43030 + Interview Questions in Mathematics

1.	Write the equation of the parabola with focus (0,0) and directrix x+y-4=0.
Answer» Write the equation of the parabola with focus (0,0) and directrix x+y-4=0.

Discussion

2.	A sequence is defined by an=n3−6n2+11n−6, nϵN. Show that the first three terms of the sequence are zero and all other terms are positive.
Answer» A sequence is defined by $a_{n} = n^{3} - 6 n^{2} + 11 n - 6, n ϵ N$ . Show that the first three terms of the sequence are zero and all other terms are positive.

Discussion

3.	The sides of a triangle area=5, b=6 and c=8, show that:8 cos A+16 cos B+4 cos C=17.
Answer» $The sides of a triangle are a = 5, b = 6 a n d c = 8, show that:8 c o s A + 16 c o s B + 4 c o s C = 17.$

Discussion

4.	If A = {(x,y):y=ex,x ϵ R} and B = {x,y:y=e−x,x ϵ R} , then write A∩B.
Answer» If A = { $(x, y) : y = e^{x}, x ϵ R$ } and B = { $x, y : y = e^{- x}, x ϵ R$ } , then write $A \cap B$ .

Discussion

5.	Sides of a triangle ABC are in AP, then cosA is equal to
Answer» Sides of a triangle ABC are in AP, then cosA is equal to

Discussion

6.	Let f:R→R be a continuously differentiable function such that f(2)=6 and f′(2)=148. If f(x)∫64t3 dt=(x−2)g(x), then limx→2 g(x) is equal to
Answer» Let $f : R \to R$ be a continuously differentiable function such that $f (2) = 6$ and $f^{'} (2) = \frac{1}{48} .$ If $f (x) \int 6 4 t^{3} d t = (x - 2) g (x),$ then $lim x \to 2 g (x)$ is equal to

Discussion

7.	In a square matrix A of order 3, the elements, ai,i's are the sum of the roots of the equation x2−(a+b)x+ab=0; aj,(j−1)'s are the all unity,aj,(j+1)'s are product of the roots and rest of the elements are all zero. Then value of the determinant is ___
Answer» In a square matrix A of order 3, the elements, $a_{i, i}$ 's are the sum of the roots of the equation $x^{2} - (a + b) x + a b = 0$ ; $a_{j, (j - 1)}$ 's are the all unity, $a_{j, (j + 1)}$ 's are product of the roots and rest of the elements are all zero. Then value of the determinant is ___

Discussion

8.	A man takes a step forward with probability 0.4 and one step backward with probability 0.6. then the probability that at the end of eleven steps he is one step away from the starting point is
Answer» A man takes a step forward with probability 0.4 and one step backward with probability 0.6. then the probability that at the end of eleven steps he is one step away from the starting point is

Discussion

9.	The minimum value of f(x)=\|x−6\|+\|x+3\|+\|x−8\|+\|x+4\|+\|x−3\|, x∈R is
Answer» The minimum value of $f (x) = \| x - 6 \| + \| x + 3 \| + \| x - 8 \| + \| x + 4 \| + \| x - 3 \|, x \in R$ is

Discussion

10.	If the sum of the series 12C5+7.12C6+21.12C7+35.12C8+35.12C9+21.12C10+7.12C11+12C12 is equal to 2n+1C12 then n is
Answer» If the sum of the series $^{12} C_{5} + 7 .^{12} C_{6} + 21 .^{12} C_{7} + 35 .^{12} C_{8} + 35 .^{12} C_{9} + 21 .^{12} C_{10} + {7.}^{12} C_{11} +^{12} C_{12}$ is equal to $^{2 n + 1} C_{12}$ then $n$ is

Discussion

11.	The sum of the series 131+13+231+3+13+23+331+3+5+…… upto 16 terms is
Answer» The sum of the series $\frac{1^{3}}{1} + \frac{1^{3} + 2^{3}}{1 + 3} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 3 + 5} + \dots \dots$ upto $16$ terms is

Discussion

12.	π2∫−π2dxesinx+1 is equal to
Answer» $\frac{π}{2} \int - \frac{π}{2} \frac{d x}{e^{sin x} + 1}$ is equal to

