4.	Four vertices of a quadrilateral are W(4,2), X(5,0), Y(7,1), and Z(5,4). Choose the incorrect option about the new quadrilateral formed if it is being compared to the given quadrilateral in the following image.
Answer» Four vertices of a quadrilateral are W(4,2), X(5,0), Y(7,1), and Z(5,4). Choose the incorrect option about the new quadrilateral formed if it is being compared to the given quadrilateral in the following image.

Discussion

5.	The coordinates of the point(s) which divide(s) the line segment joining the point (5,−2) and (9,6) in the ratio 3:1, are
Answer» The coordinates of the point(s) which divide(s) the line segment joining the point $(5, - 2)$ and $(9, 6)$ in the ratio $3 : 1,$ are

Discussion

6.	If both sum of roots and product of roots of x2−(λ2−5λ+5)x+(2λ2−3λ−4)=0 are less than 1, then the range of λ is
Answer» If both sum of roots and product of roots of $x^{2} - (λ^{2} - 5 λ + 5) x + (2 λ^{2} - 3 λ - 4) = 0$ are less than $1,$ then the range of $λ$ is

Discussion

7.	Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
Answer» Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

Discussion

8.	When dxy and dx2-y2 have interchangeable values how. Is that dx2-y2 has max probability density
Answer» When dxy and dx2-y2 have interchangeable values how. Is that dx2-y2 has max probability density

Discussion

9.	Find the range of the function f(x) = x²/1+x²
Answer» Find the range of the function f(x) = x²/1+x²

Discussion

10.	General solution of the equation 2sin2x+3cot2x−4sinx−6cotx+5=0 is
Answer» General solution of the equation $2 {sin}^{2} x + 3 {cot}^{2} x - 4 sin x - 6 cot x + 5 = 0$ is

Discussion

11.	Find the value of discriminant for each of the following equations.(1) 2y2-y+2=0(2) 5m2-m=0(3) 5x2-x-5=0
Answer» Find the value of discriminant for each of the following equations. (1) $2 y^{2} - y + 2 = 0$ (2) $5 m^{2} - m = 0$ (3) $\sqrt{5} x^{2} - x - \sqrt{5} = 0$

Discussion

12.	If tan(πsinθ)=cot(πcosθ), then \|cot(θ−π4)\| is
Answer» If $tan (π sin θ) = cot (π cos θ),$ then $\| cot (θ - \frac{π}{4}) \|$ is

Discussion

13.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
Answer» Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Discussion

14.	Let z be a complex no. Such that the imaginary part of z is nonzero & a=z+z+1 is real. Then a cannot take the value
Answer» Let z be a complex no. Such that the imaginary part of z is nonzero & a=z+z+1 is real. Then a cannot take the value

Discussion

15.	If a→ and b→ are two non-zero non-collinear vectors such that a→×b→=1 and a→ . b→=3, then the angle between a→ and b→ is _____________.
Answer» If $\vec{a} and \vec{b}$ are two non-zero non-collinear vectors such that $\|\vec{a} \times \vec{b}\| = 1 and \|\vec{a} . \vec{b}\| = \sqrt{3}$ , then the angle between $\vec{a} and \vec{b}$ is _____________.

Discussion

16.	For x E (0,4π) , the equation sinx + 2cos2x - sin3x = 4 has how many solutions ?
Answer» For x E (0,4π) , the equation sinx + 2cos2x - sin3x = 4 has how many solutions ?

Discussion

17.	The point of inflection for y=f(x)=xex is:
Answer» The point of inflection for $y = f (x) = x e^{x}$ is:

Discussion

18.	Find the equation of the plane passing through the line of intersection of the planes r.(^i+^j+^k)=1 and r.(2^i+3^j−^k)+4=0 and parallel to X-axis.
Answer» Find the equation of the plane passing through the line of intersection of the planes $r . (^i +^j +^k) = 1 a n d r . (2^i + 3^j -^k) + 4 = 0$ and parallel to X-axis.

Discussion

19.	Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain : (i) just one ace (ii) at least one ace?
Answer» Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain : (i) just one ace (ii) at least one ace?

19.

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain : (i) just one ace (ii) at least one ace?

