43030 + Interview Questions in Mathematics

1.	Suppose A1, A2,....................., A30 are thirty sets each having 5 elements each and B1, B2,................Bn are n sets each with 3 elements each. Let 30⋃i=1Ai=n⋃j=1Bj=S and each element of S belongs to exactly 10 of Ai's and exactly 9 of the Bj's. Then n is equal to
Answer» Suppose $A_{1}, A_{2}, . . . . . . . . . . . . . . . . . . . . ., A_{30}$ are thirty sets each having 5 elements each and $B_{1}, B_{2}, . . . . . . . . . . . . . . . . B_{n}$ are $n$ sets each with 3 elements each. Let $30 ⋃ i = 1 A_{i} = n ⋃ j = 1 B_{j} = S$ and each element of $S$ belongs to exactly 10 of $A_{i}$ 's and exactly 9 of the $B_{j}$ 's. Then $n$ is equal to

Discussion

2.	5. if tangent and normal to the curve y=2sinx+sin2x are drawn at a point p=pi/3then find the area of quadrilateral formed by the tangent normal and oordinate, x axis.
Answer» 5. if tangent and normal to the curve y=2sinx+sin2x are drawn at a point p=pi/3then find the area of quadrilateral formed by the tangent normal and oordinate, x axis.

Discussion

3.	If the length of subtangent is 9 units and that of sub normal is 4 units at a point (α,β) on the curve y=f(x), then \|β\| is equal to
Answer» If the length of subtangent is $9$ units and that of sub normal is $4$ units at a point $(α, β)$ on the curve $y = f (x)$ , then $\| β \|$ is equal to

Discussion

4.	Findrif (i) (ii) .
Answer» Find r if (i) (ii) .

Discussion

5.	Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.
Answer» Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.

Discussion

6.	The number of solutions of \|x-1\|-\|x+2\|=k when -3
Answer» The number of solutions of \|x-1\|-\|x+2\|=k when -3

Discussion

7.	How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
Answer» How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Discussion

8.	Let A=⎡⎢⎣xyzyzxzxy⎤⎥⎦, where x,y and z are real numbers such that x+y+z>0 axyz=2. If A2=I3, then the value of x3+y3+z3 is
Answer» Let $A = ⎡ ⎢ ⎣ \begin{matrix} x & y & z y & z & x z & x & y \end{matrix} ⎤ ⎥ ⎦$ , where $x, y$ and $z$ are real numbers such that $x + y + z > 0$ a $x y z = 2$ . If $A^{2} = I_{3}$ , then the value of $x^{3} + y^{3} + z^{3}$ is

Discussion

9.	Why does SiO2 does not have a linear structure
Answer» Why does SiO2 does not have a linear structure

Discussion

10.	The position vector of a point which moves in x-yplane is given by-The angle between the velocity v and theacceleration a when t 2 s is
Answer» The position vector of a point which moves in x-yplane is given by-The angle between the velocity v and theacceleration a when t 2 s is

Discussion

11.	A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60∘ with the ground. At what height from the bottom the tree is broken by the wind?
Answer» A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle $60^{\circ}$ with the ground. At what height from the bottom the tree is broken by the wind?

Discussion

12.	The number of integral terms in the expansion of (512+716)642 is
Answer» The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{6}})^{642}$ is

12.

The number of integral terms in the expansion of (512+716)642 is

Answer»

The number of integral terms in the expansion of

$(5^{\frac{1}{2}} + 7^{\frac{1}{6}})^{642}$ is

Discussion

13.	The ratio of the sums of m and n terms of an A.P. is m2:n2. Show that the ratio of mthand nth terms is (2m−1):(2n−1).
Answer» The ratio of the sums of $m$ and $n$ terms of an A.P. is $m^{2} : n^{2}$ . Show that the ratio of $m^{t h}$ and $n^{t h}$ terms is $(2 m - 1) : (2 n - 1) .$

Discussion

14.	Verify Mean Value Theorem, ifin the interval [a, b], where a = 1 and b= 3. Find all forwhich
Answer» Verify Mean Value Theorem, if in the interval [a, b], where a = 1 and b = 3. Find all for which

Discussion

15.	Simplify: 3−2×8134÷729−13
Answer» Simplify: $3^{- 2} \times 81^{\frac{3}{4}} \div 729^{- \frac{1}{3}}$

Discussion

16.	limn→∞(1n2sec21n2+2n2sec24n2+...+nn2 sec21)equals to
Answer» $l i m n \to \infty (\frac{1}{n^{2}} s e c^{2} \frac{1}{n^{2}} + \frac{2}{n^{2}} s e c^{2} \frac{4}{n^{2}} + . . . + \frac{n}{n^{2}} s e c^{2} 1) e q u a l s t o$

Discussion

17.	Find a(vector) . b(vector) and a(vector)*b(vector) if a= i+2j+k and magnitude of b=3 acting along c(vector) = i+j+k.
Answer» Find a(vector) . b(vector) and a(vector)*b(vector) if a= i+2j+k and magnitude of b=3 acting along c(vector) = i+j+k.

