43030 + Interview Questions in Mathematics Page 173 InterviewSolution

8601.	In triangle ABC, the equation of side BC is y=x. The centroid of Triangle ABC is (8,3) and Circumcentre id (9,3). if the circumradius of Triangle is R, then R/root 5 =
Answer» In triangle ABC, the equation of side BC is y=x. The centroid of Triangle ABC is (8,3) and Circumcentre id (9,3). if the circumradius of Triangle is R, then R/root 5 =

Discussion

8602.	If 0 < x < π2, then sin-1 (cos x) + cos-1 (sin x) = ___________________.
Answer» If 0 < x < $\frac{π}{2}$ , then sin^-1 (cos x) + cos^-1(sin x) = ___________________.

Discussion

8603.	The coefficient of x10 in the expansion of [1+x2(1−x)]8 is
Answer» The coefficient of $x^{10}$ in the expansion of $[1 + x^{2} (1 - x)]^{8}$ is

Discussion

8604.	The value of sin−1(sin4)+cos−1(cos5)+tan−1(tan6)+cot−1(cot7) is
Answer» The value of ${sin}^{- 1} (sin 4) + {cos}^{- 1} (cos 5) + {tan}^{- 1} (tan 6) + {cot}^{- 1} (cot 7)$ is

Discussion

8605.	If A=⎡⎢⎣101012004⎤⎥⎦, then show that \|3A\|=27\|A\|.
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 1 0 & 1 & 2 0 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦$ , then show that $\| 3 A \| = 27 \| A \|$ .

Discussion

8606.	The common chord of the circle x2+y2+4x+1=0 and x2+y2+6x+2y+3=0 is
Answer» The common chord of the circle $x^{2} + y^{2} + 4 x + 1 = 0$ and $x^{2} + y^{2} + 6 x + 2 y + 3 = 0$ is

Discussion

8607.	The sides of a triangle are in A.P. If the angles A and C are the greatest and smallest angle respectively, then 4(1−cosA)(1−cosC) is equal to
Answer» The sides of a triangle are in $A . P .$ If the angles $A$ and $C$ are the greatest and smallest angle respectively, then $4 (1 - cos A) (1 - cos C)$ is equal to

Discussion

8608.	Let a=5i-j=7k and , if and b=i-j+lambda k, if a+b and a-b are orthogonal then the value of λ is
Answer» Let a=5i-j=7k and , if and b=i-j+lambda k, if a+b and a-b are orthogonal then the value of λ is

Discussion

8609.	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): f(x)= (ax+b)n(cx+d)m
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): f(x)= $(a x + b)^{n} (c x + d)^{m}$

Discussion

8610.	A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble?
Answer» A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble?

Discussion

8611.	If the coefficient of x in the expansion of (x2+kx)5 is 270, then k =
Answer» If the coefficient of x in the expansion of $(x^{2} + \frac{k}{x})^{5}$ is 270, then k =

8611.

If the coefficient of x in the expansion of (x2+kx)5 is 270, then k =

Answer»

If the coefficient of x in the expansion of $(x^{2} + \frac{k}{x})^{5}$ is 270, then k =

Discussion

8612.	If , find A −1 . Using A −1 solve the system of equations
Answer» If , find A −1 . Using A −1 solve the system of equations

Discussion

8613.	For the equation px4+qx3+rx2+sx+t=0;p>0, all the roots are positive real numbers, then which of the following is/are true?
Answer» For the equation $p x^{4} + q x^{3} + r x^{2} + s x + t = 0; p > 0$ , all the roots are positive real numbers, then which of the following is/are true?

Discussion

8614.	If a , b and c are real numbers, and , Show that either a + b + c = 0 or a = b = c .
Answer» If a , b and c are real numbers, and , Show that either a + b + c = 0 or a = b = c .