Discussion

13.	The degree of the polynomial f(x)=(x2−1)(x−3) is
Answer» The degree of the polynomial $f (x) = (x^{2} - 1) (x - 3)$ is

Discussion

14.	sin20°+sin25°+sin210°+....sin290° is equal to
Answer» ${sin}^{2} 0 ° + {sin}^{2} 5 ° + {sin}^{2} 10 ° + . . . . {sin}^{2} 90 °$ is equal to

Discussion

15.	In this year 2019 Neet will be twice a year or not
Answer» In this year 2019 Neet will be twice a year or not

Discussion

16.	The value of 2∫−2\|3x2−3x−6\| dx is
Answer» The value of $2 \int - 2 \| 3 x^{2} - 3 x - 6 \| d x$ is

Discussion

17.	What is the volume of material required to make a hollow cylinder having inner and outer radius as 2 cm and 3 cm respectively and height as 14 cm?
Answer» What is the volume of material required to make a hollow cylinder having inner and outer radius as 2 cm and 3 cm respectively and height as 14 cm?

Discussion

18.	If z = ii . Express logez in A+iB form.Find the value of A and B.
Answer» If z = $i^{i}$ . Express ${l o g}_{e}$ z in A+iB form.Find the value of A and B.

Discussion

19.	If the minimum distance between the parabolas y2−4x−8y+40=0 and x2−8x−4y+40=0 is d, then the value of d2 is
Answer» If the minimum distance between the parabolas $y^{2} - 4 x - 8 y + 40 = 0$ and $x^{2} - 8 x - 4 y + 40 = 0$ is $d$ , then the value of $d^{2}$ is

Discussion

20.	Find the general solution of the differential equation dydx+√1−y21−x2=0
Answer» Find the general solution of the differential equation $\frac{d y}{d x} + \sqrt{\frac{1 - y^{2}}{1 - x^{2}}} = 0$

Discussion

21.	Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line 7x−9y+10=0 upon the lines 3x+4y=5 and 12x+5y=7 respectively. Then
Answer» Let $d_{1}$ and $d_{2}$ be the lengths of the perpendiculars drawn from any point of the line $7 x - 9 y + 10 = 0$ upon the lines $3 x + 4 y = 5$ and $12 x + 5 y = 7$ respectively. Then

Discussion

22.	In the binary number 10010, the MSB is
Answer» In the binary number 10010, the MSB is

Discussion

23.	If in a triangle ABC, ∠C=60o, then 1a+c+1b+c= [IIT 1975]
Answer» If in a triangle ABC, $∠ C = 60^{o},$ then $\frac{1}{a + c} + \frac{1}{b + c} =$ [IIT 1975]

Discussion

24.	P(t = 2) is a point on the parabola y2=4ax. What is the point of the intersection of tangent at P and the directrix of the parabola?
Answer» P(t = 2) is a point on the parabola $y^{2} = 4 a x$ . What is the point of the intersection of tangent at P and the directrix of the parabola?

Discussion

25.	limx→0(1+x)1x+e(x−1)sin−1x=
Answer» ${lim}_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} + e (x - 1)}{s i n^{- 1} x} =$

Discussion

26.	The circle x2+y2=4x+8y+5 interesects the line 3x - 4y = m at two distinct points if (2010)
Answer» The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ interesects the line 3x - 4y = m at two distinct points if (2010)

Discussion

27.	The value of expression i92 + i93 + i94 + i95 is__
Answer» The value of expression $i^{92}$ + $i^{93}$ + $i^{94}$ + $i^{95}$ is__

Discussion

28.	* is a binary operation on Z such that: a * b = a + b + ab. The solution of (3* 4) *x = - 1 is
Answer» * is a binary operation on Z such that: a * b = a + b + ab. The solution of (3* 4) *x = - 1 is

Discussion

29.	If the ends of a focal chord of the parabola y2=4ax are (x1,y1) and (x2,y2) then x1,x2+y1y2=
Answer» If the ends of a focal chord of the parabola $y^{2} = 4 a x$ are $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ then $x_{1}, x_{2} + y_{1} y_{2} =$

