43030 + Interview Questions in Mathematics

1.	Coefficient of x100in1+(1+x)+(1+x)2+(1+x)3…(1+x)n is 201C101,(n>100) then n =
Answer» Coefficient of $x^{100} i n 1 + (1 + x) + (1 + x)^{2} + (1 + x)^{3} \dots (1 + x)^{n}$ is $^{201} C_{101}, (n > 100)$ then n =

Discussion

2.	Find the number of words with or without meaning which can be made using all the letters of the word SWEET.
Answer» Find the number of words with or without meaning which can be made using all the letters of the word SWEET.

Discussion

3.	Solve for \|2x+3\|+x=10, 'x' is a real number
Answer» Solve for $\| 2 x + 3 \| + x = 10$ , 'x' is a real number

Discussion

4.	If z is a complex number of unit modulus and argument θ, then arg(1+z1+¯z)=
Answer» If $z$ is a complex number of unit modulus and argument $θ$ , then $arg (\frac{1 + z}{1 + ¯ z}) =$

Discussion

5.	Sin15.COS15=?
Answer» Sin15.COS15=?

Discussion

6.	Q41. What will come in place of (?) in the following number series?
Answer» Q41. What will come in place of (?) in the following number series?

6.

Q41. What will come in place of (?) in the following number series?

Answer»

Q41. What will come in place of (?) in the following number series?

Discussion

7.	37. Let A = {1, 2, 3}. Then find the number of equivalence relations containing (1, 2
Answer» 37. Let A = {1, 2, 3}. Then find the number of equivalence relations containing (1, 2

Discussion

8.	Sir for when sum of 4 unknown consencutive terms of an ap is given then we take it as a-3d,a-d,a+d,a+3d.why dont we take it as a-2d,a-d,a+d,a+2d. Does this have to do any thing with odd and even. Please explain. Thak you.
Answer» Sir for when sum of 4 unknown consencutive terms of an ap is given then we take it as a-3d,a-d,a+d,a+3d.why dont we take it as a-2d,a-d,a+d,a+2d. Does this have to do any thing with odd and even. Please explain. Thak you.

8.

Sir for when sum of 4 unknown consencutive terms of an ap is given then we take it as a-3d,a-d,a+d,a+3d.why dont we take it as a-2d,a-d,a+d,a+2d. Does this have to do any thing with odd and even. Please explain. Thak you.

Answer»

Sir for when sum of 4 unknown consencutive terms of an ap is given then we take it as a-3d,a-d,a+d,a+3d.why dont we take it as a-2d,a-d,a+d,a+2d.

Does this have to do any thing with odd and even.

Please explain.

Thak you.

Discussion

9.	The equation of the straight line passing through the point (4,3) and making an intercept on the coordinate axes whose sum is -1 is?
Answer» The equation of the straight line passing through the point (4,3) and making an intercept on the coordinate axes whose sum is -1 is?

Discussion

10.	The lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units. The equation of the circle is
Answer» The lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units. The equation of the circle is

Discussion

11.	If (1+x)n=C0+C1x+C2x2+⋯+Cnxn, then the value of ∑∑0≤r<s≤n(r⋅s)CrCs is
Answer» If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},$ then the value of $\sum \sum 0 \leq r < s \leq n (r \cdot s) C_{r} C_{s}$ is

Discussion

12.	If x⩾1 or x ⩽−1, then cosec−1(x)=
Answer» $I f x ⩾ 1 o r x ⩽ - 1, t h e n c o s e c^{- 1} (x) =$

Discussion

13.	Find the area of the region bounded by curve y2=4x,x=1, and x=4 and the x-axis in the first quadrant.
Answer» Find the area of the region bounded by curve $y^{2} = 4 x, x = 1, and x = 4$ and the x-axis in the first quadrant.

Discussion

14.	Find the square root of (x2−y2) + 2ixy.
Answer» Find the square root of $(x^{2} - y^{2})$ + 2ixy.

Discussion

15.	A value of θ for which 2+3i sin θ1−2i sin θ is purely imaginary, is:
Answer» A value of $θ$ for which $\frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}$ is purely imaginary, is:

Discussion

16.	If 32 tan8θ=2 cos2α−3 cos α and 3 cos3θ+6 cos2θ−2 cos θ−4=0, then general values of α is
Answer» If $32 t a n^{8} θ = 2 c o s^{2} α - 3 c o s α a n d 3 c o s^{3} θ + 6 c o s^{2} θ - 2 c o s θ - 4 = 0$ , then general values of $α$ is

Discussion

17.	Prove that line x=y divides the intersecting area of the curves y2=4x and x2=4y into two equal parts.
Answer» Prove that line $x = y$ divides the intersecting area of the curves $y^{2} = 4 x$ and $x^{2} = 4 y$ into two equal parts.

