43030 + Interview Questions in Mathematics

1.	The integral ∫14√(x−1)3(x+2)5dx is equal to:(where C is a constant of integration)
Answer» The integral $\int \frac{1}{\sqrt[4]{(x - 1)^{3} (x + 2)^{5}}} d x$ is equal to: (where $C$ is a constant of integration)

Discussion

2.	Equation of the circle having centre at (3,−1) and making an intercept of length 6 units on the line 2x−5y+18=0, is
Answer» Equation of the circle having centre at $(3, - 1)$ and making an intercept of length $6$ units on the line $2 x - 5 y + 18 = 0$ , is

Discussion

3.	A chord ax+y=1 subtends 90∘ at the centre of the circle x2+y2=32. Then the value of a is
Answer» A chord $a x + y = 1$ subtends $90^{\circ}$ at the centre of the circle $x^{2} + y^{2} = \frac{3}{2} .$ Then the value of $a$ is

Discussion

4.	The rectangular component of a vector are (2,2) .the corresponding rectangular component of another vector (1,3) find the angle between two vectors
Answer» The rectangular component of a vector are (2,2) .the corresponding rectangular component of another vector (1,3) find the angle between two vectors

Discussion

5.	what is the method(steps) for finding out the domain and range of a given function
Answer» what is the method(steps) for finding out the domain and range of a given function

Discussion

6.	What's the meaning of Quantised?
Answer» What's the meaning of Quantised?

Discussion

7.	A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :
Answer» A hyperbola has its centre at the origin, passes through the point $(4, 2)$ and has transverse axis of length $4$ along the $x$ -axis. Then the eccentricity of the hyperbola is :

Discussion

8.	Write the first five terms of the sequences whose nth term is
Answer» Write the first five terms of the sequences whose n^th term is

Discussion

9.	x>6 can be represented on number line by
Answer» $x > 6$ can be represented on number line by

Discussion

10.	The shortest distance between the lines →r=3→i+5→j+7→k+λ(→i+2→j+→k) and →r=−→i−→j−→k+μ(7→i−6→j+→k) is
Answer» The shortest distance between the lines $\to r = 3 \to i + 5 \to j + 7 \to k + λ (\to i + 2 \to j + \to k) a n d \to r = - \to i - \to j - \to k + μ (7 \to i - 6 \to j + \to k) i s$

Discussion

11.	The range of values of n for which one root of the equation x2−(n+1)x+n2+n−8=0 is greater than 2 and the other less than 2
Answer» The range of values of $n$ for which one root of the equation $x^{2} - (n + 1) x + n^{2} + n - 8 = 0$ is greater than $2$ and the other less than $2$

Discussion

12.	If A = { a , b, c, d, e}, B = { c, d, e, f }, C = {b, d}, D = { a , e} then which of the following statements are true and which are false ?( i ) C ⊆ B ( ii ) A ⊆ D ( iii ) D ⊆B ( iv ) D⊆A ( v ) B ⊆A (vi) C ⊆A
Answer» If A = { a , b, c, d, e}, B = { c, d, e, f }, C = {b, d}, D = { a , e} then which of the following statements are true and which are false ? ( i ) C $\subseteq$ B ( ii ) A $\subseteq$ D ( iii ) D $\subseteq$ B ( iv ) D $\subseteq$ A ( v ) B $\subseteq$ A (vi) C $\subseteq$ A

Discussion

13.	The value of cos−1(cos5π3)+sin−1(cos5π3) is
Answer» The value of ${cos}^{- 1} (cos \frac{5 π}{3}) + {sin}^{- 1} (cos \frac{5 π}{3})$ is

Discussion

14.	Solve the following equations using trial and error method:3x – 7 = 5
Answer» Solve the following equations using trial and error method: 3x – 7 = 5

Discussion

15.	The value of the limit limx→0 ax−bxx a > 0, b > 0, is
Answer» The value of the limit $lim x \to 0 \frac{a^{x} - b^{x}}{x}$ a > 0, b > 0, is

Discussion

16.	If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.
Answer» If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

Discussion

17.	10. If z=3-4i then z-3z-3z+99z-95= option A)5 B)6 C)-5 D)-4
Answer» 10. If z=3-4i then z-3z-3z+99z-95= option A)5 B)6 C)-5 D)-4

Discussion

18.	Prove that: tan2 2x-tan2 x1-tan2 2x tan2 x=tan 3x tan x
Answer» Prove that: $\frac{\tan^{2} 2 x - \tan^{2} x}{1 - \tan^{2} 2 x \tan^{2} x} = \tan 3 x \tan x$

Discussion

19.	Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of G.P. is
Answer» Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of G.P. is

Discussion

20.	Prove that (Cos 6x + 6 cos 4x + 15 cos 2x + 10) / (cos5x + 5 cos 3x+ 10 cos x) =2cosx
Answer» Prove that (Cos 6x + 6 cos 4x + 15 cos 2x + 10) / (cos5x + 5 cos 3x+ 10 cos x) =2cosx

Discussion

21.	Vectors A,B and C are such that A.B = 0 and A.C=0. Then the vector parallel to A vector is ?
Answer» Vectors A,B and C are such that A.B = 0 and A.C=0. Then the vector parallel to A vector is ?

