43030 + Interview Questions in Mathematics

1.	Q.If the sum of two consecutive numbers 93 and one of them is x then other number is 93-x. (TRUE/FALSE)
Answer» Q.If the sum of two consecutive numbers 93 and one of them is x then other number is 93-x. (TRUE/FALSE)

1.

Q.If the sum of two consecutive numbers 93 and one of them is x then other number is 93-x. (TRUE/FALSE)

Answer»

Q.If the sum of two consecutive numbers 93 and one of them is x then other number is

93-x. (TRUE/FALSE)

2.	Let f(x)=⎧⎨⎩sinx,x≤0x2+l,0<x<1mx+3,1≤x≤3. If both limx→0f(x) and limx→1f(x) exist, then the value of limx→5(lx2+mx+17) is equal to
Answer» Let $f (x) = ⎧ ⎨ ⎩ \begin{matrix} sin x, & x \leq 0 x^{2} + l, & 0 < x < 1 m x + 3, & 1 \leq x \leq 3 \end{matrix}$ . If both $lim x \to 0 f (x)$ and $lim x \to 1 f (x)$ exist, then the value of $lim x \to 5 (l x^{2} + m x + 17)$ is equal to

Discussion

3.	Find the area between the curves y = x and y = x 2
Answer» Find the area between the curves y = x and y = x 2

Discussion

4.	Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6
Answer» Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6

Discussion

5.	∫(cos2x−cos2θcosx−cosθ)dx is equal to{θ is a constant}
Answer» $\int (\frac{cos 2 x - cos 2 θ}{cos x - cos θ}) d x$ is equal to ${θ is a constant}$

Discussion

6.	If a,b,c,n are rational numbers such that 1} n is not a perfect cube of a rational number .2} a + bn ^1\3 + cn ^ 2\3 = 0 , then prove that a=b=c =0
Answer» If a,b,c,n are rational numbers such that 1} n is not a perfect cube of a rational number . 2} a + bn ^1\3 + cn ^ 2\3 = 0 , then prove that a=b=c =0

Discussion

7.	Consider the grammar S→(S)\|aLet the number of states in SLR (1), LR (1) and LALR (1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good
Answer» Consider the grammar $S \to (S) \| a$ Let the number of states in SLR (1), LR (1) and LALR (1) parsers for the grammar be $n_{1}, n_{2} and n_{3}$ respectively. The following relationship holds good

Discussion

8.	The half of the chapter of linear inequalities do not present in a byju's?
Answer» The half of the chapter of linear inequalities do not present in a byju's?

Discussion

9.	Foot of perpendicular drawn from the origin to the plane 2x–3y+4z=29 is ____
Answer» Foot of perpendicular drawn from the origin to the plane $2 x - 3 y + 4 z = 29$ is ____

Discussion

10.	32. Find graphically the coordinates of the vertices of triangle whose sides have the equations Y=x-3 , 2y = x-4 and x-4 =0
Answer» 32. Find graphically the coordinates of the vertices of triangle whose sides have the equations Y=x-3 , 2y = x-4 and x-4 =0

Discussion

11.	If line x+y=3 is a tangent to the ellipse with foci at (4,3) and (6,k) at point (1,2), then the value of k is
Answer» If line $x + y = 3$ is a tangent to the ellipse with foci at $(4, 3)$ and $(6, k)$ at point $(1, 2),$ then the value of $k$ is

Discussion

12.	Find the equation of the tangent to the circle x² + y² - 2ax - 2ay + a² = 0 which makes with the coordinate axes a triangle of area a².
Answer» Find the equation of the tangent to the circle x² + y² - 2ax - 2ay + a² = 0 which makes with the coordinate axes a triangle of area a².

