43030 + Interview Questions in Mathematics

1.	Find a vector in the direction of vector 5^i−^j+2^k which has magnitude 8 unit.
Answer» Find a vector in the direction of vector $5^i -^j + 2^k$ which has magnitude 8 unit.

Discussion

2.	A man rides his motorcycle at the speed of 50km/h.He has to spend Rs 2 per km in petrol.If he rides it at a faster speed of 80km/h,the petrol cost increases to Rs 3 per km.He has atmost Rs 120 to spend on petrol and one hour's time.Using LPP find the maximum distance he can travel.
Answer» A man rides his motorcycle at the speed of 50km/h.He has to spend Rs 2 per km in petrol.If he rides it at a faster speed of 80km/h,the petrol cost increases to Rs 3 per km.He has atmost Rs 120 to spend on petrol and one hour's time.Using LPP find the maximum distance he can travel.

Discussion

3.	Find the following integrals. ∫x3+5x2−4x2dx.
Answer» Find the following integrals. $\int \frac{x^{3} + 5 x^{2} - 4}{x^{2}} d x .$

Discussion

4.	Find the sum of the order and degree of the given differential equation : y = x (dydx)3+d2ydx2.
Answer» Find the sum of the order and degree of the given differential equation : y = x ${(\frac{d y}{d x})}^{3} + \frac{d^{2} y}{d x^{2}} .$

Discussion

5.	The memers of a consulting firm rent cars from three rental agencies: 50% from agency X, 20% from agency Y and 20% from agency Z. Form past experience, it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of cars from agency Y need a service and tuning before renting and 10% of the cars from agency Z need a service and tuning before renting. If the rental car delivered to the firm need service and tuning, find the probability that agency Z is not to be blamed.
Answer» The memers of a consulting firm rent cars from three rental agencies: 50% from agency X, 20% from agency Y and 20% from agency Z. Form past experience, it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of cars from agency Y need a service and tuning before renting and 10% of the cars from agency Z need a service and tuning before renting. If the rental car delivered to the firm need service and tuning, find the probability that agency Z is not to be blamed.

Discussion

6.	Refer to question 27. Maximum of Z occurs at (a)(5,0) (b)(6,5) (c)(6,8) (d)(4,10)
Answer» Refer to question 27. Maximum of Z occurs at (a)(5,0) (b)(6,5) (c)(6,8) (d)(4,10)

Discussion

7.	Integrate the following functions. ∫(x3−1)13x5dx.
Answer» Integrate the following functions. $\int (x^{3} - 1)^{\frac{1}{3}} x^{5} d x .$

Discussion

8.	Let a2,a3 ∈ R such that \|a2−a3\|=6 and f(x)=∣∣∣∣1a3a21a32a2−x12a3−xa2∣∣∣∣, xϵR, then the greatest value of f(x) is -
Answer» Let $a_{2}, a_{3} \in R$ such that $\| a_{2} - a_{3} \| = 6$ and $f (x) = ∣ ∣∣ ∣ \begin{matrix} 1 & a_{3} & a_{2} 1 & a_{3} & 2 a_{2} - x 1 & 2 a_{3} - x & a_{2} \end{matrix} ∣ ∣∣ ∣, x ϵ R$ , then the greatest value of $f (x)$ is -

Discussion

9.	If one of the roots of equation px^2-14x+8=0 is six times the other then p equal to
Answer» If one of the roots of equation px^2-14x+8=0 is six times the other then p equal to

Discussion

10.	If the ratio of area of triangle inscribed in the ellipse x2a2+y2b2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 12, then the eccentricity of the ellipse is
Answer» If the ratio of area of triangle inscribed in the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ to that of triangle formed by the corresponding points on the auxiliary circle is $\frac{1}{2}$ , then the eccentricity of the ellipse is

Discussion

11.	A pollution filtering machine is installed in a factory, on a floor with area 2500 sq. feet. The machine is expected to filter at least 3500 liters of air and water. It filters air at the rate of 600 liters per hour and it filters water at the rate of 250 liter per hour. Which of the following inequalities represents the number of hours the machine should filter air (A) and water (W) to meet the expectation?
Answer» A pollution filtering machine is installed in a factory, on a floor with area 2500 sq. feet. The machine is expected to filter at least 3500 liters of air and water. It filters air at the rate of 600 liters per hour and it filters water at the rate of 250 liter per hour. Which of the following inequalities represents the number of hours the machine should filter air (A) and water (W) to meet the expectation?