Discussion

22.

A weather station recorded the temperatures of a place over a period of 7 days as follows:DayTemperature (in ∘C )Monday 45Tuesday38Wednesday40Thursday42Friday41Saturday37Sunday36Find the probability of a day having a temperature of less than 40 ∘ C.

Answer»

A weather station recorded the temperatures of a place over a period of 7 days as follows:

Day	Temperature (in $^{\circ}$ C )
Monday	45
Tuesday	38
Wednesday	40
Thursday	42
Friday	41
Saturday	37
Sunday	36

Find the probability of a day having a temperature of less than 40

^{\circ}

C.

Discussion

23.	If x lies in the first quadrant and cos x=817, then prove that:cos π6+x+cos π4-x+cos 2π3-x=3-12+122317
Answer» If x lies in the first quadrant and $\cos x = \frac{8}{17}$ , then prove that: $\cos (\frac{π}{6} + x) + \cos (\frac{π}{4} - x) + \cos (\frac{2 π}{3} - x) = (\frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}}) \frac{23}{17}$

Discussion

24.	If the inequality \operatorname{sin^2x+a\operatorname{cosx+a^2>1+\operatorname{cosx holds for any x∈ R, then the largest negative integral value of a is
Answer» If the inequality \operatorname{sin^2x+a\operatorname{cosx+a^2>1+\operatorname{cosx holds for any x∈ R, then the largest negative integral value of a is

Discussion

25.	The angle between two diagonals of a cube will be [MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]
Answer» The angle between two diagonals of a cube will be [MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]

Discussion

26.	13. If y=cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx,then dy/dx is
Answer» 13. If y=cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx,then dy/dx is

Discussion

27.	If the length of subnormal is equal to the length of subtangent at a point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at A and B, then twice the value of maximum area of the triangle OAB, where O is origin is:
Answer» If the length of subnormal is equal to the length of subtangent at a point $(3, 4)$ on the curve $y = f (x)$ and the tangent at $(3, 4)$ to $y = f (x)$ meets the coordinate axes at $A$ and $B$ , then twice the value of maximum area of the triangle $O A B$ , where $O$ is origin is:

Discussion

28.	In a survey of 200 students of a higher secondary school, it was found that 120 studied mathematics; 90 studied physics and 70 studied chemistry; 40 studied mathematics and physics; 30 studied physics and chemistry; 50 studied chemistry and mathematics, and 20 studied none of these subjects. Then the number of students who studied all the three subjects, is
Answer» In a survey of $200$ students of a higher secondary school, it was found that $120$ studied mathematics; $90$ studied physics and $70$ studied chemistry; $40$ studied mathematics and physics; $30$ studied physics and chemistry; $50$ studied chemistry and mathematics, and $20$ studied none of these subjects. Then the number of students who studied all the three subjects, is

Discussion

29.	sin4θ+cos4θ1-2sin2θ cos2θ=1
Answer» $\frac{\sin^{4} θ + \cos^{4} θ}{1 - 2 \sin^{2} θ \cos^{2} θ} = 1$

Discussion

30.	3.[Hint: Put x=-]
Answer» 3.[Hint: Put x=-]

Discussion

31.	Shape of XeF2 is:
Answer» Shape of XeF₂ is:

Discussion

32.	Write each of the following statement in the form “if-then”. (i) You get a job implies that your credentials are good. (ii) The Banana trees will bloom if it stays warm for a month. (iii) A quadrilateral is a parallelogram if its diagonals bisect each other. (iv) To get A + in the class, it is necessary that you do the exercises of the book.
Answer» Write each of the following statement in the form “if-then”. (i) You get a job implies that your credentials are good. (ii) The Banana trees will bloom if it stays warm for a month. (iii) A quadrilateral is a parallelogram if its diagonals bisect each other. (iv) To get A + in the class, it is necessary that you do the exercises of the book.

Discussion

33.	What's cardinality of set ? Give me a example.
Answer» What's cardinality of set ? Give me a example.

Discussion

34.	If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to
Answer» If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to

Discussion

35.	what are the number of significant figures in 5000?what are the number of significant figures in 5000km?
Answer» what are the number of significant figures in 5000? what are the number of significant figures in 5000km?