Discussion

18.	If x, y, z are not all zero and if ax + by + cz = 0, bx + cy + az = 0 and cx + ay + bz = 0, then x : y : z may be
Answer» If x, y, z are not all zero and if ax + by + cz = 0, bx + cy + az = 0 and cx + ay + bz = 0, then x : y : z may be

Discussion

19.	Show that the Modulus Function f : R → R given by , is neither one-one nor onto, where is x , if x is positive or 0 and is − x , if x is negative.
Answer» Show that the Modulus Function f : R → R given by , is neither one-one nor onto, where is x , if x is positive or 0 and is − x , if x is negative.

Discussion

20.	If xy+yx=ab the find dydx. OR If ey(x+1)=1, then show that d2ydx2=(dydx)2.
Answer» If $x^{y} + y^{x} = a^{b}$ the find $\frac{d y}{d x}$ . OR If $e^{y} (x + 1) = 1,$ then show that $\frac{d^{2} y}{d x^{2}} = {(\frac{d y}{d x})}^{2}$ .

Discussion

21.	Solve }\operatorname{log}_{(x+3)}(x^2-x)
Answer» Solve }\operatorname{log}_{(x+3)}(x^2-x)<1

Discussion

22.	limx→−1(1+x+x2+⋯+x100) is equal to
Answer» $lim x \to - 1 (1 + x + x^{2} + \dots + x^{100})$ is equal to

Discussion

23.	The angle between the planes 3x - 4y + 5z = 0 and 2x -y - 2z = 5 is [MP PET 1988]
Answer» The angle between the planes 3x - 4y + 5z = 0 and 2x -y - 2z = 5 is [MP PET 1988]

Discussion

24.	The Arithmetic Mean of the observations 1.3.5,3.5.7,5.7.9,...,(2n−1)(2n+1)(2n+3) is (∀n∈N)
Answer» The Arithmetic Mean of the observations $1.3.5, 3.5.7, 5.7.9, . . ., (2 n - 1) (2 n + 1) (2 n + 3)$ is $(\forall n \in N)$

Discussion

25.	An integer x is chosen from the first 50 positive integers. The probability that, x+100x>50, is:
Answer» An integer x is chosen from the first 50 positive integers. The probability that, $x + \frac{100}{x} > 50$ , is:

Discussion

26.	In a triangle ABC, if a = 2, b = 4 and A+B=2π3, then area of ∆ABC is __________.
Answer» In a triangle ABC, if a = 2, b = 4 and $A + B = \frac{2 π}{3},$ then area of ∆ABC is __________.

Discussion

27.	If the normal at point (1,2) on the parabola y2=4x meets the parabola again a point (t2,2t), then the value of t is
Answer» If the normal at point $(1, 2)$ on the parabola $y^{2} = 4 x$ meets the parabola again a point $(t^{2}, 2 t),$ then the value of $t$ is

Discussion

28.	The value of 1sin20∘−1√3cos20∘ is
Answer» The value of $\frac{1}{sin 20^{\circ}} - \frac{1}{\sqrt{3} cos 20^{\circ}}$ is

Discussion

29.	Let a=(41/401−1) and for each n≥2, let bn=nC1+nC2⋅a+nC3⋅a2+⋯+nCn⋅an−1. Then the value of (b2006−b2005) is
Answer» Let $a = (4^{1 / 401} - 1)$ and for each $n \geq 2,$ let $b_{n} =^{n} C_{1} +^{n} C_{2} \cdot a +^{n} C_{3} \cdot a^{2} + \dots +^{n} C_{n} \cdot a^{n - 1} .$ Then the value of $(b_{2006} - b_{2005})$ is

Discussion

30.	729 small spherical water drops, each of radius 1 mm, combine to form a spherical big drop. The decrease in surface energy is about (Take surface tension of water = 6 × 10–2 N/m)
Answer» 729 small spherical water drops, each of radius 1 mm, combine to form a spherical big drop. The decrease in surface energy is about (Take surface tension of water = 6 × 10–2 N/m)

Discussion

31.	If 3x+5y+17=0 is polar for the circle x2+y2+4x+6y+9=0, then the pole is
Answer» If $3 x + 5 y + 17 = 0$ is polar for the circle $x^{2} + y^{2} + 4 x + 6 y + 9 = 0$ , then the pole is