Discussion

12.	If the line 2x + √6y = 2 is tangent to the hyperbola x2 − 2y2 = 4 then the point of contact is.
Answer» If the line $2 x + \sqrt{6} y = 2$ is tangent to the hyperbola $x^{2} - 2 y^{2} = 4$ then the point of contact is.

Discussion

13.	If z is any complex number satisfying \|z−3−2i\|≤2, then the minimum value of \|2z−6+5i\| is
Answer» If $z$ is any complex number satisfying $\| z - 3 - 2 i \| \leq 2,$ then the minimum value of $\| 2 z - 6 + 5 i \|$ is

Discussion

14.	A plane P intersects lines L1, L2, L3 and L4 at A, B, C, D L1:x−32=y−31=z−32 L2:x−32=y−31=z2L3:x2=y−31=z2 L4:x2=y−31=z−32 then the minimum area of quadrilateral ABCD is ___.
Answer» A plane P intersects lines $L_{1}, L_{2}, L_{3} a n d L_{4}$ at A, B, C, D $L_{1} : \frac{x - 3}{2} = \frac{y - 3}{1} = \frac{z - 3}{2} L_{2} : \frac{x - 3}{2} = \frac{y - 3}{1} = \frac{z}{2} L_{3} : \frac{x}{2} = \frac{y - 3}{1} = \frac{z}{2} L_{4} : \frac{x}{2} = \frac{y - 3}{1} = \frac{z - 3}{2}$ then the minimum area of quadrilateral ABCD is ___.

Discussion

15.	If the circles x2+y2+2ax+cy+a=0 and x2+y2−3ax+dy−1=0 interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for (2005)
Answer» If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for (2005)

Discussion

16.	5 boys and 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together and the other 2 girls are also together but seprate from the first 2 ?
Answer» 5 boys and 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together and the other 2 girls are also together but seprate from the first 2 ?

Discussion

17.	A group of r boys is to be formed from 9 boys. The value of r for which we get maximun number of different groups is
Answer» A group of $r$ boys is to be formed from $9$ boys. The value of $r$ for which we get maximun number of different groups is

Discussion

18.	The integral value(s) of x which satisfies the inequality 4x+5≤2x+17 is/are
Answer» The integral value(s) of $x$ which satisfies the inequality $4 x + 5 \leq 2 x + 17$ is/are

Discussion

19.	If ∫cos2xsin6xdx=Acot5x+Bcot3x+k, then A+B equals
Answer» If $\int \frac{c o s^{2} x}{s i n^{6} x} d x = A c o t^{5} x + B c o t^{3} x + k$ , then A+B equals

Discussion

20.	If \|z\|=1 and \|ω−1\|=1 where z,ω∈C, then the largest set of values of \|2z−1\|2+\|2ω−1\|2 equals
Answer» If \|z\|=1 and $\| ω - 1 \| = 1$ where $z, ω \in C$ , then the largest set of values of $\| 2 z - 1 \|^{2} + \| 2 ω - 1 \|^{2}$ equals

Discussion

21.	In a hyperbola the distance between the foci is three times the distance between the directories then its eccentricity is
Answer» In a hyperbola the distance between the foci is three times the distance between the directories then its eccentricity is

Discussion

22.	If ax+by+cz=d intersects the coordinate axis at A, B, C and the area of the triangle ABC is (a2+b2)√2(a2+c2+b2)a2b2(a2+b2). If a2, c2, b2 are in A.P. then find the perpendicular distance of the plane from the origin.
Answer» If $a x + b y + c z = d$ intersects the coordinate axis at $A, B, C$ and the area of the triangle $A B C$ is $(a^{2} + b^{2}) \sqrt{\frac{2 (a^{2} + c^{2} + b^{2})}{a^{2} b^{2} (a^{2} + b^{2})}}$ . If $a^{2}, c^{2}, b^{2}$ are in A.P. then find the perpendicular distance of the plane from the origin.