Discussion

18.	A plane passes through (1, -2, 1) and is perpendicular to two planes 2x−2y+z=0 and x−y+2z=4, then the distance of the plane form the point (1, 2, 2) is
Answer» A plane passes through (1, -2, 1) and is perpendicular to two planes $2 x - 2 y + z = 0$ and $x - y + 2 z = 4,$ then the distance of the plane form the point (1, 2, 2) is

Discussion

19.	Let a,b be the roots of the equation x2−2x+4=0, then the value of a66+b66266 is
Answer» Let $a, b$ be the roots of the equation $x^{2} - 2 x + 4 = 0$ , then the value of $\frac{a^{66} + b^{66}}{2^{66}}$ is

Discussion

20.	The area enclosed by the parabolas x=−2y2 and x=1−3y2 is ab, where a,b are co-prime. Then a+b is
Answer» The area enclosed by the parabolas $x = - 2 y^{2}$ and $x = 1 - 3 y^{2}$ is $\frac{a}{b},$ where $a, b$ are co-prime. Then $a + b$ is

Discussion

21.	The points on the parabola y2=12x whose focal distance is 4 , are
Answer» The points on the parabola $y^{2} = 12 x$ whose focal distance is 4 , are

Discussion

22.	If an and bn are positive integers and an+√2bn=(2+√2)n, then limn→∞(anbn)=
Answer» If $a_{n}$ and $b_{n}$ are positive integers and $a_{n} + \sqrt{2 b_{n}} = (2 + \sqrt{2})^{n}$ , then ${lim}_{n \to \infty} (\frac{a_{n}}{b_{n}})$ =

Discussion

23.	If asinx+bcos(x+θ)+bcos(x−θ)=d, then the minimum value of \|cosθ\| is equal to
Answer» If $a sin x + b cos (x + θ) + b cos (x - θ) = d$ , then the minimum value of $\| cos θ \|$ is equal to

Discussion

24.	The sides of a parallelogram are given by the vectors <2,4,-5> and <1,2,3> , then the unit vector parallel to one of the diagonals is
Answer» The sides of a parallelogram are given by the vectors <2,4,-5> and <1,2,3> , then the unit vector parallel to one of the diagonals is

Discussion

25.	The standard deviation of the data : x:1aa2...anf:nC0nC1nC2...nCn
Answer» The standard deviation of the data : $\begin{matrix} x : & 1 & a & a^{2} & . . . & a^{n} f : & ^{n} C_{0} & ^{n} C_{1} & ^{n} C_{2} & . . . & ^{n} C_{n} \end{matrix}$

25.

The standard deviation of the data : x:1aa2...anf:nC0nC1nC2...nCn

Answer»

The standard deviation of the data :

$\begin{matrix} x : & 1 & a & a^{2} & . . . & a^{n} f : & ^{n} C_{0} & ^{n} C_{1} & ^{n} C_{2} & . . . & ^{n} C_{n} \end{matrix}$

Discussion

26.	Can there exist a set of numbers which does not contain real numbers? If yes, how do we represent it .
Answer» Can there exist a set of numbers which does not contain real numbers? If yes, how do we represent it .

Discussion

27.	The rational number which is equal to the number 2.357 with recurring decimal is
Answer» The rational number which is equal to the number 2.357 with recurring decimal is

Discussion

28.	OTCEI was started on the lines of (a) NASDAQ (b) NYSE (c) NASAQ (d) NSE
Answer» OTCEI was started on the lines of (a) NASDAQ (b) NYSE (c) NASAQ (d) NSE

28.

OTCEI was started on the lines of (a) NASDAQ (b) NYSE (c) NASAQ (d) NSE

Answer»

OTCEI was started on the lines of

(a) NASDAQ

(b) NYSE

(c) NASAQ

(d) NSE

Discussion

29.	The maximum number of different permutations of 4 letters of the word EARTHQUAKE is a)2910. b)2550. c)2190. d)2091
Answer» The maximum number of different permutations of 4 letters of the word EARTHQUAKE is a)2910. b)2550. c)2190. d)2091

Discussion

30.	If the function f(x) = sin x and g(x) = cos x are one-one in [0,π2], prove that f + g is not one-one in [0,π2].
Answer» If the function f(x) = sin x and g(x) = cos x are one-one in $[0, \frac{π}{2}]$ , prove that f + g is not one-one in $[0, \frac{π}{2}]$ .

