43030 + Interview Questions in Mathematics

1.	Prove that :sin^2 x . cos^2 y - cos^2 x . sin^2 y = sin^2 x - sin^2 y
Answer» Prove that : sin^2 x . cos^2 y - cos^2 x . sin^2 y = sin^2 x - sin^2 y

Discussion

2.	If vectors A-->= cos wt i^ + sin wt j^ and B--> = cos wt /2^i + sin wt/2 j^ are functions of time, then value of t at which they are orthogonal to each other is:
Answer» If vectors A^-->= cos wt i^{^} + sin wt j^{^} and B^-->= cos wt /2^{^}i + sin wt/2 j^{^}are functions of time, then value of t at which they are orthogonal to each other is:

Discussion

3.	How to do wavy curve method
Answer» How to do wavy curve method

Discussion

4.	The number of six digit numbers, all digits of which are odd, is __________.
Answer» The number of six digit numbers, all digits of which are odd, is __________.

Discussion

5.	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

6.	Sum of integers from 1 to 100 that are divisible by 2 is a, by 5 is b and by both 2 and 5 is c. Find the sum of integers which are divisible 2 or 5.
Answer» Sum of integers from 1 to 100 that are divisible by 2 is a, by 5 is b and by both 2 and 5 is c. Find the sum of integers which are divisible 2 or 5.

Discussion

7.	7。e® cos 3x
Answer» 7。e® cos 3x

Discussion

8.	mx-n/5 + nx+m/7 + nx = m/8Find the value of x
Answer» mx-n/5 + nx+m/7 + nx = m/8 Find the value of x

Discussion

9.	Find the equation of the striaght lines passing through the following pair of points: (i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin α, b + c cos α) (iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) (at1, a/t1) and (at2, a/t2) (vi) (a cos α, a sin α) and (a cos β, a sin β)
Answer» Find the equation of the striaght lines passing through the following pair of points: (i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin $α$ , b + c cos $α$ ) (iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) $(a t_{1}, a / t_{1}) a n d (a t_{2}, a / t_{2})$ (vi) $(a c o s α, a s i n α) a n d (a c o s β, a s i n β)$

9.

Find the equation of the striaght lines passing through the following pair of points: (i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin α, b + c cos α) (iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) (at1, a/t1) and (at2, a/t2) (vi) (a cos α, a sin α) and (a cos β, a sin β)

Answer»

Find the equation of the striaght lines passing through the following pair of points:

(i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin $α$ , b + c cos $α$ )

(iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) $(a t_{1}, a / t_{1}) a n d (a t_{2}, a / t_{2})$ (vi) $(a c o s α, a s i n α) a n d (a c o s β, a s i n β)$

Discussion

10.	Middle point of the chord of the circle x2+y2=25 intercepted on the line x−2y=2 is
Answer» Middle point of the chord of the circle $x^{2} + y^{2} = 25$ intercepted on the line $x - 2 y = 2$ is

Discussion

11.	A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0,0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is
Answer» A chord $M P$ parallel to the latus rectum of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ with centre at $O (0, 0)$ intersects the auxiliary circle at $Q$ . Then the locus of the point of intersection of normals at $P$ and $Q$ to the respective curve is

Discussion

12.	The value of ∫sin(7x2)sin(3x2)dx is(where C is constant of integration)
Answer» The value of $\int sin (\frac{7 x}{2}) sin (\frac{3 x}{2}) d x$ is (where $C$ is constant of integration)

Discussion

13.	Calculate the mean deviation about the median of the following frequency distribution : xi57911131517fi246810128
Answer» Calculate the mean deviation about the median of the following frequency distribution : $\begin{matrix} x_{i} & 5 & 7 & 9 & 11 & 13 & 15 & 17 f_{i} & 2 & 4 & 6 & 8 & 10 & 12 & 8 \end{matrix}$

13.

Calculate the mean deviation about the median of the following frequency distribution : xi57911131517fi246810128

Answer»

Calculate the mean deviation about the median of the following frequency distribution :

$\begin{matrix} x_{i} & 5 & 7 & 9 & 11 & 13 & 15 & 17 f_{i} & 2 & 4 & 6 & 8 & 10 & 12 & 8 \end{matrix}$

Discussion

14.	The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.
Answer» The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

Discussion

15.	20. If a + b + c = 15 and a2 + b2 + c2 = 83, find the value of a3 + b3 + c3 3abc.
Answer» 20. If a + b + c = 15 and a2 + b2 + c2 = 83, find the value of a3 + b3 + c3 3abc.