Discussion

23.	The total number of positive integral solutions (x,y,z) such that xyz=24 is
Answer» The total number of positive integral solutions $(x, y, z)$ such that $x y z = 24$ is

Discussion

24.	The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their A.Ms are
Answer» The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their A.Ms are

Discussion

25.	If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g−1(x), is
Answer» If $f (x)$ is an invertible function and $g (x) = 2 f (x) + 5$ , then the value of $g^{- 1} (x)$ , is

Discussion

26.	The differential equation whose general solution is given by, y=(c1cos(x+c2))−(c3e(−x+c4))+(c5sin x) where c1,c2,c3,c4,c5 are arbitrary constants, is
Answer» The differential equation whose general solution is given by, $y = (c_{1} c o s (x + c_{2})) - (c_{3} e^{(- x + c_{4})}) + (c_{5} s i n x)$ where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants, is

Discussion

27.	A randomly selected year is containing 53 Mondays then probability that it is a leap year
Answer» A randomly selected year is containing 53 Mondays then probability that it is a leap year

Discussion

28.	The value of (1+i)5(1−i)5 is
Answer» The value of $(1 + i)^{5} (1 - i)^{5}$ is

Discussion

29.	If 1b−a+1b−c = 1a+1c, then a,b,c are in
Answer» If $\frac{1}{b - a} + \frac{1}{b - c}$ = $\frac{1}{a} + \frac{1}{c}$ , then a,b,c are in

Discussion

30.	Show that the four points A(4,5,1), B(0,−1,−1), C(3,9,4) and D(−4,4,4) are co-planar.
Answer» Show that the four points $A (4, 5, 1), B (0, - 1, - 1), C (3, 9, 4)$ and $D (- 4, 4, 4)$ are co-planar.

Discussion

31.	∫esinx(x cos3x−sinxcos2x)dx,is equal to
Answer» $\int e^{s i n x} (\frac{x c o s^{3} x - s i n x}{c o s^{2} x}) d x$ ,is equal to

Discussion

32.	Given six non-parallel line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is _____.
Answer» Given six non-parallel line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is _____.

Discussion

33.	An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/ s2 west for 3 second. During this time the object travels a distance of :
Answer» An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/ $s^{2}$ west for 3 second. During this time the object travels a distance of :

Discussion

34.	Matching type questions: Column−I Column−II(P)No.of points of intersection of curves \|y\|=ln\|x\|and(x−1)2+y2−4=0(1)1(Q)Sn=∑nr=1(n>6) then Sn–7[Sn7] is (where[x] denotes integer less than or equal to x)(2)2(R)Equation of tangent at z0 to the circle \|z\|=r is Re(zz0)=λ,then l is(3)3(S)Normal drawn at any point of an ellipsex225+y29,is tangent to the(4)5 circle x2+y2=r2then maximum value of r is (5)5
Answer» Matching type questions: $\begin{matrix} C o l u m n - I & C o l u m n - I I (P) & N o . o f p o i n t s o f i n t e r s e c t i o n o f c u r v e s \| y \| = l n \| x \| a n d (x - 1)^{2} + y^{2} - 4 = 0 & (1) & 1 (Q) & S_{n} = \sum_{r = 1}^{n} (n > 6) t h e n S_{n} - 7 [\frac{S_{n}}{7}] i s (w h e r e [x] d e n o t e s i n t e g e r l e s s t h a n o r e q u a l t o x) & (2) & 2 (R) & E q u a t i o n o f t a n g e n t a t z_{0} t o t h e c i r c l e \| z \| = r i s R e (\frac{z}{z_{0}}) = λ, t h e n l i s & (3) & 3 (S) & N o r m a l d r a w n a t a n y p o i n t o f a n e l l i p s e \frac{x^{2}}{25} + \frac{y^{2}}{9}, i s t a n g e n t t o t h e & (4) & 5 c i r c l e x^{2} + y^{2} = r^{2} t h e n m a x i m u m v a l u e o f r i s (5) & 5 \end{matrix}$

34.