Discussion

31.	If the sum of the first ten terms of the series (135)2+(225)2+(315)2+42+(445)2+....., Is 165 m, then m is equal to:
Answer» If the sum of the first ten terms of the series ${(1 \frac{3}{5})}^{2} + {(2 \frac{2}{5})}^{2} + {(3 \frac{1}{5})}^{2} + 4^{2} + {(4 \frac{4}{5})}^{2} + . . . . .,$ Is $\frac{16}{5}$ m, then m is equal to:

31.

If the sum of the first ten terms of the series (135)2+(225)2+(315)2+42+(445)2+....., Is 165 m, then m is equal to:

Answer»

If the sum of the first ten terms of the series

${(1 \frac{3}{5})}^{2} + {(2 \frac{2}{5})}^{2} + {(3 \frac{1}{5})}^{2} + 4^{2} + {(4 \frac{4}{5})}^{2} + . . . . .,$

Is $\frac{16}{5}$ m, then m is equal to:

Discussion

32.	limx→−∞(√x2−8x+x)
Answer» ${lim}_{x \to - \infty} (\sqrt{x^{2} - 8 x} + x)$

Discussion

33.	π2∫0log[4+3cosx4+3sinx] dx is equal to
Answer» $\frac{π}{2} \int 0 log [\frac{4 + 3 cos x}{4 + 3 sin x}] d x$ is equal to

Discussion

34.	If P is any point on the hyperbola whose axis are equal, prove that SP.SP=CP2
Answer» If P is any point on the hyperbola whose axis are equal, prove that SP.SP= $C P^{2}$

Discussion

35.	If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x+a)n are A and B respectively, then the value of (x2−a2)n is
Answer» If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $(x + a)^{n}$ are A and B respectively, then the value of $(x^{2} - a^{2})^{n}$ is

Discussion

36.	Find the locus of a point such that the sum of its distances from (0,2) and (0,-2) is 6.
Answer» $Find the locus of a point such that the sum of its distances from (0,2) and (0,-2) is 6 .$

Discussion

37.	A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ? How many of these committees would consists of 1 man and 2 women ?
Answer» A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ? How many of these committees would consists of 1 man and 2 women ?

37.

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ? How many of these committees would consists of 1 man and 2 women ?

Answer»

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ?

How many of these committees would consists of 1 man and 2 women ?

Discussion

38.	If f(x−4x+2)=2x+1,(x∈R−{1,−2}), then ∫f(x) dx is equal to : (where C is a constant of integration)
Answer» If $f (\frac{x - 4}{x + 2}) = 2 x + 1, (x \in R - {1, - 2}),$ then $\int f (x) d x$ is equal to : (where $C$ is a constant of integration)

Discussion

39.	tanA1−cotA+cotA1−tanA=(secAcosecA+1)
Answer» $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A} = (s e c A c o s e c A + 1)$

Discussion

40.	Prove that 1n+1+1n+2+....+12n>1324, for all natural numbers n > 1.
Answer» Prove that $\frac{1}{n + 1} + \frac{1}{n + 2} + . . . . + \frac{1}{2 n} > \frac{13}{24}$ , for all natural numbers n > 1.

Discussion

41.	Let A and B be two sets such that : n (A) = 20 , n(A∪B)=42 and n(A∩B)=4. Find (i) n (B) (ii) n (A - B) (iii) n (B - A)
Answer» Let A and B be two sets such that : n (A) = 20 , $n (A \cup B) = 42 a n d n (A \cap B) = 4$ . Find (i) n (B) (ii) n (A - B) (iii) n (B - A)

41.

Let A and B be two sets such that : n (A) = 20 , n(A∪B)=42 and n(A∩B)=4. Find (i) n (B) (ii) n (A - B) (iii) n (B - A)

Answer»

Let A and B be two sets such that : n (A) = 20 , $n (A \cup B) = 42 a n d n (A \cap B) = 4$ . Find

(i) n (B) (ii) n (A - B)

(iii) n (B - A)

Discussion

42.	The equation of the smallest degree with real coefficients having 1 + i as one of the roots is
Answer» The equation of the smallest degree with real coefficients having 1 + i as one of the roots is

Discussion

43.	If sin x = √53 and x lies in IInd quadrant, find the values of cos x2, and sin x2 and tan x2.
Answer» If sin x = $\frac{\sqrt{5}}{3}$ and x lies in IInd quadrant, find the values of $c o s \frac{x}{2}, a n d s i n \frac{x}{2}$ and $t a n \frac{x}{2}$ .