Answer»

Five cards are drawn from a pack of 52 cards.
What is the chance that these 5 will contain :
(i) just one ace

(ii) at least one ace?

Discussion

20.	What is the difference between Magnitude and Direction in quantities?
Answer» What is the difference between Magnitude and Direction in quantities?

Discussion

21.	What is the difference between coplanar and collinear vectors?
Answer» What is the difference between coplanar and collinear vectors?

Discussion

22.	Water is filled into a right inverted conical tank at a constant rate of 3m3/sec, whose semi vertical angle is cos−145. The rate (in m/sec), at which the level of water is rising at the instant when the depth of water in the tank is 4m, is
Answer» Water is filled into a right inverted conical tank at a constant rate of $3 m^{3} /sec,$ whose semi vertical angle is ${cos}^{- 1} \frac{4}{5} .$ The rate $(in m /sec),$ at which the level of water is rising at the instant when the depth of water in the tank is $4 m,$ is

Discussion

23.	If ∫sin2xdxa2+b2sin2x=1b2log\|f(x)\|+C, then the difference of the maximum and minimum value of f(x) is
Answer» If $\int \frac{sin 2 x d x}{a^{2} + b^{2} s i n^{2} x} = \frac{1}{b^{2}} log \| f (x) \| + C$ , then the difference of the maximum and minimum value of $f (x)$ is

Discussion

24.	//Let f: {1, 2, 3} → {1, 2, 3} be a function. If the number of functions g : {1, 2, 3} → fx) = g(x) for atleast onex{1, 2, 3} is k, then (k-10) is equal to
Answer» //Let f: {1, 2, 3} → {1, 2, 3} be a function. If the number of functions g : {1, 2, 3} → fx) = g(x) for atleast onex{1, 2, 3} is k, then (k-10) is equal to

Discussion

25.	If f(x) = sin x - cosx, then f'π6 = ________________________.
Answer» If f(x) = $\|\sin x - \cos x\|, then f' (\frac{π}{6}) =________________________.$

Discussion

26.	The product of two consecutive positive integers is divisible by 2: Is this statement true or false? Give reasons.
Answer» The product of two consecutive positive integers is divisible by 2: Is this statement true or false? Give reasons.

Discussion

27.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
Answer» Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Discussion

28.	1. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the card is : (i) divisible by 3 or 5 (ii) a perfect square number.
Answer» 1. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the card is : (i) divisible by 3 or 5 (ii) a perfect square number.

Discussion

29.	If ax + by = a + b And ax ( 1/a-b + 1/a+b) + by(1/b-a + 1/b+a) = 2a/a+b Find x and y.
Answer» If ax + by = a + b And ax ( 1/a-b + 1/a+b) + by(1/b-a + 1/b+a) = 2a/a+b Find x and y.

Discussion

30.	What is the meaning of 1s^2, 2s^2
Answer» What is the meaning of 1s^2, 2s^2

Discussion

31.	Which of the following is/are function(s)?
Answer» Which of the following is/are function(s)?

Discussion

32.	the value of sin^-1(sin 5)is equal to
Answer» the value of sin^-1(sin 5)is equal to

Discussion

33.	The domain of the function f(x)=√logx2−1x is
Answer» The domain of the function $f (x) = \sqrt{{log}_{x^{2} - 1} x}$ is

Discussion

34.	15. If the numbers of different reflexive relation on a set A is equal to the number of different symmetric relation on set A, then the number of element in A is ?
Answer» 15. If the numbers of different reflexive relation on a set A is equal to the number of different symmetric relation on set A, then the number of element in A is ?

Discussion

35.	Let α, β be such that π<α−β<3π.Ifsin α+sin β=2165 and cos α+cos β=−2765,then the value of cosα−β2 is
Answer» $L e t α, β b e s u c h t h a t π < α - β < 3 π . I f s i n α + s i n β = \frac{21}{65} a n d c o s α + c o s β = - \frac{27}{65}, t h e n t h e v a l u e o f c o s \frac{α - β}{2} i s$

Discussion

36.	Sketch the graphs of the following functions:f(x) = 2 cosec πx
Answer» Sketch the graphs of the following functions: f(x) = 2 cosec πx

Discussion

37.	Find the range of values of x which satisfies −223 ≤ x+13 <313, x∈ R.
Answer» Find the range of values of x which satisfies $- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}, x \in R$ .