Matching type questions: Column−I Column−II(P)No.of points of intersection of curves |y|=ln|x|and(x−1)2+y2−4=0(1)1(Q)Sn=∑nr=1(n>6) then Sn–7[Sn7] is (where[x] denotes integer less than or equal to x)(2)2(R)Equation of tangent at z0 to the circle |z|=r is Re(zz0)=λ,then l is(3)3(S)Normal drawn at any point of an ellipsex225+y29,is tangent to the(4)5 circle x2+y2=r2then maximum value of r is (5)5

Answer»

Matching type questions:

$\begin{matrix} C o l u m n - I & C o l u m n - I I (P) & N o . o f p o i n t s o f i n t e r s e c t i o n o f c u r v e s | y | = l n | x | a n d (x - 1)^{2} + y^{2} - 4 = 0 & (1) & 1 (Q) & S_{n} = \sum_{r = 1}^{n} (n > 6) t h e n S_{n} - 7 [\frac{S_{n}}{7}] i s (w h e r e [x] d e n o t e s i n t e g e r l e s s t h a n o r e q u a l t o x) & (2) & 2 (R) & E q u a t i o n o f t a n g e n t a t z_{0} t o t h e c i r c l e | z | = r i s R e (\frac{z}{z_{0}}) = λ, t h e n l i s & (3) & 3 (S) & N o r m a l d r a w n a t a n y p o i n t o f a n e l l i p s e \frac{x^{2}}{25} + \frac{y^{2}}{9}, i s t a n g e n t t o t h e & (4) & 5 c i r c l e x^{2} + y^{2} = r^{2} t h e n m a x i m u m v a l u e o f r i s (5) & 5 \end{matrix}$

Discussion

35.	Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorders; and one college teachers owns all three. Then how many of the 50 college teachers own none of three, colour TV, VCR or tape recorder?
Answer» Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, $22$ own colour TV, $15$ own VCR and $14$ own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorders; and one college teachers owns all three. Then how many of the $50$ college teachers own none of three, colour TV, VCR or tape recorder?

Discussion

36.	x2−6x+5≤ 0, x2−2x> 0 where x is an integer. Find all the possible values of x.
Answer» $x^{2} - 6 x + 5 \leq 0, x^{2} - 2 x$ > 0 where $x$ is an integer. Find all the possible values of $x$ .

Discussion

37.	The function f (x) = -3x + 12 on R.is
Answer» The function f (x) = -3x + 12 on R.is

Discussion

38.	The number of solutions of the equation\|cot x\| = cot x + 1sinx ,0 < x < 2π, is
Answer» The number of solutions of the equation\|cot x\| = cot x + $\frac{1}{s i n x}$ ,0 < x < 2 $π$ , is

Discussion

39.	Let OABC be a rectangle, where O is the origin and A, C lie on the parabola y=x2. If B lies on a parabola whose vertex coordinates is (α,β), then the value of α+β is
Answer» Let $O A B C$ be a rectangle, where $O$ is the origin and $A$ , $C$ lie on the parabola $y = x^{2}$ . If $B$ lies on a parabola whose vertex coordinates is $(α, β)$ , then the value of $α + β$ is

Discussion

40.	Let f and g are two real valued differentiable functions satisfying. f(x)=α→0Lt1α4∫α0(ex+t−ex)(ln2(t+1))2t2+3dtand∫x0g(t)dt=3x+∫0xcos2t g(t) dt f(ln6) =
Answer» Let f and g are two real valued differentiable functions satisfying. $f (x) = α \to 0 L t \frac{1}{α^{4}} \int_{0}^{α} \frac{(e^{x + t} - e^{x}) (l n^{2} (t + 1))}{2 t^{2} + 3} d t a n d \int_{0}^{x} g (t) d t = 3 x + \int_{x}^{0} c o s^{2} t g (t) d t$ f(ln6) =

40.