Discussion

44.	Column IColumn 2Column 3(I)cos(sin−1(sin5π6))=(i)1(P)f(x)=3x3−13x2+14x−2 hasthree roots α,β,γ, then value of\|sin(tan−1α+tan−1β+tan−1γ)\|=(II)cos(cos−1(−sin7π6))=(ii)1√2(Q)(√3cosec20∘−sec20∘)8=(III)∣∣cos{tan−1(tan15π4)}∣∣=(iii)12(R)4√2(sin12∘)(sin48∘)(sin54∘)=(IV)sin((cos−1{1√2(cos9π10−sin9π10)}+7π20)−1×π2)(iv)√32(S)If the angles A, B and C of atriangle are in an arithmetic progressionand if a,b and c denote the lengths ofsides opposite to A,B and C respectively,then the value of the expression12(acsin2C+casin2A)is Which of the following options is only correct combination?
Answer» $\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & c o s (s i n^{- 1} (s i n \frac{5 π}{6})) = & (i) & 1 & (P) & f (x) = 3 x^{3} - 13 x^{2} + 14 x - 2 h a s t h r e e r o o t s α, β, γ, t h e n v a l u e o f \| s i n (t a n^{- 1} α + t a n^{- 1} β + t a n^{- 1} γ) \| = (I I) & c o s (c o s^{- 1} (- s i n \frac{7 π}{6})) = & (i i) & \frac{1}{\sqrt{2}} & (Q) & \frac{(\sqrt{3} c o s e c 20^{\circ} - s e c 20^{\circ})}{8} = (I I I) & ∣ ∣ c o s {t a n^{- 1} (t a n \frac{15 π}{4})} ∣ ∣ = & (i i i) & \frac{1}{2} & (R) & 4 \sqrt{2} (s i n 12^{\circ}) (s i n 48^{\circ}) (s i n 54^{\circ}) = (I V) & s i n ({(c o s^{- 1} {\frac{1}{\sqrt{2}} (c o s \frac{9 π}{10} - s i n \frac{9 π}{10})} + \frac{7 π}{20})}^{- 1} \times π^{2}) & (i v) & \frac{\sqrt{3}}{2} & (S) & I f t h e a n g l e s A, B a n d C o f a t r i a n g l e a r e i n a n a r i t h m e t i c p r o g r e s s i o n a n d i f a, b a n d c d e n o t e t h e l e n g t h s o f s i d e s o p p o s i t e t o A, B a n d C r e s p e c t i v e l y, t h e n t h e v a l u e o f t h e e x p r e s s i o n \frac{1}{2} (\frac{a}{c} s i n 2 C + \frac{c}{a} s i n 2 A) i s \end{matrix}$ Which of the following options is only correct combination?

44.

Column IColumn 2Column 3(I)cos(sin−1(sin5π6))=(i)1(P)f(x)=3x3−13x2+14x−2 hasthree roots α,β,γ, then value of|sin(tan−1α+tan−1β+tan−1γ)|=(II)cos(cos−1(−sin7π6))=(ii)1√2(Q)(√3cosec20∘−sec20∘)8=(III)∣∣cos{tan−1(tan15π4)}∣∣=(iii)12(R)4√2(sin12∘)(sin48∘)(sin54∘)=(IV)sin((cos−1{1√2(cos9π10−sin9π10)}+7π20)−1×π2)(iv)√32(S)If the angles A, B and C of atriangle are in an arithmetic progressionand if a,b and c denote the lengths ofsides opposite to A,B and C respectively,then the value of the expression12(acsin2C+casin2A)is Which of the following options is only correct combination?