Discussion

38.	tan−1(tan5π6)+cos−1(cos13π6)
Answer» $t a n^{- 1} (t a n \frac{5 π}{6}) + c o s^{- 1} (c o s \frac{13 π}{6})$

Discussion

39.	If tanθ=ab, prove that asin 2θ+bcos2θ=b
Answer» If $t a n θ = \frac{a}{b}$ , prove that $a s i n 2 θ + b c o s 2 θ = b$

Discussion

40.	The remainder when }7^{63} is divided by }25 is , explain in detail .}
Answer» The remainder when }7^{63} is divided by }25 is , explain in detail .}

Discussion

41.	If the tangents are drawn to the ellipse x2+2y2=2, then the locus of the mid-point of the intercept made by the tangents between the coordinate-axes is
Answer» If the tangents are drawn to the ellipse $x^{2} + 2 y^{2} = 2$ , then the locus of the mid-point of the intercept made by the tangents between the coordinate-axes is

Discussion

42.	Insert 5 geometric means between 329 and 812.
Answer» Insert 5 geometric means between $\frac{32}{9}$ and $\frac{81}{2}$ .

42.

Insert 5 geometric means between 329 and 812.

Answer»

Insert 5 geometric means between $\frac{32}{9}$ and $\frac{81}{2}$ .

Discussion

43.	If cos θ+√3 sin θ=2,thenθ=
Answer» $I f c o s θ + \sqrt{3} s i n θ = 2, t h e n θ =$

Discussion

44.	On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.5x - 4y + 8 = 07x + 6y - 9 = 0
Answer» On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x - 4y + 8 = 0 7x + 6y - 9 = 0

Discussion

45.	The direction of angle bisector between ¯a and ¯b can be given by ¯a+¯b2
Answer» The direction of angle bisector between $¯ a$ and $¯ b$ can be given by $\frac{¯ a + ¯ b}{2}$

Discussion

46.	what is enomers?
Answer» what is enomers?

Discussion

47.	y = x+sinx is the solution of which of these differential equations?
Answer» $y = x + sinx is the solution of which of these differential equations ?$

Discussion

48.	If the sum of the first 40 term of the series 3+4+8+9+13+14+18+19+⋯ is 102(m), then the value of m is
Answer» If the sum of the first $40$ term of the series $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \dots$ is $102 (m)$ , then the value of $m$ is

Discussion

49.	If P(4,125) is a point on the ellipse such that the normal at it meets the major axis of ellipse x225+y216=1 at Q, and S, S′ are the focii of the given ellipse, where S′ lies on positive x-axis, then the ratio S′Q:SQ is √ab. The value of a+b is
Answer» If $P (4, \frac{12}{5})$ is a point on the ellipse such that the normal at it meets the major axis of ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ at $Q$ , and $S, S^{'}$ are the focii of the given ellipse, where $S^{'}$ lies on positive x-axis, then the ratio $S^{'} Q : S Q$ is $\frac{\sqrt{a}}{b}$ . The value of $a + b$ is

Discussion

50.	If in a triangle ABC, r1=2, r2=3 and r3=6, then a=
Answer» If in a triangle $A B C$ , $r_{1} = 2, r_{2} = 3$ and $r_{3} = 6$ , then $a =$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let f : R → R be defined by fx=1x. Then, f is(a) one-one(b) onto(e) bijective(d) not defined

Find the following integrals. ∫(4e3x+1)dx.

The value of C20+3C21+5C22+⋯ up to 51 terms is equal to( where Cr= 50Cr)

Four vertices of a quadrilateral are W(4,2), X(5,0), Y(7,1), and Z(5,4). Choose the incorrect option about the new quadrilateral formed if it is being compared to the given quadrilateral in the following image.

