43030 + Interview Questions in Mathematics

1.	In a ΔABC, AB=AC and the length of the altitude from A to BC is h. The area and perimeter of ΔABC is A and P respectively. The circumradius of ΔABC is r. The value of 1rlimh→0AP3 is
Answer» In a $Δ A B C$ , $A B = A C$ and the length of the altitude from $A$ to $B C$ is $h$ . The area and perimeter of $Δ A B C$ is $A$ and $P$ respectively. The circumradius of $Δ A B C$ is $r$ . The value of $\frac{1}{r lim h \to 0 \frac{A}{P^{3}}}$ is

Discussion

2.	The number of permutations that can be formed out of the letters of the word "SERIES" taking three letters together is:
Answer» The number of permutations that can be formed out of the letters of the word $" S E R I E S "$ taking three letters together is:

Discussion

3.	Locus of the point of intersection of the tangents which meet at right angles is called.
Answer» Locus of the point of intersection of the tangents which meet at right angles is called.

Discussion

4.	f(x)=⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩2x2−5,x≤−83x+p,−8<x<−3(k−7)(\|3−x\|+\|3+x\|),−3≤x≤33x+9,3<x<85−2x2,x≥8 If f(x) is an odd function then the value of k−p is
Answer» $f (x) = ⎧ ⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪ ⎩ \begin{matrix} 2 x^{2} - 5, & x \leq - 8 3 x + p, & - 8 < x < - 3 (k - 7) (\| 3 - x \| + \| 3 + x \|), & - 3 \leq x \leq 3 3 x + 9, & 3 < x < 8 5 - 2 x^{2}, & x \geq 8 \end{matrix}$ If $f (x)$ is an odd function then the value of $k - p$ is

Discussion

5.	If cosec θ=135 and θ∉1stquadrant. Then the value of secθ is
Answer» If $cosec θ = \frac{13}{5}$ and $θ \notin 1^{st} quadrant$ . Then the value of $sec θ$ is

Discussion

6.	If (x−1)4−16=0, then the sum of non real complex values of x, is
Answer» If $(x - 1)^{4} - 16 = 0,$ then the sum of non real complex values of $x,$ is

Discussion

7.	If P(A)=611,P(B)=511andP(A∪B)=711, find P(A∩B) P(AB) P(BA)
Answer» If $P (A) = \frac{6}{11}, P (B) = \frac{5}{11} a n d P (A \cup B) = \frac{7}{11},$ find $P (A \cap B)$ $P (\frac{A}{B})$ $P (\frac{B}{A})$

7.

If P(A)=611,P(B)=511andP(A∪B)=711, find P(A∩B) P(AB) P(BA)

Answer»

If $P (A) = \frac{6}{11}, P (B) = \frac{5}{11} a n d P (A \cup B) = \frac{7}{11},$ find
$P (A \cap B)$

$P (\frac{A}{B})$

$P (\frac{B}{A})$

Discussion

8.	Find a vector of magnitude 6 , which is perpendicular to both the vectors 2^i−^j+2^k and 4^i−^j+3^k.
Answer» Find a vector of magnitude 6 , which is perpendicular to both the vectors $2^i -^j + 2^k and 4^i -^j + 3^k .$

Discussion

9.	Find the distance of the point 3^i−2^j+^k from the plane 3x + y - z +2=0 measured parallel to the x−12=y+2−3=z−11. Also find the foot of perpendicular from the given point upon the given plane.
Answer» Find the distance of the point $3^i - 2^j +^k$ from the plane 3x + y - z +2=0 measured parallel to the $\frac{x - 1}{2} = \frac{y + 2}{- 3} = \frac{z - 1}{1}$ . Also find the foot of perpendicular from the given point upon the given plane.

Discussion

10.	Let ∗ be a binary operation on the Q of rational number as follows: (v)a∗b=ab4 Find which of the binary operation are commutative and which are associative?
Answer» Let $$ be a binary operation on the Q of rational number as follows: $(v) a b = \frac{a b}{4}$ Find which of the binary operation are commutative and which are associative?

Discussion

11.	A problem in Mathematics is given to 4 students. A, B, C and D. Their chances of solving the problems respectively are 13,14,15 and 23. What is the probability that (i) the problem will be solved ? (ii) at most one of them will solve the problem ?
Answer» A problem in Mathematics is given to 4 students. A, B, C and D. Their chances of solving the problems respectively are $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ and $\frac{2}{3}$ . What is the probability that (i) the problem will be solved ? (ii) at most one of them will solve the problem ?