Discussion

30.	In these questions, certain symbols have been used to indicate relationships between elements as follows A ★ B means A is either equal to or greater than B. A $ B means A is equal to B. A pounds B means A is either equal to or smaller than B. A & B means A is smaller than B. A B means that A is greater than B. In each question, three statements showing relationships have been given, which are followed by two conclusions I and II. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true. Statements: S ★ K, T & K, K ★ B Conclusions: I. S $ B II. S B
Answer» In these questions, certain symbols have been used to indicate relationships between elements as follows A $★$ B means A is either equal to or greater than B. A $$$ B means A is equal to B. A pounds B means A is either equal to or smaller than B. A & B means A is smaller than B. A B means that A is greater than B. In each question, three statements showing relationships have been given, which are followed by two conclusions I and II. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true. Statements: S $★$ K, T & K, K $★$ B Conclusions: I. S $$$ B II. S B

Discussion

31.	If α be a real root of the equation x3+px2+qx+r=0 where p, q and r are real. If p2−4q−2pα−3α2≥0 then other roots are ________.
Answer» If $α$ be a real root of the equation $x^{3} + p x^{2} + q x + r = 0$ where p, q and r are real. If $p^{2} - 4 q - 2 p α - 3 α^{2} \geq 0$ then other roots are ________.

Discussion

32.	What is the nth term of H.P with first 2 terms as 411 and 23 ?
Answer» What is the nth term of H.P with first 2 terms as $\frac{4}{11}$ and $\frac{2}{3}$ ?

Discussion

33.	In a class of 345 students, the students who took English, Math and Physics are equal in number. 30 students took English and Math, 26 choose Math and Physics, 28 choose Physics and English and 14 choose all three subjects. 43 students didn’t take any of the subjects. How many students have taken English as subject?
Answer» In a class of $345$ students, the students who took English, Math and Physics are equal in number. $30$ students took English and Math, $26$ choose Math and Physics, $28$ choose Physics and English and $14$ choose all three subjects. $43$ students didn’t take any of the subjects. How many students have taken English as subject?

Discussion

34.	The locus of point P when three normals drawn from it to parabola y2=4ax are such that two of them make complementary angles is
Answer» The locus of point $P$ when three normals drawn from it to parabola $y^{2} = 4 a x$ are such that two of them make complementary angles is

Discussion

35.	If y=√x+√y+√x+√y+...∞, then dydx is equal to
Answer» If $y = \sqrt{x + \sqrt{y + \sqrt{x + \sqrt{y + . . . \infty,}}}}$ then $\frac{d y}{d x}$ is equal to

Discussion

36.	Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) cross the YZ-plane.
Answer» Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) cross the YZ-plane.

Discussion

37.	The value of the limit limx→∞ (√x+3−√x}√x+1 is
Answer» The value of the limit $lim x \to \infty (\sqrt{x + 3} - \sqrt{x}} \sqrt{x + 1}$ is

Discussion

38.	If nCx= nCy and n≠y then prove that x+y=n.
Answer» If $^{n} C_{x} =^{n} C_{y}$ and $n \neq y$ then prove that $x + y = n .$

Discussion

39.	Find the interval in which the following function is strictly incerasing or decreasing, 6−9x−x2
Answer» Find the interval in which the following function is strictly incerasing or decreasing, $6 - 9 x - x^{2}$

39.

Find the interval in which the following function is strictly incerasing or decreasing, 6−9x−x2

Answer»

Find the interval in which the following function is strictly incerasing or decreasing,

$6 - 9 x - x^{2}$

Discussion

40.	In ΔABC, AB=AC and h is the altitude from A to BC. Given, area of ΔABC is A, and perimeter P=2(√2hr−h2+√2hr), where r is the circumradius of ΔABC, then 1rlimh→0AP3=
Answer» In $Δ A B C, A B = A C$ and $h$ is the altitude from $A$ to $B C$ . Given, area of $Δ A B C$ is $A$ , and perimeter $P = 2 (\sqrt{2 h r - h^{2}} + \sqrt{2 h r})$ , where $r$ is the circumradius of $Δ A B C$ , then $\frac{1}{r lim h \to 0 \frac{A}{P^{3}}} =$