Discussion

36.	∫sin−1√x−cos−1√xsin−1√x+cos−1√x dx.
Answer» $\int \frac{s i n^{- 1} \sqrt{x} - c o s^{- 1} \sqrt{x}}{s i n^{- 1} \sqrt{x} + c o s^{- 1} \sqrt{x}} d x .$

Discussion

37.	The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….
Answer» The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….

Discussion

38.	From the data given below state which group is more variable, A or B? Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7
Answer» From the data given below state which group is more variable, A or B? Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7

Discussion

39.	Let →u and →v be two unit vectors. If →w is a vector such that →w+(→w×→u)=→v, then →u⋅(→v×→w) is equal to
Answer» Let $\to u$ and $\to v$ be two unit vectors. If $\to w$ is a vector such that $\to w + (\to w \times \to u) = \to v$ , then $\to u \cdot (\to v \times \to w)$ is equal to

Discussion

40.	Suppose Xhas a binomial distribution.Show that X = 3 is the most likely outcome.(Hint: P(X= 3) is the maximum among all P (xi), xi= 0, 1, 2, 3, 4, 5, 6)
Answer» Suppose X has a binomial distribution. Show that X = 3 is the most likely outcome. (Hint: P(X = 3) is the maximum among all P (x_i), x_i = 0, 1, 2, 3, 4, 5, 6)

40.

Suppose Xhas a binomial distribution.Show that X = 3 is the most likely outcome.(Hint: P(X= 3) is the maximum among all P (xi), xi= 0, 1, 2, 3, 4, 5, 6)

Answer»

Suppose X
has a binomial distribution.
Show that X = 3 is the most likely outcome.

(Hint: P(X
= 3) is the maximum among all P (x_i), x_i
= 0, 1, 2, 3, 4, 5, 6)

Discussion

41.	Find the conjuagates of the following complex numbers : (i) 4−5i(ii) 13+5i(iii) 11+i(iv) (3−i)22+i(v) (1+i)(2+i)3+i(vi) (3−2i)(2+3i)(1+2i)(2−i)
Answer» Find the conjuagates of the following complex numbers : $(i) 4 - 5 i (i i) \frac{1}{3 + 5 i} (i i i) \frac{1}{1 + i} (i v) \frac{(3 - i)^{2}}{2 + i} (v) \frac{(1 + i) (2 + i)}{3 + i} (v i) \frac{(3 - 2 i) (2 + 3 i)}{(1 + 2 i) (2 - i)}$

41.

Find the conjuagates of the following complex numbers : (i) 4−5i(ii) 13+5i(iii) 11+i(iv) (3−i)22+i(v) (1+i)(2+i)3+i(vi) (3−2i)(2+3i)(1+2i)(2−i)

Answer»

Find the conjuagates of the following complex numbers :

$(i) 4 - 5 i (i i) \frac{1}{3 + 5 i} (i i i) \frac{1}{1 + i} (i v) \frac{(3 - i)^{2}}{2 + i} (v) \frac{(1 + i) (2 + i)}{3 + i} (v i) \frac{(3 - 2 i) (2 + 3 i)}{(1 + 2 i) (2 - i)}$

Discussion

42.	Which of the following functions is/are decreasing in (0,π2)?
Answer» Which of the following functions is/are decreasing in $(0, \frac{π}{2})$ ?

Discussion

43.	If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is
Answer» If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is

Discussion

44.	If cos(α + β )=0, then sin(α -β ) can be equal to (1) cos 2β (2) cos β (3) sin α (4) sin 2α
Answer» If cos(α + β )=0, then sin(α -β ) can be equal to (1) cos 2β (2) cos β (3) sin α (4) sin 2α

Discussion

45.	The sum of 7 numbers in geometric progression is 108. The sum of their reciprocals is 12. The geometric mean of 3 middle terms of the geometric progression is :
Answer» The sum of 7 numbers in geometric progression is 108. The sum of their reciprocals is 12. The geometric mean of 3 middle terms of the geometric progression is :

Discussion

46.	2. Solve- 12x> 30, when(i)xis a natural number.(ii) x is an integer.
Answer» 2. Solve- 12x> 30, when(i)xis a natural number.(ii) x is an integer.

Discussion

47.	If P is a 2 × 2 matrix such that PT = 3P + I, then tr (P) is equal to
Answer» If P is a 2 × 2 matrix such that PT = 3P + I, then tr (P) is equal to

Discussion

48.	3. Find value of X if (x-26)(53 + 52)/(53- 52) = 1
Answer» 3. Find value of X if (x-26)(53 + 52)/(53- 52) = 1

Discussion

49.	A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is
Answer» A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is

Discussion

50.	if for a mattix A,A^2+I =0,where I is the identity matrix ,then A equal
Answer» if for a mattix A,A^2+I =0,where I is the identity matrix ,then A equal

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The integral ∫14√(x−1)3(x+2)5dx is equal to:(where C is a constant of integration)

Equation of the circle having centre at (3,−1) and making an intercept of length 6 units on the line 2x−5y+18=0, is

A chord ax+y=1 subtends 90∘ at the centre of the circle x2+y2=32. Then the value of a is

The rectangular component of a vector are (2,2) .the corresponding rectangular component of another vector (1,3) find the angle between two vectors

what is the method(steps) for finding out the domain and range of a given function

What's the meaning of Quantised?