Discussion

12.	(i) Show that the matrix, A=⎡⎢⎣1−15−121513⎤⎥⎦ is a symmetric matrix (ii) Show that the matrix, A=⎡⎢⎣01−1−1011−10⎤⎥⎦ is a skew -symmetric matrix.
Answer» (i) Show that the matrix, $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 5 - 1 & 2 & 1 5 & 1 & 3 \end{matrix} ⎤ ⎥ ⎦$ is a symmetric matrix (ii) Show that the matrix, $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & - 1 - 1 & 0 & 1 1 & - 1 & 0 \end{matrix} ⎤ ⎥ ⎦$ is a skew -symmetric matrix.

12.

(i) Show that the matrix, A=⎡⎢⎣1−15−121513⎤⎥⎦ is a symmetric matrix (ii) Show that the matrix, A=⎡⎢⎣01−1−1011−10⎤⎥⎦ is a skew -symmetric matrix.

Answer»

(i) Show that the matrix, $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 5 - 1 & 2 & 1 5 & 1 & 3 \end{matrix} ⎤ ⎥ ⎦$ is a symmetric matrix

(ii) Show that the matrix, $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & - 1 - 1 & 0 & 1 1 & - 1 & 0 \end{matrix} ⎤ ⎥ ⎦$ is a skew -symmetric matrix.

Discussion

13.	Show that the lines x−57=y+2−5=z1 and x1=y2=z3 perpendicular to each other.
Answer» Show that the lines $\frac{x - 5}{7} = \frac{y + 2}{- 5} = \frac{z}{1} a n d \frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ perpendicular to each other.

Discussion

14.	If \|z1\|=\|z2\|=\|z3\|=...=\|zn\|=1 then prove that ∣∣∣1z1+1z2+1z3+...+1zn∣∣∣=\|z1+z2+z3+...+zn\|.
Answer» If $\| z_{1} \| = \| z_{2} \| = \| z_{3} \| = . . . = \| z_{n} \| = 1$ then prove that $∣ ∣ ∣ \frac{1}{z_{1} + \frac{1}{z_{2}} + \frac{1}{z_{3}}} + . . . + \frac{1}{z_{n}} ∣ ∣ ∣ = \| z_{1} + z_{2} + z_{3} + . . . + z_{n} \| .$

Discussion

15.	In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Answer» In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Discussion

16.	If the length of the transverse and conjugate axes of a hyperbola are 8 and 6 units respectively, then the absolute value of difference of focal distances of any point of the hyperbola is unit.
Answer» If the length of the transverse and conjugate axes of a hyperbola are $8$ and $6$ units respectively, then the absolute value of difference of focal distances of any point of the hyperbola is unit.

Discussion

17.	Let the projection of the line L:x−12=y+2−1=z−23 in the plane 3x+2y+z=5 is L′. If the distance of a plane from the origin which contains the lines L and L′ is p, then the value of 6p2 is
Answer» Let the projection of the line $L : \frac{x - 1}{2} = \frac{y + 2}{- 1} = \frac{z - 2}{3}$ in the plane $3 x + 2 y + z = 5$ is $L^{'}$ . If the distance of a plane from the origin which contains the lines $L$ and $L^{'}$ is $p$ , then the value of $6 p^{2}$ is

Discussion

18.	Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral ∫10(acxb+1+a3bx3b+5) dx is independent of ‘b’ equals
Answer» Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral $\int_{0}^{1} (a c x^{b + 1} + a^{3} b x^{3 b + 5})$ dx is independent of ‘b’ equals

Discussion

19.	The equation of a circle passing through points of intersection of the circles x2+y2+13x−3y=0 and 2x2+2y2+4x−7y−25=0 and point (1, 1) is
Answer» The equation of a circle passing through points of intersection of the circles $x^{2} + y^{2} + 13 x - 3 y = 0$ and $2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0$ and point (1, 1) is

19.