Discussion

41.	If 4^i+7^j+8^k, 2^i+3^j+4^k and 2^i+5^j+7^k are the position vectors of the vertices A,B and C, respectively, of triangle ABC, the position vector of the point where the bisector of angle A meets BC, is
Answer» If $4^i + 7^j + 8^k, 2^i + 3^j + 4^k$ and $2^i + 5^j + 7^k$ are the position vectors of the vertices A,B and C, respectively, of triangle ABC, the position vector of the point where the bisector of angle A meets BC, is

Discussion

42.	What’s the equation of the circle passing through the points (0, 0), (0, 1) (6, 0)
Answer» What’s the equation of the circle passing through the points (0, 0), (0, 1) (6, 0)

Discussion

43.	The value of the integral I = ∫10x(1−x)n dx is
Answer» The value of the integral I = $\int_{0}^{1} x (1 - x)^{n} d x$ is

Discussion

44.	Consider the family of curves Ax2+By2=1. If this family of curve is represented by the differential equation P.y′′+Q(y′)2=yy′, where P and Q are functions of x and y, then which of the following statement (s) is/are correct? (y′=dydx and y′′=d2ydx2)
Answer» Consider the family of curves $A x^{2} + B y^{2} = 1$ . If this family of curve is represented by the differential equation $P . y^{''} + Q (y^{'})^{2} = y y^{'}$ , where P and Q are functions of x and y, then which of the following statement (s) is/are correct? $(y^{'} = \frac{d y}{d x} and y^{''} = \frac{d^{2} y}{d x^{2}})$

Discussion

45.	(tanA + cotA)2 = sec2A.cosec2A Prove it?
Answer» (tanA + cotA)² = sec²A.cosec²A Prove it?

45.

(tanA + cotA)2 = sec2A.cosec2A Prove it?

Answer»

(tanA + cotA)² = sec²A.cosec²A

Prove it?

Discussion

46.	The smallest set A such that A∪{1,2}={1,2,3,5,9} is
Answer» The smallest set $A$ such that $A \cup {1, 2} = {1, 2, 3, 5, 9}$ is

Discussion

47.	Distinguish between training and development.
Answer» Distinguish between training and development.

Discussion

48.	Positive numbers x,y and z satisfy xyz=1081 and (log10x)(log10yz)+(log10y)(log10z)=468. Then the value of (log10x)2+(log10y)2+(log10z)2 is
Answer» Positive numbers $x, y$ and $z$ satisfy $x y z = 10^{81}$ and $({log}_{10} x) ({log}_{10} y z) + ({log}_{10} y) ({log}_{10} z) = 468.$ Then the value of $({log}_{10} x)^{2} + ({log}_{10} y)^{2} + ({log}_{10} z)^{2}$ is

Discussion

49.	Write the sum to n terms of a series whose rth term is :r + 2r.
Answer» Write the sum to n terms of a series whose $r^{t h}$ term is :r + $2^{r}$ .

49.

Write the sum to n terms of a series whose rth term is :r + 2r.

Answer»

Write the sum to n terms of a series whose $r^{t h}$ term is :r + $2^{r}$ .

Discussion

50.	For equation x4−2x3−2x2+18x−63=0 if two of its roots are equal in magnitude but opposite in sign the other two roots are
Answer» For equation $x^{4} - 2 x^{3} - 2 x^{2} + 18 x - 63 = 0$ if two of its roots are equal in magnitude but opposite in sign the other two roots are

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Write the equation of the parabola with focus (0,0) and directrix x+y-4=0.

A sequence is defined by an=n3−6n2+11n−6, nϵN. Show that the first three terms of the sequence are zero and all other terms are positive.

The sides of a triangle area=5, b=6 and c=8, show that:8 cos A+16 cos B+4 cos C=17.

If A = {(x,y):y=ex,x ϵ R} and B = {x,y:y=e−x,x ϵ R} , then write A∩B.