Discussion

13.	The equation of the plane mid-parallel to the planes 2x−3y+6z−7=0 and 2x−3y+6z+7=0 is
Answer» The equation of the plane mid-parallel to the planes $2 x - 3 y + 6 z - 7 = 0$ and $2 x - 3 y + 6 z + 7 = 0$ is

Discussion

14.	Let A1 be the rea of the region bounded by the curve y=sinx,y=cosx and y−axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y=sinx,y=cosx,x−axis and x=π2 in the first quadrant. Then,
Answer» Let $A_{1}$ be the rea of the region bounded by the curve $y = sin x, y = cos x$ and $y -$ axis in the first quadrant. Also, let $A_{2}$ be the area of the region bounded by the curves $y = sin x, y = cos x, x -$ axis and $x = \frac{π}{2}$ in the first quadrant. Then,

Discussion

15.	A tangent is drawn to parabola y2−4x+4=0 at a point P which cuts the directrix at the point Q. If a point R is such that it divides QP externally in ratio 1:2, then the locus of point R is
Answer» A tangent is drawn to parabola $y^{2} - 4 x + 4 = 0$ at a point $P$ which cuts the directrix at the point $Q$ . If a point $R$ is such that it divides $Q P$ externally in ratio $1 : 2$ , then the locus of point $R$ is

Discussion

16.	A circle passes through (0, 0) and (1, 0) and touches the circle x2+y2=9, then the centre of circle is
Answer» A circle passes through (0, 0) and (1, 0) and touches the circle $x^{2} + y^{2} = 9$ , then the centre of circle is

Discussion

17.	If a coin be tossed n times then the probability that the head comes odd times is
Answer» If a coin be tossed $n$ times then the probability that the head comes odd times is

Discussion

18.	Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Answer» Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Discussion

19.	sin (T-x)15, lim
Answer» sin (T-x)15, lim

Discussion

20.	Dimension of w(omega) and k in sin(wt-k).
Answer» Dimension of w(omega) and k in sin(wt-k).

Discussion

21.	6 married couples are present in a room. If 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is?
Answer» 6 married couples are present in a room. If 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is?

Discussion

22.	A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0,0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is
Answer» A chord $M P$ parallel to the latus rectum of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ with centre at $O (0, 0)$ intersects the auxiliary circle at $Q$ . Then the locus of the point of intersection of normals at $P$ and $Q$ to the respective curve is

Discussion

23.	If the system of linear equations x+y+z=5x+2y+3z=9x+3y+αz=βhas infinitely many solutions, then β−α equals:
Answer» If the system of linear equations $x + y + z = 5$ $x + 2 y + 3 z = 9$ $x + 3 y + α z = β$ has infinitely many solutions, then $β - α$ equals:

Discussion

24.	37. What is the difference between probability of At least & at most of an event.
Answer» 37. What is the difference between probability of At least & at most of an event.

Discussion

25.	limx→∞[(x2+1x)e1/x−x−x2] is equal to
Answer» $lim x \to \infty [(x^{2} + \frac{1}{x}) e^{1 / x} - x - x^{2}]$ is equal to

Discussion

26.	If tan3x+tanx=2tan2x then x is equal to (n∈Z)
Answer» If $tan 3 x + tan x = 2 tan 2 x$ then $x$ is equal to $(n \in Z)$

Discussion

27.	29. (x +secx) (x -tanx)
Answer» 29. (x +secx) (x -tanx)

Discussion

28.	Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available?
Answer» Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff, if five different flags are available?

Discussion

29.	A particle executes SHM between x = - A and x = + A. The time taken by it to go from 0 to A2 is T1 and to go from A2 to A is T2. Then
Answer» A particle executes SHM between x = - A and x = + A. The time taken by it to go from 0 to $\frac{A}{2}$ is $T_{1}$ and to go from $\frac{A}{2}$ to A is $T_{2}$ . Then

Discussion

30.	For how many values of k does the following system of equations have at-least one solution? x+y=1; kx+y=3; x+ky=5;
Answer» For how many values of k does the following system of equations have at-least one solution? x+y=1; kx+y=3; x+ky=5;