The equation of a circle passing through points of intersection of the circles x2+y2+13x−3y=0 and 2x2+2y2+4x−7y−25=0 and point (1, 1) is

Answer»

The equation of a circle passing through points of intersection of the circles $x^{2} + y^{2} + 13 x - 3 y = 0$ and

$2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0$ and point (1, 1) is

Discussion

20.	If A,B,C are acute positive angles such that A+B+C=π and cotAcotBcotC=k, then
Answer» If $A, B, C$ are acute positive angles such that $A + B + C = π$ and $cot A cot B cot C = k$ , then

Discussion

21.	If p=(8+3√7)n and f=p−[p], then the value of p(1−f) is (where [.] denotes the greatest integer function)
Answer» If $p = (8 + 3 \sqrt{7})^{n}$ and $f = p - [p]$ , then the value of $p (1 - f)$ is (where [.] denotes the greatest integer function)

Discussion

22.	If the vertices of a triangle be (a, b - c), (b, c - a) and (c, a - b), then the centroid of the triangle lies
Answer» If the vertices of a triangle be (a, b - c), (b, c - a) and (c, a - b), then the centroid of the triangle lies

Discussion

23.	f:R→R, f(x)=x\|x\| is
Answer» $f : R \to R, f (x) = x \| x \| i s$

Discussion

24.

A random variable ′X′ has the following probability distribution: X 1 2 3 4 5 6 7 P(X) k−1 3k k 3k 3k2 k2 k2+k Then the value of k is

Answer»

A random variable $^{'} X^{'}$ has the following probability distribution:

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X)$	$k - 1$	$3 k$	$k$	$3 k$	$3 k^{2}$	$k^{2}$	$k^{2} + k$

Then the value of

k

is

Discussion

25.	The coefficient of xn in (1+x)2(1−x)3 is :
Answer» The coefficient of $x^{n}$ in $\frac{(1 + x)^{2}}{(1 - x)^{3}}$ is :

Discussion

26.	If Φ(x)=∫dxsin12x cos72x, then Φ(π4)−Φ(0)=
Answer» If $Φ (x) = \int \frac{d x}{s i n^{\frac{1}{2}} x c o s^{\frac{7}{2}} x}$ , then $Φ (\frac{π}{4}) - Φ (0) =$

Discussion

27.	If f(x)=∫xa t3et dt, then ddxf(x)= [MP PET 1989]
Answer» If $f (x) = \int_{a}^{x} t^{3} e^{t} d t, t h e n \frac{d}{d x} f (x) =$ [MP PET 1989]

Discussion

28.	∣∣∣∣xCrxCr+1xCr+2yCryCr+1yCr+2zCrzCr+1zCr+2∣∣∣∣−∣∣∣∣∣xCrx+1Cr+1x+2Cr+2yCry+1Cr+1y+2Cr+2zCrz+1Cr+1z+2Cr+2∣∣∣∣∣=
Answer» $∣ ∣∣ ∣ \begin{matrix} ^{x} C_{r} & ^{x} C_{r + 1} & ^{x} C_{r + 2}^{y} C_{r} & ^{y} C_{r + 1} & ^{y} C_{r + 2}^{z} C_{r} & ^{z} C_{r + 1} & ^{z} C_{r + 2} \end{matrix} ∣ ∣∣ ∣ - ∣ ∣∣∣ ∣ \begin{matrix} ^{x} C_{r} & ^{x + 1} C_{r + 1} & ^{x + 2} C_{r + 2}^{y} C_{r} & ^{y + 1} C_{r + 1} & ^{y + 2} C_{r + 2}^{z} C_{r} & ^{z + 1} C_{r + 1} & ^{z + 2} C_{r + 2} \end{matrix} ∣ ∣∣∣ ∣ =$

Discussion

29.	sec−1 (sin x) is real, if
Answer» $s e c^{- 1}$ (sin x) is real, if

Discussion

30.	Find the solution of the differential equation: x√1+y2 dx+y√1+x2 dy=0.
Answer» Find the solution of the differential equation: $x \sqrt{1 + y^{2}} d x + y \sqrt{1 + x^{2}} d y = 0.$

Discussion

31.	An A.P., a G.P., and a H.P. have a and b for their first two terms their (n+2)th terms will be in G.P. if b2n+2−a2n+2ab(b2n−a2n)
Answer» An A.P., a G.P., and a H.P. have a and b for their first two terms their $(n + 2)^{t h}$ terms will be in G.P. if $\frac{b^{2 n + 2} - a^{2 n + 2}}{a b (b^{2 n} - a^{2 n})}$