Answer»

$\begin{matrix} C o l u m n I & C o l u m n 2 & C o l u m n 3 (I) & c o s (s i n^{- 1} (s i n \frac{5 π}{6})) = & (i) & 1 & (P) & f (x) = 3 x^{3} - 13 x^{2} + 14 x - 2 h a s t h r e e r o o t s α, β, γ, t h e n v a l u e o f | s i n (t a n^{- 1} α + t a n^{- 1} β + t a n^{- 1} γ) | = (I I) & c o s (c o s^{- 1} (- s i n \frac{7 π}{6})) = & (i i) & \frac{1}{\sqrt{2}} & (Q) & \frac{(\sqrt{3} c o s e c 20^{\circ} - s e c 20^{\circ})}{8} = (I I I) & ∣ ∣ c o s {t a n^{- 1} (t a n \frac{15 π}{4})} ∣ ∣ = & (i i i) & \frac{1}{2} & (R) & 4 \sqrt{2} (s i n 12^{\circ}) (s i n 48^{\circ}) (s i n 54^{\circ}) = (I V) & s i n ({(c o s^{- 1} {\frac{1}{\sqrt{2}} (c o s \frac{9 π}{10} - s i n \frac{9 π}{10})} + \frac{7 π}{20})}^{- 1} \times π^{2}) & (i v) & \frac{\sqrt{3}}{2} & (S) & I f t h e a n g l e s A, B a n d C o f a t r i a n g l e a r e i n a n a r i t h m e t i c p r o g r e s s i o n a n d i f a, b a n d c d e n o t e t h e l e n g t h s o f s i d e s o p p o s i t e t o A, B a n d C r e s p e c t i v e l y, t h e n t h e v a l u e o f t h e e x p r e s s i o n \frac{1}{2} (\frac{a}{c} s i n 2 C + \frac{c}{a} s i n 2 A) i s \end{matrix}$

Which of the following options is only correct combination?

Discussion

45.	The principal solution of tanθ=−1 is
Answer» The principal solution of $t a n θ = - 1$ is

Discussion

46.	The value of 15∑r=015Cr(r−152)2 is
Answer» The value of $15 \sum r = 0^{15} C_{r} {(r - \frac{15}{2})}^{2}$ is

Discussion

47.	Let f: R→R be defined byf(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩α+sin[x]2if x>0 2if x=0β+[sin x−xx3]if x<0where [y] denotes the integral part of y. If f is continuous at x=0, then β−α=
Answer» Let f: $R \to R$ be defined by $f (x) = ⎧ ⎪⎪⎪ ⎨ ⎪⎪⎪ ⎩ \begin{matrix} α + \frac{s i n [x]}{2} & i f x > 0 2 & i f x = 0 β + [\frac{s i n x - x}{x^{3}}] & i f x < 0 \end{matrix}$ where $[y]$ denotes the integral part of y. If f is continuous at $x = 0, t h e n β - α =$

Discussion

48.	If the system of equations ax+y+z=0;x+by+z=0 and x+y+cz=0 has a non-trivial solution, then the value of 11−a+11−b+11−c is
Answer» If the system of equations $a x + y + z = 0; x + b y + z = 0$ and $x + y + c z = 0$ has a non-trivial solution, then the value of $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$ is

Discussion

49.	If P and Q are the points of contact of tangents drawn from the point T to y2=4ax and PQ be a normal of the parabola at P, then the locus of the point which bisects TP is
Answer» If $P$ and $Q$ are the points of contact of tangents drawn from the point $T$ to $y^{2} = 4 a x$ and $P Q$ be a normal of the parabola at $P$ , then the locus of the point which bisects $T P$ is

Discussion

50.	Identify the pair of functions which are not identical
Answer» Identify the pair of functions which are not identical

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Coefficient of x100in1+(1+x)+(1+x)2+(1+x)3…(1+x)n is 201C101,(n&gt;100) then n =

Find the number of words with or without meaning which can be made using all the letters of the word SWEET.

Solve for |2x+3|+x=10, 'x' is a real number

If z is a complex number of unit modulus and argument θ, then arg(1+z1+¯z)=

Sin15.COS15=?

Q41. What will come in place of (?) in the following number series?

37. Let A = {1, 2, 3}. Then find the number of equivalence relations containing (1, 2

Sir for when sum of 4 unknown consencutive terms of an ap is given then we take it as a-3d,a-d,a+d,a+3d.why dont we take it as a-2d,a-d,a+d,a+2d. Does this have to do any thing with odd and even. Please explain. Thak you.

The equation of the straight line passing through the point (4,3) and making an intercept on the coordinate axes whose sum is -1 is?

The lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units. The equation of the circle is

If (1+x)n=C0+C1x+C2x2+⋯+Cnxn, then the value of ∑∑0≤r&lt;s≤n(r⋅s)CrCs is

If x⩾1 or x ⩽−1, then cosec−1(x)=

Find the area of the region bounded by curve y2=4x,x=1, and x=4 and the x-axis in the first quadrant.