Let f and g are two real valued differentiable functions satisfying. f(x)=α→0Lt1α4∫α0(ex+t−ex)(ln2(t+1))2t2+3dtand∫x0g(t)dt=3x+∫0xcos2t g(t) dt f(ln6) =

Answer»

Let f and g are two real valued differentiable functions satisfying.
$f (x) = α \to 0 L t \frac{1}{α^{4}} \int_{0}^{α} \frac{(e^{x + t} - e^{x}) (l n^{2} (t + 1))}{2 t^{2} + 3} d t a n d \int_{0}^{x} g (t) d t = 3 x + \int_{x}^{0} c o s^{2} t g (t) d t$

f(ln6) =

Discussion

41.	What is value of x in equation 81=54x-2x × 2x
Answer» What is value of x in equation 81=54x-2x × 2x

Discussion

42.	If d≠0 and a(a+d),(a+d)(a+2d),(a+2d)a are in G.P., then the common ratio is
Answer» If $d \neq 0$ and $a (a + d), (a + d) (a + 2 d), (a + 2 d) a$ are in G.P., then the common ratio is

Discussion

43.	The solution of the differential equation 2x2ydy+(1−y2)(x2y2+y2−1)dx=0 [Where c is a constant]
Answer» The solution of the differential equation $2 x^{2} y d y + (1 - y^{2}) (x^{2} y^{2} + y^{2} - 1) d x = 0$ [Where c is a constant]

Discussion

44.	tan3xtanx never lies between
Answer» $\frac{t a n 3 x}{t a n x}$ never lies between

Discussion

45.	If there are 36 gems on a necklace and out of them 1/3 are red, then the number of red gems is
Answer» If there are 36 gems on a necklace and out of them 1/3 are red, then the number of red gems is

Discussion

46.	Which of the following relation(s) is true regarding the adjoint of a matrix?
Answer» Which of the following relation(s) is true regarding the adjoint of a matrix?

Discussion

47.	(z+a)(¯z+a) , where a is real, is equivalent to
Answer» (z+a)( $¯ z$ +a) , where a is real, is equivalent to

Discussion

48.	The number of solutions of the equation x7={x} is (where {.} is the fractional part function)
Answer» The number of solutions of the equation $\frac{x}{7} = {x}$ is (where {.} is the fractional part function)

Discussion

49.	The number of real values of a satisfying the equation a2−2a sinx+1=0 is
Answer» The number of real values of a satisfying the equation $a^{2} - 2 a s i n x + 1$ =0 is

Discussion

50.	We can split the middle term of a4 + 5a2 + 6 as :
Answer» We can split the middle term of a⁴ + 5a² + 6 as :

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find a vector in the direction of vector 5^i−^j+2^k which has magnitude 8 unit.

A man rides his motorcycle at the speed of 50km/h.He has to spend Rs 2 per km in petrol.If he rides it at a faster speed of 80km/h,the petrol cost increases to Rs 3 per km.He has atmost Rs 120 to spend on petrol and one hour's time.Using LPP find the maximum distance he can travel.

Find the following integrals. ∫x3+5x2−4x2dx.

Find the sum of the order and degree of the given differential equation : y = x (dydx)3+d2ydx2.

Refer to question 27. Maximum of Z occurs at (a)(5,0) (b)(6,5) (c)(6,8) (d)(4,10)

Integrate the following functions. ∫(x3−1)13x5dx.

Let a2,a3 ∈ R such that |a2−a3|=6 and f(x)=∣∣∣∣1a3a21a32a2−x12a3−xa2∣∣∣∣, xϵR, then the greatest value of f(x) is -

If one of the roots of equation px^2-14x+8=0 is six times the other then p equal to

If the ratio of area of triangle inscribed in the ellipse x2a2+y2b2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 12, then the eccentricity of the ellipse is

If the line 2x + √6y = 2 is tangent to the hyperbola x2 − 2y2 = 4 then the point of contact is.