Discussion

32.	Evaluate the following determinant:(i) 1352610311138(ii) 671921391314812426(iii) ahghbfgfc(iv) 1-324-12352(v) 149491691625(vi) 6-322-12-1052(vii) 13927392719271327139(viii)
Answer» Evaluate the following determinant: (i) $\|\begin{matrix} 1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38 \end{matrix}\|$ (ii) $\|\begin{matrix} 67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26 \end{matrix}\|$ (iii) $\|\begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix}\|$ (iv) $\|\begin{matrix} 1 & - 3 & 2 \\ 4 & - 1 & 2 \\ 3 & 5 & 2 \end{matrix}\|$ (v) $\|\begin{matrix} 1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25 \end{matrix}\|$ (vi) $\|\begin{matrix} 6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2 \end{matrix}\|$ (vii) $\|\begin{matrix} 1 & 3 & 9 & 27 \\ 3 & 9 & 27 & 1 \\ 9 & 27 & 1 & 3 \\ 27 & 1 & 3 & 9 \end{matrix}\|$ (viii)

Discussion

33.	Let z=x+iy be a complex number. The equation arg(z+1z)=π4 represents
Answer» Let $z = x + i y$ be a complex number. The equation $a r g (\frac{z + 1}{z}) = \frac{π}{4}$ represents

Discussion

34.	Find the derivative of (x+a), where a is a fixed non-zero constant.
Answer» Find the derivative of $(x + a),$ where $a$ is a fixed non-zero constant.

Discussion

35.	Find the least value of a suchthat the function f given isstrictly increasing on (1, 2).
Answer» Find the least value of a such that the function f given is strictly increasing on (1, 2).

Discussion

36.	Which of the following is correct? A. Determinant is a square matrix. B. Determinant is a number associated to a matrix. C. Determinant is a number associated to a square matrix. D. None of these
Answer» Which of the following is correct? A. Determinant is a square matrix. B. Determinant is a number associated to a matrix. C. Determinant is a number associated to a square matrix. D. None of these

Discussion

37.	If 0<a<b, then which of the following is correct :
Answer» If $0 < a < b,$ then which of the following is correct :

Discussion

38.	106.The number of solution for (5x+7) -(3x+1) = (x+3)
Answer» 106.The number of solution for (5x+7) -(3x+1) = (x+3)

Discussion

39.	A wheel has been divided in 5 equal sector three ok which are green ,one blue and the remaining one red . If i spin the wheel once ,what is probably of getting a non blue sector?
Answer» A wheel has been divided in 5 equal sector three ok which are green ,one blue and the remaining one red . If i spin the wheel once ,what is probably of getting a non blue sector?

Discussion

40.	Prove, cos−145+cos−11213=cos−13365
Answer» Prove, $c o s^{- 1} \frac{4}{5} + c o s^{- 1} \frac{12}{13} = c o s^{- 1} \frac{33}{65}$

Discussion

41.	limx→02x−sinxtanx+x
Answer» ${lim}_{x \to 0} \frac{2 x - s i n x}{t a n x + x}$

Discussion

42.	Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests : Ravi :25504530704236483560Hashina :10705020955542604880 Who is more intelligent and who is more consistent ?
Answer» Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests : $\begin{matrix} Ravi : & 25 & 50 & 45 & 30 & 70 & 42 & 36 & 48 & 35 & 60 Hashina : & 10 & 70 & 50 & 20 & 95 & 55 & 42 & 60 & 48 & 80 \end{matrix}$ Who is more intelligent and who is more consistent ?

42.

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests : Ravi :25504530704236483560Hashina :10705020955542604880 Who is more intelligent and who is more consistent ?

Answer»

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests :

$\begin{matrix} Ravi : & 25 & 50 & 45 & 30 & 70 & 42 & 36 & 48 & 35 & 60 Hashina : & 10 & 70 & 50 & 20 & 95 & 55 & 42 & 60 & 48 & 80 \end{matrix}$

Who is more intelligent and who is more consistent ?