Discussion

8615.	Write the polynomial in x using the given information.(i) Monomial with degree 7 (ii) Binomial with degree 35(iii) Trinomial with degree 8
Answer» Write the polynomial in x using the given information. (i) Monomial with degree 7 (ii) Binomial with degree 35 (iii) Trinomial with degree 8

Discussion

8616.	70. If cosx+cos7x+cos3x+cos5x=0 then x= (A)n(pi)/4,n=Z (B)n(pi)/2,n=I (C)n(pi)/8;n+8k,n,z=Z (D)n(pi)/3;n=Z
Answer» 70. If cosx+cos7x+cos3x+cos5x=0 then x= (A)n(pi)/4,n=Z (B)n(pi)/2,n=I (C)n(pi)/8;n+8k,n,z=Z (D)n(pi)/3;n=Z

Discussion

8617.	7.The angle that the vector OA = 5i+5/ makes withy-axis is(1) 30^° (2) 45^° (3) 60^° -1(4) tan
Answer» 7.The angle that the vector OA = 5i+5/ makes withy-axis is(1) 30^° (2) 45^° (3) 60^° -1(4) tan

Discussion

8618.	If y(x) is a solution of (2+sinx1+y)dydx=−cosx and y(0)=1,then find the value of y(π2).
Answer» If y(x) is a solution of $(\frac{2 + s i n x}{1 + y}) \frac{d y}{d x} = - c o s x a n d y (0) = 1,$ then find the value of $y (\frac{π}{2}) .$

Discussion

8619.	If the function f(x) = x4+bx2+8x+1 has a horizontal tangent and a point of inflection for the same value of x, then the value of b is equal to
Answer» If the function f(x) = $x^{4} + b x^{2} + 8 x + 1$ has a horizontal tangent and a point of inflection for the same value of x, then the value of b is equal to

Discussion

8620.	Let the mirror image of the point (1,3,a) with respect to the plane →r⋅(2^i−^j+^k)−b=0 be (–3,5,2). Then, the value of \|a+b\| is equal to
Answer» Let the mirror image of the point $(1, 3, a)$ with respect to the plane $\to r \cdot (2^i -^j +^k) - b = 0$ be $(- 3, 5, 2) .$ Then, the value of $\| a + b \|$ is equal to

Discussion

8621.	Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with atleast one letter repeated is
Answer» Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with atleast one letter repeated is

Discussion

8622.	If f(x)=x+sinx, then the differential coefficient of f(x) at x=0, is
Answer» If $f (x) = x + sin x,$ then the differential coefficient of $f (x)$ at $x = 0,$ is

Discussion

8623.	Find the value of c if the line y = 3x + c is a tangent to the circle x2+y2=10
Answer» Find the value of c if the line y = 3x + c is a tangent to the circle $x^{2} + y^{2} = 10$

Discussion

8624.	If →a,→b,→c are three non coplanar vectors and a vector →r satisfying the vector equation →r.→a=→r.→b=→r.→c=1 is:
Answer» If $\to a, \to b, \to c$ are three non coplanar vectors and a vector $\to r$ satisfying the vector equation $\to r . \to a = \to r . \to b = \to r . \to c = 1$ is:

Discussion

8625.	20. A.All squares ,rectangles ,rhombuses are parallelogram while converse need not to true. B. All squares are Rhombus while Converse is not true.
Answer» 20. A.All squares ,rectangles ,rhombuses are parallelogram while converse need not to true. B. All squares are Rhombus while Converse is not true.

Discussion

8626.	If z is a complex number and l1,l2,l3,m1,m2,m3 are all real, then ∣∣∣∣l1z+m1¯zm1z+l1¯zm1z+l1l2z+m2¯zm2z+l2¯zm2z+l2l3z+m3¯zm3z+l3¯zm3z+l3∣∣∣∣ is equal to
Answer» If z is a complex number and $l_{1}, l_{2}, l_{3}, m_{1}, m_{2}, m_{3}$ are all real, then $∣ ∣∣ ∣ \begin{matrix} l_{1} z + m_{1} ¯ z & m_{1} z + l_{1} ¯ z & m_{1} z + l_{1} l_{2} z + m_{2} ¯ z & m_{2} z + l_{2} ¯ z & m_{2} z + l_{2} l_{3} z + m_{3} ¯ z & m_{3} z + l_{3} ¯ z & m_{3} z + l_{3} \end{matrix} ∣ ∣∣ ∣$ is equal to

Discussion

8627.	If A=023-4 and k A=03a2b24, then (k, a, b) =___________.
Answer» If $A = [\begin{matrix} 0 & 2 \\ 3 & - 4 \end{matrix}]$ and k $A = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}],$ then (k, a, b) =___________.