Discussion

32.	If the rth term tr of a series is given by tr=rr4+r2+1 then limn→∞∑nr=1tr is
Answer» If the $r^{th}$ term $t_{r}$ of a series is given by $t_{r} = \frac{r}{r^{4} + r^{2} + 1}$ then $lim n \to \infty \sum_{r = 1}^{n} t_{r}$ is

Discussion

33.	The value of [∫π402(1+x) ln (1+x)⋅sinx+cosx2(1+x)cos3xdx] is (where [.] denotes the greatest integer function)
Answer» The value of $[\int_{0}^{\frac{π}{4}} \frac{2 (1 + x) ln (1 + x) \cdot sin x + cos x}{2 (1 + x) {cos}^{3} x} d x]$ is (where [.] denotes the greatest integer function)

Discussion

34.	The vectors →c,→a=x^i+y^j+z^k and →b=^j are such that →a,→c and →b form a right handed system then →c can be
Answer» The vectors $\to c, \to a = x^i + y^j + z^k$ and $\to b =^j$ are such that $\to a, \to c$ and $\to b$ form a right handed system then $\to c$ can be

Discussion

35.	Let A = {12, 13, 14, 15, 16, 17} and f:A→Z be a function given by f(x) = highest prime factor of x.
Answer» Let A = {12, 13, 14, 15, 16, 17} and $f : A \to Z$ be a function given by f(x) = highest prime factor of x.

Discussion

36.	What the distance between the centre of the circle x2+y2+2gx+2fy+c=0 and a point situated outside, p(x1,y1).
Answer» What the distance between the centre of the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and a point situated outside, $p (x_{1}, y_{1}) .$

Discussion

37.	The equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 – 11x – 7y – 4 = 0 are
Answer» The equation of the asymptotes of the hyperbola $2 x^{2}$ + 5xy + $2 y^{2}$ – 11x – 7y – 4 = 0 are

Discussion

38.	If 2,b,c are in A.P., b,c,d are in G.P., and c,d,18 are in H.P. (where b,c,d∈R+), then the value of b+c+d is
Answer» If $2, b, c$ are in A.P., $b, c, d$ are in G.P., and $c, d, 18$ are in H.P. $($ where $b, c, d \in R^{+})$ , then the value of $b + c + d$ is

Discussion

39.	Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1,L2):L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
Answer» Let L be the set of all lines in XY plane and R be the relation in L defined as R = { $(L_{1}, L_{2}) : L_{1}$ is parallel to $L_{2}$ }. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

Discussion

40.	The length of the perpendicular drawn from the point P(3, 3, 4) from the y-axis is
Answer» The length of the perpendicular drawn from the point P(3, 3, 4) from the y-axis is

40.

The length of the perpendicular drawn from the point P(3, 3, 4) from the y-axis is

Answer»

The length of the perpendicular drawn from the point P(3, 3, 4) from the

y-axis is

Discussion

41.	If x2+y2+z2=1, then yz+zx+xy lies in the interval
Answer» If $x^{2} + y^{2} + z^{2} = 1$ , then $y z + z x + x y$ lies in the interval

Discussion

42.	The value of {3200328} is (where {.} denotes the fractional part function)
Answer» The value of ${\frac{3^{2003}}{28}}$ is (where {.} denotes the fractional part function)

Discussion

43.	A regular polygon of 10 sides is constructed. The number of ways in which 3 vertices can be selected so that no two vertices are consecutive is
Answer» A regular polygon of $10$ sides is constructed. The number of ways in which $3$ vertices can be selected so that no two vertices are consecutive is

Discussion

44.	If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: ah+bk=1.
Answer» If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: $\frac{a}{h} + \frac{b}{k} = 1.$