Discussion

31.	If An=1+q+q2+q3+⋯+qn and Bn=1+(q+12)+(q+12)2+⋯+(q+12)n,q≠1, then n+1C1+ n+1C2⋅A1+ n+1C3⋅A2+⋯+ n+1Cn+1⋅An=
Answer» If $A_{n} = 1 + q + q^{2} + q^{3} + \dots + q^{n}$ and $B_{n} = 1 + (\frac{q + 1}{2}) + {(\frac{q + 1}{2})}^{2} + \dots + {(\frac{q + 1}{2})}^{n}, q \neq 1$ , then $^{n + 1} C_{1} +^{n + 1} C_{2} \cdot A_{1} +^{n + 1} C_{3} \cdot A_{2} + \dots +^{n + 1} C_{n + 1} \cdot A_{n} =$

Discussion

32.	If the equation of a plane P, passing through the intersection of the planes, x+4y−z+7=0 and 3x+y+5z=8 is ax+by+6z=15 for some a,b∈R, then the distance of the point (3,2,−1) from the plane P is
Answer» If the equation of a plane $P$ , passing through the intersection of the planes, $x + 4 y - z + 7 = 0$ and $3 x + y + 5 z = 8$ is $a x + b y + 6 z = 15$ for some $a, b \in R,$ then the distance of the point $(3, 2, - 1)$ from the plane $P$ is

Discussion

33.	If n (A) = 20, n (B) = 28 and n (A∪B) = 36 then n (A ∩ B) = ?
Answer» If n (A) = 20, n (B) = 28 and n (A $\cup$ B) = 36 then n (A $\cap$ B) = ?

Discussion

34.	The number of words that can be formed from the letters of word ′USAINBOLT′ whose middle place is a vowel, start with a vowel and end with a consonant is
Answer» The number of words that can be formed from the letters of word $^{'} U S A I N B O L T^{'}$ whose middle place is a vowel, start with a vowel and end with a consonant is

Discussion

35.	Find the range of the solution of given inequalities. x5−2> 2(x+3)3
Answer» Find the range of the solution of given inequalities. $\frac{x}{5} - 2 > \frac{2 (x + 3)}{3}$

35.

Find the range of the solution of given inequalities. x5−2> 2(x+3)3

Answer»

Find the range of the solution of given inequalities.

$\frac{x}{5} - 2 > \frac{2 (x + 3)}{3}$

Discussion

36.	If a→, b→, c→ are non-coplanar vectors, then vectors a→-b→, b→-c→ and c→-a→ from a parallelopiped whose volume is ______________.
Answer» If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors, then vectors $\vec{a} - \vec{b}, \vec{b} - \vec{c} and \vec{c} - \vec{a}$ from a parallelopiped whose volume is ______________.

Discussion

37.	A pair of perpendicular straight lines passing through the origin also passes through the points of intersection of the curve x2+y2=4 with the line x+y=a, then value(s) of a can be
Answer» A pair of perpendicular straight lines passing through the origin also passes through the points of intersection of the curve $x^{2} + y^{2} = 4$ with the line $x + y = a$ , then value(s) of $a$ can be

Discussion

38.	Define motif
Answer» Define motif

Discussion

39.	Which of the following is a monotonically decreasing function?
Answer» Which of the following is a monotonically decreasing function?

Discussion

40.	If the distance between parallel planes 2x−y+3z−4=0 and 6x−3y+9z+13=0 is D. Then the value of 126D2=
Answer» If the distance between parallel planes $2 x - y + 3 z - 4 = 0$ and $6 x - 3 y + 9 z + 13 = 0$ is $D$ . Then the value of $126 D^{2} =$

Discussion

41.	For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation. y=cosx +C and y'+sinx=0
Answer» For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation. y=cosx +C and y'+sinx=0

Discussion

42.	Find the coordinates of the point P where the line through A (3,-4,-5) and B (2,-3,1) crosses the plane passing through three points L(2,2,1), M(3,0,1) and N(4,-1,0). Also, find the ratio in which P diveides the line segment AB.
Answer» Find the coordinates of the point P where the line through A (3, $-$ 4, $-$ 5) and B (2, $-$ 3,1) crosses the plane passing through three points L(2,2,1), M(3,0,1) and N(4, $-$ 1,0). Also, find the ratio in which P diveides the line segment AB.