Discussion

8628.	Prove that following identities: sin3 A+sin3(2π3+A)+sin3(4π3+A)
Answer» Prove that following identities: $s i n^{3} A + s i n^{3} (\frac{2 π}{3} + A) + s i n^{3} (\frac{4 π}{3} + A)$

8628.

Prove that following identities: sin3 A+sin3(2π3+A)+sin3(4π3+A)

Answer»

Prove that following identities:

$s i n^{3} A + s i n^{3} (\frac{2 π}{3} + A) + s i n^{3} (\frac{4 π}{3} + A)$

Discussion

8629.	Find the value of x in each of the following :3 sin x=cos x
Answer» Find the value of x in each of the following : $\sqrt{3} \sin x = \cos x$

Discussion

8630.	A particle moves along a straight line OX . At a time t(in seconds) the distance x=40+12t-t . How long would the particle travel before coming to rest?
Answer» A particle moves along a straight line OX . At a time t(in seconds) the distance x=40+12t-t . How long would the particle travel before coming to rest?

Discussion

8631.	If y=f(x) satisfies 2exy2+y cos(x2)=4 then value of ∣∣∣f′(0)5∣∣∣ is
Answer» If $y = f (x) satisfies 2 e^{x y^{2}} + y c o s (x^{2}) = 4$ then value of $∣ ∣ ∣ \frac{f^{'} (0)}{5} ∣ ∣ ∣$ is

Discussion

8632.	Find the missing term that should be placed in place of ? for a logical pattern.
Answer» Find the missing term that should be placed in place of ? for a logical pattern.

Discussion

8633.	Is the function f(x)=(x+2)/(x+1) monotonic decreasing? Find the maximum value of f(x) in [1,2]
Answer» Is the function f(x)=(x+2)/(x+1) monotonic decreasing? Find the maximum value of f(x) in [1,2]

Discussion

8634.	Find all points of discontinuity of f,where f isdefined by
Answer» Find all points of discontinuity of f, where f is defined by

8634.

Find all points of discontinuity of f,where f isdefined by

Answer»

Find all points of discontinuity of f,
where f is
defined by

Discussion

8635.	The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is2α. The equation of the locus of the point P is
Answer» The angle between a pair of tangents drawn from a point P to the circle $x^{2} + y^{2} + 4 x - 6 y + 9 s i n^{2} α + 13 c o s^{2} α = 0 i s 2 α$ . The equation of the locus of the point P is

Discussion

8636.	6. If x and y are prime numbers the the number of possible solutions of 11x + 13y = 367. Are
Answer» 6. If x and y are prime numbers the the number of possible solutions of 11x + 13y = 367. Are

Discussion

8637.	P is a variable point on the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQRS is completed. If P≡(3,4), then coordinate of S is
Answer» $P$ is a variable point on the line $L = 0$ . Tangents are drawn to the circle $x^{2} + y^{2} = 4$ from $P$ to touch it at $Q$ and $R$ . The parallelogram $P Q R S$ is completed. If $P \equiv (3, 4)$ , then coordinate of $S$ is

Discussion

8638.	If α,β be the roots of the equation ax2+bx+c=0. Let Sn=αn+βn, for n≥1 If Δ=∣∣∣∣31+S11+S21+S11+S21+S31+S21+S31+S4∣∣∣∣, then Δ is equal to
Answer» If $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$ . Let $S_{n} = α^{n} + β^{n},$ for $n \geq 1$ If $Δ = ∣ ∣∣ ∣ \begin{matrix} 3 & 1 + S_{1} & 1 + S_{2} 1 + S_{1} & 1 + S_{2} & 1 + S_{3} 1 + S_{2} & 1 + S_{3} & 1 + S_{4} \end{matrix} ∣ ∣∣ ∣$ , then $Δ$ is equal to

Discussion

8639.	39. Point z moves on curve \|z-3i-4\|+\|z-5-12i\|=82 value of \|z\|min+\|z\|max is 1) 10 2)18
Answer» 39. Point z moves on curve \|z-3i-4\|+\|z-5-12i\|=82 value of \|z\|min+\|z\|max is 1) 10 2)18