Discussion

45.	Solve the following equations :(i) cos θ+cps 2θ+cos 3θ=0(ii) cos θ+cos 3θ−cos 2θ=0(iii) sin θ+sin 5θ=sin 3θ(iv) cos θ cos 2θ cos 3θ=14(v) cos θ+sin θ=cos 2θ+sin2θ(vi) sin θ+sin 2θ+sin 3θ=0(vii) sin θ+sin 2θ+sin 3θ+sin 4θ=0(viii) sin 3θ−sin θ=4 cos2θ−2(ix) sin 2θ−sin 4θ+sin 6θ=0
Answer» $Solve the following equations : (i) c o s θ + c p s 2 θ + c o s 3 θ = 0 (i i) c o s θ + c o s 3 θ - c o s 2 θ = 0 (i i i) s i n θ + s i n 5 θ = s i n 3 θ (i v) c o s θ c o s 2 θ c o s 3 θ = \frac{1}{4} (v) c o s θ + s i n θ = c o s 2 θ + s i n 2 θ (v i) s i n θ + s i n 2 θ + s i n 3 θ = 0 (v i i) s i n θ + s i n 2 θ + s i n 3 θ + s i n 4 θ = 0 (v i i i) s i n 3 θ - s i n θ = 4 c o s^{2} θ - 2 (i x) s i n 2 θ - s i n 4 θ + s i n 6 θ = 0$

Discussion

46.	If Z=∣∣∣∣25−i7+i5+i23−i7−i3+i7∣∣∣∣ and arg (z) = θ then θ = ___
Answer» If $Z = ∣ ∣∣ ∣ \begin{matrix} 2 & 5 - i & 7 + i 5 + i & 2 & 3 - i 7 - i & 3 + i & 7 \end{matrix} ∣ ∣∣ ∣$ and arg (z) = $θ$ then $θ$ = ___

Discussion

47.	Evaluate ∫3x2+4x+3(x−2)(x2+3x+2) dx.
Answer» Evaluate $\int \frac{3 x^{2} + 4 x + 3}{(x - 2) (x^{2} + 3 x + 2)} d x$ .

Discussion

48.	If (1+x)n=n∑r=0arxr. Then (1+a1a0)(1+a2a1)…(1+anan−1) is equal to
Answer» If $(1 + x)^{n} = n \sum r = 0 a_{r} x^{r} .$ Then $(1 + \frac{a_{1}}{a_{0}}) (1 + \frac{a_{2}}{a_{1}}) \dots (1 + \frac{a_{n}}{a_{n - 1}})$ is equal to

Discussion

49.	Integrate the function. ∫e2xsinxdx.
Answer» Integrate the function. $\int e^{2 x} s i n x d x .$

Discussion

50.	Find the equation of a curve passing through the point (0,0) and whose differential equation is y′=exsinx
Answer» Find the equation of a curve passing through the point (0,0) and whose differential equation is $y^{'} = e^{x} s i n x$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In a ΔABC, AB=AC and the length of the altitude from A to BC is h. The area and perimeter of ΔABC is A and P respectively. The circumradius of ΔABC is r. The value of 1rlimh→0AP3 is

The number of permutations that can be formed out of the letters of the word "SERIES" taking three letters together is:

Locus of the point of intersection of the tangents which meet at right angles is called.

f(x)=⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩2x2−5,x≤−83x+p,−8&lt;x&lt;−3(k−7)(|3−x|+|3+x|),−3≤x≤33x+9,3&lt;x&lt;85−2x2,x≥8 If f(x) is an odd function then the value of k−p is

If cosec θ=135 and θ∉1stquadrant. Then the value of secθ is

If (x−1)4−16=0, then the sum of non real complex values of x, is

If P(A)=611,P(B)=511andP(A∪B)=711, find P(A∩B) P(AB) P(BA)

Find a vector of magnitude 6 , which is perpendicular to both the vectors 2^i−^j+2^k and 4^i−^j+3^k.

Find the distance of the point 3^i−2^j+^k from the plane 3x + y - z +2=0 measured parallel to the x−12=y+2−3=z−11. Also find the foot of perpendicular from the given point upon the given plane.

Let ∗ be a binary operation on the Q of rational number as follows: (v)a∗b=ab4 Find which of the binary operation are commutative and which are associative?

A problem in Mathematics is given to 4 students. A, B, C and D. Their chances of solving the problems respectively are 13,14,15 and 23. What is the probability that (i) the problem will be solved ? (ii) at most one of them will solve the problem ?

(i) Show that the matrix, A=⎡⎢⎣1−15−121513⎤⎥⎦ is a symmetric matrix (ii) Show that the matrix, A=⎡⎢⎣01−1−1011−10⎤⎥⎦ is a skew -symmetric matrix.