Discussion

43.	12. State whether each of the following statement is true or false. Justify your answer(i) {2,3, 4, 5 ] and 3, 6) are disjoint sets.(ii) t a, e, i, o, u \| and { a, b, c, d jare disjoint sets(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.(iv) 2,6, 10 ) and 3, 7, 11] are disjoint sets
Answer» 12. State whether each of the following statement is true or false. Justify your answer(i) {2,3, 4, 5 ] and 3, 6) are disjoint sets.(ii) t a, e, i, o, u \| and { a, b, c, d jare disjoint sets(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.(iv) 2,6, 10 ) and 3, 7, 11] are disjoint sets

Discussion

44.	The maximum value of f(x) = x e−x is _______________.
Answer» The maximum value of f(x) = x e⁻^x is _______________.

Discussion

45.	Which of the following transformations in order will give −\|(−x)+3\| from \|x\|? (1) f(x) → f(−x) (2) f(x) → f(x+3) (3) f(x) → −f(x) (4) f(x) → f(x−3)
Answer» Which of the following transformations in order will give $- \| (- x) + 3 \|$ from $\| x \|$ ? (1) $f (x) \to f (- x)$ (2) $f (x) \to f (x + 3)$ (3) $f (x) \to - f (x)$ (4) $f (x) \to f (x - 3)$

45.

Which of the following transformations in order will give −|(−x)+3| from |x|? (1) f(x) → f(−x) (2) f(x) → f(x+3) (3) f(x) → −f(x) (4) f(x) → f(x−3)

Answer»

Which of the following transformations in order will give $- | (- x) + 3 |$ from $| x |$ ?
(1) $f (x) \to f (- x)$
(2) $f (x) \to f (x + 3)$
(3) $f (x) \to - f (x)$

(4) $f (x) \to f (x - 3)$

Discussion

46.	What do you mean by imaginary number. I am not knowing about the apt definition. I know only about the definition of imaginary part
Answer» What do you mean by imaginary number. I am not knowing about the apt definition. I know only about the definition of imaginary part

Discussion

47.	If V is the volume of a cuboid of dimensions a, b, c and S is its surface area then prove that 1V=2S1a+1b+1c.
Answer» If V is the volume of a cuboid of dimensions a, b, c and S is its surface area then prove that $\frac{1}{V} = \frac{2}{S} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$ .

Discussion

48.	In the matrixA=⎡⎢⎢⎢⎣2519−735−25212√31−517⎤⎥⎥⎥⎦(i). Write the order of the matrix(ii). Write the numbers of element.(iii). Write the elements a13,a21,a33,a24,a23
Answer» In the matrix $A = ⎡ ⎢⎢⎢ ⎣ \begin{matrix} 2 & 5 & 19 & - 7 35 & - 2 & \frac{5}{2} & 12 \sqrt{3} & 1 & - 5 & 17 \end{matrix} ⎤ ⎥⎥⎥ ⎦$ $(i) .$ Write the order of the matrix $(i i) .$ Write the numbers of element. $(i i i) .$ Write the elements $a_{13}, a_{21}, a_{33}, a_{24}, a_{23}$

Discussion

49.	If 1P1+2⋅2P2+3⋅3P3+⋯+15⋅15P15=qPr−s, 0≤s≤1, then q+sCr−s is equal to
Answer» If $^{1} P_{1} + 2 \cdot^{2} P_{2} + 3 \cdot^{3} P_{3} + \dots + 15 \cdot^{15} P_{15} =^{q} P_{r} - s, 0 \leq s \leq 1,$ then $^{q + s} C_{r - s}$ is equal to

Discussion

50.	Find the 20 th term in the following sequence whose n th term is
Answer» Find the 20 th term in the following sequence whose n th term is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Suppose A1, A2,....................., A30 are thirty sets each having 5 elements each and B1, B2,................Bn are n sets each with 3 elements each. Let 30⋃i=1Ai=n⋃j=1Bj=S and each element of S belongs to exactly 10 of Ai's and exactly 9 of the Bj's. Then n is equal to

5. if tangent and normal to the curve y=2sinx+sin2x are drawn at a point p=pi/3then find the area of quadrilateral formed by the tangent normal and oordinate, x axis.

If the length of subtangent is 9 units and that of sub normal is 4 units at a point (α,β) on the curve y=f(x), then |β| is equal to

Findrif (i) (ii) .

Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.

The number of solutions of |x-1|-|x+2|=k when -3

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Let A=⎡⎢⎣xyzyzxzxy⎤⎥⎦, where x,y and z are real numbers such that x+y+z&gt;0 axyz=2. If A2=I3, then the value of x3+y3+z3 is

Why does SiO2 does not have a linear structure

The position vector of a point which moves in x-yplane is given by-The angle between the velocity v and theacceleration a when t 2 s is

A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle 60∘ with the ground. At what height from the bottom the tree is broken by the wind?

The number of integral terms in the expansion of (512+716)642 is

The ratio of the sums of m and n terms of an A.P. is m2:n2. Show that the ratio of mthand nth terms is (2m−1):(2n−1).