Discussion

8640.	Equation(s) of the common tangent to the parabola y2=24x and the circle x2+y2=18 is/are
Answer» Equation(s) of the common tangent to the parabola $y^{2} = 24 x$ and the circle $x^{2} + y^{2} = 18$ is/are

Discussion

8641.	E due to a ring with lambda=lambda0 cost(theeta) at its center ?Detailed explanation
Answer» E due to a ring with lambda=lambda0 cost(theeta) at its center ? Detailed explanation

Discussion

8642.	The solution set of x2−4x2−16≤0 is
Answer» The solution set of $\frac{x^{2} - 4}{x^{2} - 16} \leq 0$ is

Discussion

8643.	how to find the value sin 53 degree ?
Answer» how to find the value sin 53 degree ?

Discussion

8644.	Value of tan9°+ tan36° + tan9°tan36°
Answer» Value of tan9°+ tan36° + tan9°tan36°

8644.

Value of tan9°+ tan36° + tan9°tan36°

Answer»

Value of

tan9°+ tan36° + tan9°tan36°

Discussion

8645.	Conjugue les verbes entre parenthèses :1. Vous ................. (remplir) cette fiche.2. Les fleurs ................... (fleurir) dans le jardin.3. Nous ...................... (ne pas finir) notre travail.4. Maxime ................ (choisir) le dessin multicolore.5. Je ...................... (réussir) à mon examen de français.
Answer» Conjugue les verbes entre parenthèses : 1. Vous ................. (remplir) cette fiche. 2. Les fleurs ................... (fleurir) dans le jardin. 3. Nous ...................... (ne pas finir) notre travail. 4. Maxime ................ (choisir) le dessin multicolore. 5. Je ...................... (réussir) à mon examen de français.

Discussion

8646.	In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Answer» In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Discussion

8647.	cos(cot–1x) is equal to, where x ≥ 0cos(cot–1x) का मान है, जहाँ x ≥ 0
Answer» cos(cot^–1x) is equal to, where x ≥ 0 cos(cot^–1x) का मान है, जहाँ x ≥ 0

Discussion

8648.	The matrix A=100020004 is(a) identity matrix(b) symmetric matrix(c) skew-symmetric matrix(d) diagonal matrix
Answer» The matrix $A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{matrix}]$ is (a) identity matrix (b) symmetric matrix (c) skew-symmetric matrix (d) diagonal matrix

Discussion

8649.	the flow rate of water from a tap of diameter 1cm is 0.24 litre / minute. reynolds number for this flow is
Answer» the flow rate of water from a tap of diameter 1cm is 0.24 litre / minute. reynolds number for this flow is

Discussion

8650.	46. if sin1 + sin2 + sin3 = 3 (=thita) then cos1+cos2+cos3=?
Answer» 46. if sin1 + sin2 + sin3 = 3 (=thita) then cos1+cos2+cos3=?

Discussion

Explore topic-wise InterviewSolutions in .

In triangle ABC, the equation of side BC is y=x. The centroid of Triangle ABC is (8,3) and Circumcentre id (9,3). if the circumradius of Triangle is R, then R/root 5 =

If 0 < x < π2, then sin-1 (cos x) + cos-1 (sin x) = ___________________.

The coefficient of x10 in the expansion of [1+x2(1−x)]8 is

The value of sin−1(sin4)+cos−1(cos5)+tan−1(tan6)+cot−1(cot7) is

If A=⎡⎢⎣101012004⎤⎥⎦, then show that |3A|=27|A|.

The common chord of the circle x2+y2+4x+1=0 and x2+y2+6x+2y+3=0 is

The sides of a triangle are in A.P. If the angles A and C are the greatest and smallest angle respectively, then 4(1−cosA)(1−cosC) is equal to

Let a=5i-j=7k and , if and b=i-j+lambda k, if a+b and a-b are orthogonal then the value of λ 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): f(x)= (ax+b)n(cx+d)m

A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble?

If the coefficient of x in the expansion of (x2+kx)5 is 270, then k =

If , find A −1 . Using A −1 solve the system of equations

For the equation px4+qx3+rx2+sx+t=0;p&gt;0, all the roots are positive real numbers, then which of the following is/are true?