The coordinates of the point(s) which divide(s) the line segment joining the point (5,−2) and (9,6) in the ratio 3:1, are

If both sum of roots and product of roots of x2−(λ2−5λ+5)x+(2λ2−3λ−4)=0 are less than 1, then the range of λ is

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

When dxy and dx2-y2 have interchangeable values how. Is that dx2-y2 has max probability density

Find the range of the function f(x) = x²/1+x²

General solution of the equation 2sin2x+3cot2x−4sinx−6cotx+5=0 is

Find the value of discriminant for each of the following equations.(1) 2y2-y+2=0(2) 5m2-m=0(3) 5x2-x-5=0

If tan(πsinθ)=cot(πcosθ), then |cot(θ−π4)| is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Let z be a complex no. Such that the imaginary part of z is nonzero & a=z+z+1 is real. Then a cannot take the value

If a→ and b→ are two non-zero non-collinear vectors such that a→×b→=1 and a→ . b→=3, then the angle between a→ and b→ is _____________.

For x E (0,4π) , the equation sinx + 2cos2x - sin3x = 4 has how many solutions ?

The point of inflection for y=f(x)=xex is:

Find the equation of the plane passing through the line of intersection of the planes r.(^i+^j+^k)=1 and r.(2^i+3^j−^k)+4=0 and parallel to X-axis.

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain : (i) just one ace (ii) at least one ace?

What is the difference between Magnitude and Direction in quantities?

What is the difference between coplanar and collinear vectors?

Water is filled into a right inverted conical tank at a constant rate of 3m3/sec, whose semi vertical angle is cos−145. The rate (in m/sec), at which the level of water is rising at the instant when the depth of water in the tank is 4m, is

If ∫sin2xdxa2+b2sin2x=1b2log|f(x)|+C, then the difference of the maximum and minimum value of f(x) is

//Let f: {1, 2, 3} → {1, 2, 3} be a function. If the number of functions g : {1, 2, 3} → fx) = g(x) for atleast onex{1, 2, 3} is k, then (k-10) is equal to

​If f(x) = sin x - cosx, then f'π6 = ________________________.

The product of two consecutive positive integers is divisible by 2: Is this statement true or false? Give reasons.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

1. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the card is : (i) divisible by 3 or 5 (ii) a perfect square number.

If ax + by = a + b And ax ( 1/a-b + 1/a+b) + by(1/b-a + 1/b+a) = 2a/a+b Find x and y.

What is the meaning of 1s^2, 2s^2

Which of the following is/are function(s)?

the value of sin^-1(sin 5)is equal to

The domain of the function f(x)=√logx2−1x is

15. If the numbers of different reflexive relation on a set A is equal to the number of different symmetric relation on set A, then the number of element in A is ?

Let α, β be such that π&lt;α−β&lt;3π.Ifsin α+sin β=2165 and cos α+cos β=−2765,then the value of cosα−β2 is

Sketch the graphs of the following functions:f(x) = 2 cosec πx

Find the range of values of x which satisfies −223 ≤ x+13 &lt;313, x∈ R.

tan−1(tan5π6)+cos−1(cos13π6)

If tanθ=ab, prove that asin 2θ+bcos2θ=b

The remainder when }7^{63} is divided by }25 is , explain in detail .}

If the tangents are drawn to the ellipse x2+2y2=2, then the locus of the mid-point of the intercept made by the tangents between the coordinate-axes is

Insert 5 geometric means between 329 and 812.

If cos θ+√3 sin θ=2,thenθ=

On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.5x - 4y + 8 = 07x + 6y - 9 = 0

The direction of angle bisector between ¯a and ¯b can be given by ¯a+¯b2

what is enomers?

y = x+sinx is the solution of which of these differential equations?

If the sum of the first 40 term of the series 3+4+8+9+13+14+18+19+⋯ is 102(m), then the value of m is

If P(4,125) is a point on the ellipse such that the normal at it meets the major axis of ellipse x225+y216=1 at Q, and S, S′ are the focii of the given ellipse, where S′ lies on positive x-axis, then the ratio S′Q:SQ is √ab. The value of a+b is

If in a triangle ABC, r1=2, r2=3 and r3=6, then a=

If f(x) = sin x - cosx, then f'π6 = ________________________.

Let α, β be such that π<α−β<3π.Ifsin α+sin β=2165 and cos α+cos β=−2765,then the value of cosα−β2 is

Find the range of values of x which satisfies −223 ≤ x+13 <313, x∈ R.