Find the square root of (x2−y2) + 2ixy.

A value of θ for which 2+3i sin θ1−2i sin θ is purely imaginary, is:

If 32 tan8θ=2 cos2α−3 cos α and 3 cos3θ+6 cos2θ−2 cos θ−4=0, then general values of α is

Prove that line x=y divides the intersecting area of the curves y2=4x and x2=4y into two equal parts.

A plane passes through (1, -2, 1) and is perpendicular to two planes 2x−2y+z=0 and x−y+2z=4, then the distance of the plane form the point (1, 2, 2) is

Let a,b be the roots of the equation x2−2x+4=0, then the value of a66+b66266 is

The area enclosed by the parabolas x=−2y2 and x=1−3y2 is ab, where a,b are co-prime. Then a+b is

The points on the parabola y2=12x whose focal distance is 4 , are

If an and bn are positive integers and an+√2bn=(2+√2)n, then limn→∞(anbn)=

If asinx+bcos(x+θ)+bcos(x−θ)=d, then the minimum value of |cosθ| is equal to

The sides of a parallelogram are given by the vectors &lt;2,4,-5&gt; and &lt;1,2,3&gt; , then the unit vector parallel to one of the diagonals is

The standard deviation of the data : x:1aa2...anf:nC0nC1nC2...nCn

Can there exist a set of numbers which does not contain real numbers? If yes, how do we represent it .

The rational number which is equal to the number 2.357 with recurring decimal is

OTCEI was started on the lines of (a) NASDAQ (b) NYSE (c) NASAQ (d) NSE

The maximum number of different permutations of 4 letters of the word EARTHQUAKE is a)2910. b)2550. c)2190. d)2091

If the function f(x) = sin x and g(x) = cos x are one-one in [0,π2], prove that f + g is not one-one in [0,π2].

If the sum of the first ten terms of the series (135)2+(225)2+(315)2+42+(445)2+....., Is 165 m, then m is equal to:

limx→−∞(√x2−8x+x)

π2∫0log[4+3cosx4+3sinx] dx is equal to

If P is any point on the hyperbola whose axis are equal, prove that SP.SP=CP2

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x+a)n are A and B respectively, then the value of (x2−a2)n is

Find the locus of a point such that the sum of its distances from (0,2) and (0,-2) is 6.

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ? How many of these committees would consists of 1 man and 2 women ?

If f(x−4x+2)=2x+1,(x∈R−{1,−2}), then ∫f(x) dx is equal to : (where C is a constant of integration)

tanA1−cotA+cotA1−tanA=(secAcosecA+1)

Prove that 1n+1+1n+2+....+12n&gt;1324, for all natural numbers n &gt; 1.

Let A and B be two sets such that : n (A) = 20 , n(A∪B)=42 and n(A∩B)=4. Find (i) n (B) (ii) n (A - B) (iii) n (B - A)

The equation of the smallest degree with real coefficients having 1 + i as one of the roots is

If sin x = √53 and x lies in IInd quadrant, find the values of cos x2, and sin x2 and tan x2.

The principal solution of tanθ=−1 is

The value of 15∑r=015Cr(r−152)2 is

Let f: R→R be defined byf(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩α+sin[x]2if x&gt;0 2if x=0β+[sin x−xx3]if x&lt;0where [y] denotes the integral part of y. If f is continuous at x=0, then β−α=

If the system of equations ax+y+z=0;x+by+z=0 and x+y+cz=0 has a non-trivial solution, then the value of 11−a+11−b+11−c is

If P and Q are the points of contact of tangents drawn from the point T to y2=4ax and PQ be a normal of the parabola at P, then the locus of the point which bisects TP is

Identify the pair of functions which are not identical

Coefficient of x100in1+(1+x)+(1+x)2+(1+x)3…(1+x)n is 201C101,(n>100) then n =

If (1+x)n=C0+C1x+C2x2+⋯+Cnxn, then the value of ∑∑0≤r<s≤n(r⋅s)CrCs is

The sides of a parallelogram are given by the vectors <2,4,-5> and <1,2,3> , then the unit vector parallel to one of the diagonals is

Prove that 1n+1+1n+2+....+12n>1324, for all natural numbers n > 1.

Let f: R→R be defined byf(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩α+sin[x]2if x>0 2if x=0β+[sin x−xx3]if x<0where [y] denotes the integral part of y. If f is continuous at x=0, then β−α=