Verify Mean Value Theorem, ifin the interval [a, b], where a = 1 and b= 3. Find all forwhich

Simplify: 3−2×8134÷729−13

limn→∞(1n2sec21n2+2n2sec24n2+...+nn2 sec21)equals to

Find a(vector) . b(vector) and a(vector)*b(vector) if a= i+2j+k and magnitude of b=3 acting along c(vector) = i+j+k.

If x, y, z are not all zero and if ax + by + cz = 0, bx + cy + az = 0 and cx + ay + bz = 0, then x : y : z may be

Show that the Modulus Function f : R → R given by , is neither one-one nor onto, where is x , if x is positive or 0 and is − x , if x is negative.

If xy+yx=ab the find dydx. OR If ey(x+1)=1, then show that d2ydx2=(dydx)2.

Solve }\operatorname{log}_{(x+3)}(x^2-x)

limx→−1(1+x+x2+⋯+x100) is equal to

The angle between the planes 3x - 4y + 5z = 0 and 2x -y - 2z = 5 is [MP PET 1988]

The Arithmetic Mean of the observations 1.3.5,3.5.7,5.7.9,...,(2n−1)(2n+1)(2n+3) is (∀n∈N)

An integer x is chosen from the first 50 positive integers. The probability that, x+100x&gt;50, is:

In a triangle ABC, if a = 2, b = 4 and A+B=2π3, then area of ∆ABC is __________.

If the normal at point (1,2) on the parabola y2=4x meets the parabola again a point (t2,2t), then the value of t is

The value of 1sin20∘−1√3cos20∘ is

Let a=(41/401−1) and for each n≥2, let bn=nC1+nC2⋅a+nC3⋅a2+⋯+nCn⋅an−1. Then the value of (b2006−b2005) is

729 small spherical water drops, each of radius 1 mm, combine to form a spherical big drop. The decrease in surface energy is about (Take surface tension of water = 6 × 10–2 N/m)

If 3x+5y+17=0 is polar for the circle x2+y2+4x+6y+9=0, then the pole is

Evaluate the following determinant:(i) 1352610311138(ii) 671921391314812426(iii) ahghbfgfc(iv) 1-324-12352(v) 149491691625(vi) 6-322-12-1052(vii) 13927392719271327139(viii)

Let z=x+iy be a complex number. The equation arg(z+1z)=π4 represents

Find the derivative of (x+a), where a is a fixed non-zero constant.

Find the least value of a suchthat the function f given isstrictly increasing on (1, 2).

Which of the following is correct? A. Determinant is a square matrix. B. Determinant is a number associated to a matrix. C. Determinant is a number associated to a square matrix. D. None of these

If 0&lt;a&lt;b, then which of the following is correct :

106.The number of solution for (5x+7) -(3x+1) = (x+3)

A wheel has been divided in 5 equal sector three ok which are green ,one blue and the remaining one red . If i spin the wheel once ,what is probably of getting a non blue sector?

Prove, cos−145+cos−11213=cos−13365

limx→02x−sinxtanx+x

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests : Ravi :25504530704236483560Hashina :10705020955542604880 Who is more intelligent and who is more consistent ?

12. State whether each of the following statement is true or false. Justify your answer(i) {2,3, 4, 5 ] and 3, 6) are disjoint sets.(ii) t a, e, i, o, u | and { a, b, c, d jare disjoint sets(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.(iv) 2,6, 10 ) and 3, 7, 11] are disjoint sets

The maximum value of f(x) = x e−x is _______________.

Which of the following transformations in order will give −|(−x)+3| from |x|? (1) f(x) → f(−x) (2) f(x) → f(x+3) (3) f(x) → −f(x) (4) f(x) → f(x−3)

What do you mean by imaginary number. I am not knowing about the apt definition. I know only about the definition of imaginary part

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area then prove that 1V=2S1a+1b+1c.

In the matrixA=⎡⎢⎢⎢⎣2519−735−25212√31−517⎤⎥⎥⎥⎦(i). Write the order of the matrix(ii). Write the numbers of element.(iii). Write the elements a13,a21,a33,a24,a23

If 1P1+2⋅2P2+3⋅3P3+⋯+15⋅15P15=qPr−s, 0≤s≤1, then q+sCr−s is equal to

Find the 20 th term in the following sequence whose n th term is

Let A=⎡⎢⎣xyzyzxzxy⎤⎥⎦, where x,y and z are real numbers such that x+y+z>0 axyz=2. If A2=I3, then the value of x3+y3+z3 is

An integer x is chosen from the first 50 positive integers. The probability that, x+100x>50, is:

If 0<a<b, then which of the following is correct :