If a , b and c are real numbers, and , Show that either a + b + c = 0 or a = b = c .

Write the polynomial in x using the given information.(i) Monomial with degree 7 (ii) Binomial with degree 35(iii) Trinomial with degree 8

70. If cosx+cos7x+cos3x+cos5x=0 then x= (A)n(pi)/4,n=Z (B)n(pi)/2,n=I (C)n(pi)/8;n+8k,n,z=Z (D)n(pi)/3;n=Z

7.The angle that the vector OA = 5i+5/ makes withy-axis is(1) 30^° (2) 45^° (3) 60^° -1(4) tan

If y(x) is a solution of (2+sinx1+y)dydx=−cosx and y(0)=1,then find the value of y(π2).

If the function f(x) = x4+bx2+8x+1 has a horizontal tangent and a point of inflection for the same value of x, then the value of b is equal to

Let the mirror image of the point (1,3,a) with respect to the plane →r⋅(2^i−^j+^k)−b=0 be (–3,5,2). Then, the value of |a+b| is equal to

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with atleast one letter repeated is

If f(x)=x+sinx, then the differential coefficient of f(x) at x=0, is

Find the value of c if the line y = 3x + c is a tangent to the circle x2+y2=10

If →a,→b,→c are three non coplanar vectors and a vector →r satisfying the vector equation →r.→a=→r.→b=→r.→c=1 is:

20. A.All squares ,rectangles ,rhombuses are parallelogram while converse need not to true. B. All squares are Rhombus while Converse is not true.

If z is a complex number and l1,l2,l3,m1,m2,m3 are all real, then ∣∣∣∣l1z+m1¯zm1z+l1¯zm1z+l1l2z+m2¯zm2z+l2¯zm2z+l2l3z+m3¯zm3z+l3¯zm3z+l3∣∣∣∣ is equal to

If A=023-4 and k A=03a2b24, then (k, a, b) =___________.

Prove that following identities: sin3 A+sin3(2π3+A)+sin3(4π3+A)

Find the value of x in each of the following :3 sin x=cos x

A particle moves along a straight line OX . At a time t(in seconds) the distance x=40+12t-t . How long would the particle travel before coming to rest?

If y=f(x) satisfies 2exy2+y cos(x2)=4 then value of ∣∣∣f′(0)5∣∣∣ is

Find the missing term that should be placed in place of ? for a logical pattern.

Is the function f(x)=(x+2)/(x+1) monotonic decreasing? Find the maximum value of f(x) in [1,2]

Find all points of discontinuity of f,where f isdefined by

The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is2α. The equation of the locus of the point P is

6. If x and y are prime numbers the the number of possible solutions of 11x + 13y = 367. Are

P is a variable point on the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQRS is completed. If P≡(3,4), then coordinate of S is

If α,β be the roots of the equation ax2+bx+c=0. Let Sn=αn+βn, for n≥1 If Δ=∣∣∣∣31+S11+S21+S11+S21+S31+S21+S31+S4∣∣∣∣, then Δ is equal to

39. Point z moves on curve |z-3i-4|+|z-5-12i|=82 value of |z|min+|z|max is 1) 10 2)18

Equation(s) of the common tangent to the parabola y2=24x and the circle x2+y2=18 is/are

E due to a ring with lambda=lambda0 cost(theeta) at its center ?Detailed explanation

The solution set of x2−4x2−16≤0 is

how to find the value sin 53 degree ?

Value of tan9°+ tan36° + tan9°tan36°

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

cos(cot–1x) is equal to, where x ≥ 0cos(cot–1x) का मान है, जहाँ x ≥ 0

The matrix A=100020004 is(a) identity matrix(b) symmetric matrix(c) skew-symmetric matrix(d) diagonal matrix

the flow rate of water from a tap of diameter 1cm is 0.24 litre / minute. reynolds number for this flow is

46. if sin1 + sin2 + sin3 = 3 (=thita) then cos1+cos2+cos3=?

For the equation px4+qx3+rx2+sx+t=0;p>0, all the roots are positive real numbers, then which of the following is/are true?