Discussion

43.	The sum of the series 1.2.3 + 2.3.4 + 3.4.5 + .......to n terms is
Answer» The sum of the series 1.2.3 + 2.3.4 + 3.4.5 + .......to n terms is

Discussion

44.	The domain of the function f(x)=sin−1(\|x\|+5x2+1) is (−∞,−a]∪[a,∞). Then a is equal to :
Answer» The domain of the function $f (x) = {sin}^{- 1} (\frac{\| x \| + 5}{x^{2} + 1})$ is $(- \infty, - a] \cup [a, \infty)$ . Then $a$ is equal to :

Discussion

45.	sin−1(1−x)−2sin−1x=π2, then x is equal to
Answer» ${sin}^{- 1} (1 - x) - 2 {sin}^{- 1} x = \frac{π}{2},$ then $x$ is equal to

Discussion

46.	3. The no. Of terms in (1+x)101 (1+x2-x)*100is
Answer» 3. The no. Of terms in (1+x)101 (1+x2-x)*100is

Discussion

47.	If cos(α+β)sin(γ+δ)=cos(α−β)sin(γ−δ),provethatcotα cotβ cotγ=cotδ
Answer» If $c o s (α + β) s i n (γ + δ) = c o s (α - β) s i n (γ - δ), p r o v e t h a t c o t α c o t β c o t γ = c o t δ$

Discussion

48.	∫√1−√x√1+√xdx is equal to(where C,C1 are integration constant)
Answer» $\int \frac{\sqrt{1 - \sqrt{x}}}{\sqrt{1 + \sqrt{x}}} d x$ is equal to (where $C, C_{1}$ are integration constant)

Discussion

49.	The domain of the function f(x) = x + [x] is __________ .
Answer» The domain of the function f(x) = x + [x] is __________ .

Discussion

50.	The family of curves which satisfies the differential equation y exydx=(x exy+y2)dy, (y≠0) is (where ′C′ is the constant of integration )
Answer» The family of curves which satisfies the differential equation $y e^{\frac{x}{y}} d x = (x e^{\frac{x}{y}} + y^{2}) d y, (y \neq 0)$ is (where $^{'} C^{'}$ is the constant of integration )

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Q.If the sum of two consecutive numbers 93 and one of them is x then other number is 93-x. (TRUE/FALSE)

Let f(x)=⎧⎨⎩sinx,x≤0x2+l,0&lt;x&lt;1mx+3,1≤x≤3. If both limx→0f(x) and limx→1f(x) exist, then the value of limx→5(lx2+mx+17) is equal to

Find the area between the curves y = x and y = x 2

Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6

∫(cos2x−cos2θcosx−cosθ)dx is equal to{θ is a constant}

If a,b,c,n are rational numbers such that 1} n is not a perfect cube of a rational number .2} a + bn ^1\3 + cn ^ 2\3 = 0 , then prove that a=b=c =0

Consider the grammar S→(S)|aLet the number of states in SLR (1), LR (1) and LALR (1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good

The half of the chapter of linear inequalities do not present in a byju's?

Foot of perpendicular drawn from the origin to the plane 2x–3y+4z=29 is ____

32. Find graphically the coordinates of the vertices of triangle whose sides have the equations Y=x-3 , 2y = x-4 and x-4 =0

If line x+y=3 is a tangent to the ellipse with foci at (4,3) and (6,k) at point (1,2), then the value of k is

Find the equation of the tangent to the circle x² + y² - 2ax - 2ay + a² = 0 which makes with the coordinate axes a triangle of area a².