A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

Write the first five terms of the sequences whose nth term is

x&gt;6 can be represented on number line by

The shortest distance between the lines →r=3→i+5→j+7→k+λ(→i+2→j+→k) and →r=−→i−→j−→k+μ(7→i−6→j+→k) is

The range of values of n for which one root of the equation x2−(n+1)x+n2+n−8=0 is greater than 2 and the other less than 2

If A = { a , b, c, d, e}, B = { c, d, e, f }, C = {b, d}, D = { a , e} then which of the following statements are true and which are false ?( i ) C ⊆ B ( ii ) A ⊆ D ( iii ) D ⊆B ( iv ) D⊆A ( v ) B ⊆A (vi) C ⊆A

The value of cos−1(cos5π3)+sin−1(cos5π3) is

Solve the following equations using trial and error method:3x – 7 = 5

The value of the limit limx→0 ax−bxx a &gt; 0, b &gt; 0, is

If O be the origin and the coordinates of P be (1, 2, −3), then find the equation of the plane passing through P and perpendicular to OP.

10. If z=3-4i then z-3z-3z+99z-95= option A)5 B)6 C)-5 D)-4

Prove that: tan2 2x-tan2 x1-tan2 2x tan2 x=tan 3x tan x

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of G.P. is

Prove that (Cos 6x + 6 cos 4x + 15 cos 2x + 10) / (cos5x + 5 cos 3x+ 10 cos x) =2cosx

Vectors A,B and C are such that A.B = 0 and A.C=0. Then the vector parallel to A vector is ?

A weather station recorded the temperatures of a place over a period of 7 days as follows:DayTemperature (in ∘C )Monday 45Tuesday38Wednesday40Thursday42Friday41Saturday37Sunday36Find the probability of a day having a temperature of less than 40 ∘ C.

If x lies in the first quadrant and cos x=817, then prove that:cos π6+x+cos π4-x+cos 2π3-x=3-12+122317

If the inequality \operatorname{sin^2x+a\operatorname{cosx+a^2>1+\operatorname{cosx holds for any x∈ R, then the largest negative integral value of a is

The angle between two diagonals of a cube will be [MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]

13. If y=cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx,then dy/dx is

If the length of subnormal is equal to the length of subtangent at a point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at A and B, then twice the value of maximum area of the triangle OAB, where O is origin is:

sin4θ+cos4θ1-2sin2θ cos2θ=1

3.[Hint: Put x=-]

Shape of XeF2 is:

What's cardinality of set ? Give me a example.

If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to

what are the number of significant figures in 5000?what are the number of significant figures in 5000km?

∫sin−1√x−cos−1√xsin−1√x+cos−1√x dx.

The system of linear equations x+y+z=6, x+2y+3z=10 and x+2y+az=b has no solutions when …….

From the data given below state which group is more variable, A or B? Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7

Let →u and →v be two unit vectors. If →w is a vector such that →w+(→w×→u)=→v, then →u⋅(→v×→w) is equal to

Suppose Xhas a binomial distribution.Show that X = 3 is the most likely outcome.(Hint: P(X= 3) is the maximum among all P (xi), xi= 0, 1, 2, 3, 4, 5, 6)

Find the conjuagates of the following complex numbers : (i) 4−5i(ii) 13+5i(iii) 11+i(iv) (3−i)22+i(v) (1+i)(2+i)3+i(vi) (3−2i)(2+3i)(1+2i)(2−i)

Which of the following functions is/are decreasing in (0,π2)?

If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is

If cos(α + β )=0, then sin(α -β ) can be equal to (1) cos 2β (2) cos β (3) sin α (4) sin 2α

The sum of 7 numbers in geometric progression is 108. The sum of their reciprocals is 12. The geometric mean of 3 middle terms of the geometric progression is :

2. Solve- 12x> 30, when(i)xis a natural number.(ii) x is an integer.

If P is a 2 × 2 matrix such that PT = 3P + I, then tr (P) is equal to

3. Find value of X if (x-26)(53 + 52)/(53- 52) = 1

A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is

if for a mattix A,A^2+I =0,where I is the identity matrix ,then A equal

x>6 can be represented on number line by

The value of the limit limx→0 ax−bxx a > 0, b > 0, is