Show that the lines x−57=y+2−5=z1 and x1=y2=z3 perpendicular to each other.

If |z1|=|z2|=|z3|=...=|zn|=1 then prove that ∣∣∣1z1+1z2+1z3+...+1zn∣∣∣=|z1+z2+z3+...+zn|.

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

If the length of the transverse and conjugate axes of a hyperbola are 8 and 6 units respectively, then the absolute value of difference of focal distances of any point of the hyperbola is unit.

Let the projection of the line L:x−12=y+2−1=z−23 in the plane 3x+2y+z=5 is L′. If the distance of a plane from the origin which contains the lines L and L′ is p, then the value of 6p2 is

Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral ∫10(acxb+1+a3bx3b+5) dx is independent of ‘b’ equals

The equation of a circle passing through points of intersection of the circles x2+y2+13x−3y=0 and 2x2+2y2+4x−7y−25=0 and point (1, 1) is

If A,B,C are acute positive angles such that A+B+C=π and cotAcotBcotC=k, then

If p=(8+3√7)n and f=p−[p], then the value of p(1−f) is (where [.] denotes the greatest integer function)

If the vertices of a triangle be (a, b - c), (b, c - a) and (c, a - b), then the centroid of the triangle lies

f:R→R, f(x)=x|x| is

A random variable ′X′ has the following probability distribution: X 1 2 3 4 5 6 7 P(X) k−1 3k k 3k 3k2 k2 k2+k Then the value of k is

The coefficient of xn in (1+x)2(1−x)3 is :

If Φ(x)=∫dxsin12x cos72x, then Φ(π4)−Φ(0)=

If f(x)=∫xa t3et dt, then ddxf(x)= [MP PET 1989]

∣∣∣∣xCrxCr+1xCr+2yCryCr+1yCr+2zCrzCr+1zCr+2∣∣∣∣−∣∣∣∣∣xCrx+1Cr+1x+2Cr+2yCry+1Cr+1y+2Cr+2zCrz+1Cr+1z+2Cr+2∣∣∣∣∣=

sec−1 (sin x) is real, if

Find the solution of the differential equation: x√1+y2 dx+y√1+x2 dy=0.

An A.P., a G.P., and a H.P. have a and b for their first two terms their (n+2)th terms will be in G.P. if b2n+2−a2n+2ab(b2n−a2n)

If the rth term tr of a series is given by tr=rr4+r2+1 then limn→∞∑nr=1tr is

The value of [∫π402(1+x) ln (1+x)⋅sinx+cosx2(1+x)cos3xdx] is (where [.] denotes the greatest integer function)

The vectors →c,→a=x^i+y^j+z^k and →b=^j are such that →a,→c and →b form a right handed system then →c can be

Let A = {12, 13, 14, 15, 16, 17} and f:A→Z be a function given by f(x) = highest prime factor of x.

What the distance between the centre of the circle x2+y2+2gx+2fy+c=0 and a point situated outside, p(x1,y1).

The equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 – 11x – 7y – 4 = 0 are

If 2,b,c are in A.P., b,c,d are in G.P., and c,d,18 are in H.P. (where b,c,d∈R+), then the value of b+c+d is

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1,L2):L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

The length of the perpendicular drawn from the point P(3, 3, 4) from the y-axis is

If x2+y2+z2=1, then yz+zx+xy lies in the interval

The value of {3200328} is (where {.} denotes the fractional part function)

A regular polygon of 10 sides is constructed. The number of ways in which 3 vertices can be selected so that no two vertices are consecutive is

If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: ah+bk=1.

If Z=∣∣∣∣25−i7+i5+i23−i7−i3+i7∣∣∣∣ and arg (z) = θ then θ = ___

Evaluate ∫3x2+4x+3(x−2)(x2+3x+2) dx.

If (1+x)n=n∑r=0arxr. Then (1+a1a0)(1+a2a1)…(1+anan−1) is equal to

Integrate the function. ∫e2xsinxdx.

Find the equation of a curve passing through the point (0,0) and whose differential equation is y′=exsinx

f(x)=⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩2x2−5,x≤−83x+p,−8<x<−3(k−7)(|3−x|+|3+x|),−3≤x≤33x+9,3<x<85−2x2,x≥8 If f(x) is an odd function then the value of k−p is