Sides of a triangle ABC are in AP, then cosA is equal to

Let f:R→R be a continuously differentiable function such that f(2)=6 and f′(2)=148. If f(x)∫64t3 dt=(x−2)g(x), then limx→2 g(x) is equal to

In a square matrix A of order 3, the elements, ai,i's are the sum of the roots of the equation x2−(a+b)x+ab=0; aj,(j−1)'s are the all unity,aj,(j+1)'s are product of the roots and rest of the elements are all zero. Then value of the determinant is ___

A man takes a step forward with probability 0.4 and one step backward with probability 0.6. then the probability that at the end of eleven steps he is one step away from the starting point is

The minimum value of f(x)=|x−6|+|x+3|+|x−8|+|x+4|+|x−3|, x∈R is

If the sum of the series 12C5+7.12C6+21.12C7+35.12C8+35.12C9+21.12C10+7.12C11+12C12 is equal to 2n+1C12 then n is

The sum of the series 131+13+231+3+13+23+331+3+5+…… upto 16 terms is

π2∫−π2dxesinx+1 is equal to

The degree of the polynomial f(x)=(x2−1)(x−3) is

sin20°+sin25°+sin210°+....sin290° is equal to

In this year 2019 Neet will be twice a year or not

The value of 2∫−2|3x2−3x−6| dx is

What is the volume of material required to make a hollow cylinder having inner and outer radius as 2 cm and 3 cm respectively and height as 14 cm?

If z = ii . Express logez in A+iB form.Find the value of A and B.

If the minimum distance between the parabolas y2−4x−8y+40=0 and x2−8x−4y+40=0 is d, then the value of d2 is

Find the general solution of the differential equation dydx+√1−y21−x2=0

Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line 7x−9y+10=0 upon the lines 3x+4y=5 and 12x+5y=7 respectively. Then

In the binary number 10010, the MSB is

If in a triangle ABC, ∠C=60o, then 1a+c+1b+c= [IIT 1975]

P(t = 2) is a point on the parabola y2=4ax. What is the point of the intersection of tangent at P and the directrix of the parabola?

limx→0(1+x)1x+e(x−1)sin−1x=

The circle x2+y2=4x+8y+5 interesects the line 3x - 4y = m at two distinct points if (2010)

The value of expression i92 + i93 + i94 + i95 is__

* is a binary operation on Z such that: a * b = a + b + ab. The solution of (3* 4) *x = - 1 is

If the ends of a focal chord of the parabola y2=4ax are (x1,y1) and (x2,y2) then x1,x2+y1y2=

If α be a real root of the equation x3+px2+qx+r=0 where p, q and r are real. If p2−4q−2pα−3α2≥0 then other roots are ________.

What is the nth term of H.P with first 2 terms as 411 and 23 ?

The locus of point P when three normals drawn from it to parabola y2=4ax are such that two of them make complementary angles is

If y=√x+√y+√x+√y+...∞, then ​dydx is equal to

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) cross the YZ-plane.

The value of the limit limx→∞ (√x+3−√x}√x+1 is

If nCx= nCy and n≠y then prove that x+y=n.

Find the interval in which the following function is strictly incerasing or decreasing, 6−9x−x2

In ΔABC, AB=AC and h is the altitude from A to BC. Given, area of ΔABC is A, and perimeter P=2(√2hr−h2+√2hr), where r is the circumradius of ΔABC, then 1rlimh→0AP3=

If 4^i+7^j+8^k, 2^i+3^j+4^k and 2^i+5^j+7^k are the position vectors of the vertices A,B and C, respectively, of triangle ABC, the position vector of the point where the bisector of angle A meets BC, is

What’s the equation of the circle passing through the points (0, 0), (0, 1) (6, 0)

The value of the integral I = ∫10x(1−x)n dx is

Consider the family of curves Ax2+By2=1. If this family of curve is represented by the differential equation P.y′′+Q(y′)2=yy′, where P and Q are functions of x and y, then which of the following statement (s) is/are correct? (y′=dydx and y′′=d2ydx2)

(tanA + cotA)2 = sec​​​​2​​​A.cosec2A Prove it?

The smallest set A such that A∪{1,2}={1,2,3,5,9} is

Distinguish between training and development.

Positive numbers x,y and z satisfy xyz=1081 and (log10x)(log10yz)+(log10y)(log10z)=468. Then the value of (log10x)2+(log10y)2+(log10z)2 is

Write the sum to n terms of a series whose rth term is :r + 2r.

For equation x4−2x3−2x2+18x−63=0 if two of its roots are equal in magnitude but opposite in sign the other two roots are

If y=√x+√y+√x+√y+...∞, then dydx is equal to

(tanA + cotA)2 = sec2A.cosec2A Prove it?