If z is any complex number satisfying |z−3−2i|≤2, then the minimum value of |2z−6+5i| is

A plane P intersects lines L1, L2, L3 and L4 at A, B, C, D L1:x−32=y−31=z−32 L2:x−32=y−31=z2L3:x2=y−31=z2 L4:x2=y−31=z−32 then the minimum area of quadrilateral ABCD is ___.

If the circles x2+y2+2ax+cy+a=0 and x2+y2−3ax+dy−1=0 interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for (2005)

5 boys and 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together and the other 2 girls are also together but seprate from the first 2 ?

A group of r boys is to be formed from 9 boys. The value of r for which we get maximun number of different groups is

The integral value(s) of x which satisfies the inequality 4x+5≤2x+17 is/are

If ∫cos2xsin6xdx=Acot5x+Bcot3x+k, then A+B equals

If |z|=1 and |ω−1|=1 where z,ω∈C, then the largest set of values of |2z−1|2+|2ω−1|2 equals

In a hyperbola the distance between the foci is three times the distance between the directories then its eccentricity is

If ax+by+cz=d intersects the coordinate axis at A, B, C and the area of the triangle ABC is (a2+b2)√2(a2+c2+b2)a2b2(a2+b2). If a2, c2, b2 are in A.P. then find the perpendicular distance of the plane from the origin.

The total number of positive integral solutions (x,y,z) such that xyz=24 is

The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their A.Ms are

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g−1(x), is

The differential equation whose general solution is given by, y=(c1cos(x+c2))−(c3e(−x+c4))+(c5sin x) where c1,c2,c3,c4,c5 are arbitrary constants, is

A randomly selected year is containing 53 Mondays then probability that it is a leap year

The value of (1+i)5(1−i)5 is

If 1b−a+1b−c = 1a+1c, then a,b,c are in

Show that the four points A(4,5,1), B(0,−1,−1), C(3,9,4) and D(−4,4,4) are co-planar.

∫esinx(x cos3x−sinxcos2x)dx,is equal to

Given six non-parallel line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is _____.

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/ s2 west for 3 second. During this time the object travels a distance of :

x2−6x+5≤ 0, x2−2x&gt; 0 where x is an integer. Find all the possible values of x.

The function f (x) = -3x + 12 on R.is

The number of solutions of the equation|cot x| = cot x + 1sinx ,0 &lt; x &lt; 2π, is

Let OABC be a rectangle, where O is the origin and A, C lie on the parabola y=x2. If B lies on a parabola whose vertex coordinates is (α,β), then the value of α+β is

Let f and g are two real valued differentiable functions satisfying. f(x)=α→0Lt1α4∫α0(ex+t−ex)(ln2(t+1))2t2+3dtand∫x0g(t)dt=3x+∫0xcos2t g(t) dt f(ln6) =

What is value of x in equation 81=54x-2x × 2x

If d≠0 and a(a+d),(a+d)(a+2d),(a+2d)a are in G.P., then the common ratio is

The solution of the differential equation 2x2ydy+(1−y2)(x2y2+y2−1)dx=0 [Where c is a constant]

tan3xtanx never lies between

If there are 36 gems on a necklace and out of them 1/3 are red, then the number of red gems is

Which of the following relation(s) is true regarding the adjoint of a matrix?

(z+a)(¯z+a) , where a is real, is equivalent to

The number of solutions of the equation x7={x} is (where {.} is the fractional part function)

The number of real values of a satisfying the equation a2−2a sinx+1=0 is

We can split the middle term of a4 + 5a2 + 6 as :

x2−6x+5≤ 0, x2−2x> 0 where x is an integer. Find all the possible values of x.

The number of solutions of the equation|cot x| = cot x + 1sinx ,0 < x < 2π, is