The equation of the plane mid-parallel to the planes 2x−3y+6z−7=0 and 2x−3y+6z+7=0 is

Let A1 be the rea of the region bounded by the curve y=sinx,y=cosx and y−axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y=sinx,y=cosx,x−axis and x=π2 in the first quadrant. Then,

A tangent is drawn to parabola y2−4x+4=0 at a point P which cuts the directrix at the point Q. If a point R is such that it divides QP externally in ratio 1:2, then the locus of point R is

A circle passes through (0, 0) and (1, 0) and touches the circle x2+y2=9, then the centre of circle is

If a coin be tossed n times then the probability that the head comes odd times is

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

sin (T-x)15, lim

Dimension of w(omega) and k in sin(wt-k).

6 married couples are present in a room. If 4 people are chosen at random, then the chance that exactly one married couple is among the 4 is?

A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0,0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

If the system of linear equations x+y+z=5x+2y+3z=9x+3y+αz=βhas infinitely many solutions, then β−α equals:

37. What is the difference between probability of At least & at most of an event.

limx→∞[(x2+1x)e1/x−x−x2] is equal to

If tan3x+tanx=2tan2x then x is equal to (n∈Z)

29. (x +secx) (x -tanx)

Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available?

A particle executes SHM between x = - A and x = + A. The time taken by it to go from 0 to A2 is T1 and to go from A2 to A is T2. Then

For how many values of k does the following system of equations have at-least one solution? x+y=1; kx+y=3; x+ky=5;

If An=1+q+q2+q3+⋯+qn and Bn=1+(q+12)+(q+12)2+⋯+(q+12)n,q≠1, then n+1C1+ n+1C2⋅A1+ n+1C3⋅A2+⋯+ n+1Cn+1⋅An=

If the equation of a plane P, passing through the intersection of the planes, x+4y−z+7=0 and 3x+y+5z=8 is ax+by+6z=15 for some a,b∈R, then the distance of the point (3,2,−1) from the plane P is

If n (A) = 20, n (B) = 28 and n (A∪B) = 36 then n (A ∩ B) = ?

The number of words that can be formed from the letters of word ′USAINBOLT′ whose middle place is a vowel, start with a vowel and end with a consonant is

Find the range of the solution of given inequalities. x5−2&gt; 2(x+3)3

If a→, b→, c→ are non-coplanar vectors, then vectors a→-b→, b→-c→ and c→-a→ from a parallelopiped whose volume is ______________.

A pair of perpendicular straight lines passing through the origin also passes through the points of intersection of the curve x2+y2=4 with the line x+y=a, then value(s) of a can be

Define motif

Which of the following is a monotonically decreasing function?

If the distance between parallel planes 2x−y+3z−4=0 and 6x−3y+9z+13=0 is D. Then the value of 126D2=

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation. y=cosx +C and y'+sinx=0

Find the coordinates of the point P where the line through A (3,-4,-5) and B (2,-3,1) crosses the plane passing through three points L(2,2,1), M(3,0,1) and N(4,-1,0). Also, find the ratio in which P diveides the line segment AB.

The sum of the series 1.2.3 + 2.3.4 + 3.4.5 + .......to n terms is

The domain of the function f(x)=sin−1(|x|+5x2+1) is (−∞,−a]∪[a,∞). Then a is equal to :

sin−1(1−x)−2sin−1x=π2, then x is equal to

3. The no. Of terms in (1+x)*101 (1+x*2-x)*100is

If cos(α+β)sin(γ+δ)=cos(α−β)sin(γ−δ),provethatcotα cotβ cotγ=cotδ

∫√1−√x√1+√xdx is equal to(where C,C1 are integration constant)

The domain of the function f(x) = x + [x] is __________ .

The family of curves which satisfies the differential equation y exydx=(x exy+y2)dy, (y≠0) is (where ′C′ is the constant of integration )

Let f(x)=⎧⎨⎩sinx,x≤0x2+l,0<x<1mx+3,1≤x≤3. If both limx→0f(x) and limx→1f(x) exist, then the value of limx→5(lx2+mx+17) is equal to

Find the range of the solution of given inequalities. x5−2> 2(x+3)3

3. The no. Of terms in (1+x)101 (1+x2-x)*100is