Discussion

16.	If the focus of the parabola x2−ky+3=0 is (0,2), then the value(s) of k is/are
Answer» If the focus of the parabola $x^{2} - k y + 3 = 0$ is $(0, 2)$ , then the value(s) of $k$ is/are

Discussion

17.	The number of words that can be made by re-arranging the letters of the word Apurba so that vowels and consonants are alternate is
Answer» The number of words that can be made by re-arranging the letters of the word Apurba so that vowels and consonants are alternate is

Discussion

18.	To divide a line segment AB in the ratio 5:7, first ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is(a) 8(b) 10(c) 11(d) 12
Answer» To divide a line segment AB in the ratio 5:7, first ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is (a) 8 (b) 10 (c) 11 (d) 12

Discussion

19.	Construct a 2 × 2 matrix A = [aij] whose elements aij are given by aij=-3i+j2, if i≠ji+j2, if i=j
Answer» Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by $a_{i j} = \{\begin{cases} \frac{\|- 3 i + j\|}{2} & , if i \neq j \\ {(i + j)}^{2} & , if i = j \end{cases}$

Discussion

20.	Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = – 16y
Answer» Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = – 16y

Discussion

21.	If the equation ax2+2hxy+by2=0 has one line as the bisector of angle between the coordinate axes, then
Answer» If the equation $a x^{2} + 2 h x y + b y^{2} = 0$ has one line as the bisector of angle between the coordinate axes, then

Discussion

22.	The number of solutions of sin5x−cos5x=1cos x−1sin x (where sin x≠cos x) is
Answer» The number of solutions of ${sin}^{5} x - {cos}^{5} x = \frac{1}{cos x} - \frac{1}{sin x}$ (where $sin x \neq cos x)$ is

Discussion

23.	The value of cos10°-sin10° is
Answer» The value of cos10°-sin10° is

Discussion

24.	(→a×→b)(→c×→d)+(→b.→c)(→a.→d) is equal to
Answer» $(\to a \times \to b) (\to c \times \to d) + (\to b . \to c) (\to a . \to d)$ is equal to

Discussion

25.	If the value of limx→0tan3x−sin3xx5 is α, then 2α=
Answer» If the value of $lim x \to 0 \frac{{tan}^{3} x - {sin}^{3} x}{x^{5}}$ is $α$ , then $2 α =$

Discussion

26.	If an angle A of a △ ABC satisfies 5cosA+3=0, then the roots of the quadratic equation, 9x2+27x+20=0 are:
Answer» If an angle $A$ of a $△ A B C$ satisfies $5 cos A + 3 = 0,$ then the roots of the quadratic equation, $9 x^{2} + 27 x + 20 = 0$ are:

Discussion

27.	XOZ -plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio
Answer» XOZ -plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

Discussion

28.	If a,b,c be positive, then minimum value of b+ca + c+ab + a+bc is ___
Answer» If a,b,c be positive, then minimum value of $\frac{b + c}{a}$ + $\frac{c + a}{b}$ + $\frac{a + b}{c}$ is ___

Discussion

29.	Consider an equilateral triangle having vertices at the points A(2√3eiπ/2),B(2√3e−iπ/6) and C(2√3e−i5π/6). Let P be any point on its incircle. then AP2+BP2+CP2=
Answer» Consider an equilateral triangle having vertices at the points $A (\frac{2}{\sqrt{3}} e^{i π / 2}), B (\frac{2}{\sqrt{3}} e^{- i π / 6})$ and $C (\frac{2}{\sqrt{3}} e^{- i 5 π / 6}) .$ Let $P$ be any point on its incircle. then $A P^{2} + B P^{2} + C P^{2} =$

Discussion

30.	The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is
Answer» The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

Discussion

31.	Let 2[x+14]∫0{x2}dx={x}∫0[x+14] dx, where [⋅] and {⋅} denote the greatest integer and fractional part of x respectively. If [x]+14=λ{x}, λ∈R, then the value of λ is
Answer» Let $2 [x + 14] \int 0 {\frac{x}{2}} d x = {x} \int 0 [x + 14] d x$ , where $[\cdot]$ and ${\cdot}$ denote the greatest integer and fractional part of $x$ respectively. If $[x] + 14 = λ {x},$ $λ \in R,$ then the value of $λ$ is

Discussion

32.	If tan−1(x2+3\|x\|−4)+cot−1(4π+sin−1(sin14))=π2, then the value of sin−1(sin2\|x\|) is equal to
Answer» If ${tan}^{- 1} (x^{2} + 3 \| x \| - 4) + {cot}^{- 1} (4 π + {sin}^{- 1} (sin 14)) = \frac{π}{2},$ then the value of ${sin}^{- 1} (sin 2 \| x \|)$ is equal to

Discussion

33.	Let A = {a, b, c, d} and f : A → A be given by f = {(a, b), (b, d), (c, a), (d, c)}. Write f -1. [NCERT EXEMPLAR]
Answer» Let A = {a, b, c, d} and f : A $\to$ A be given by f = {(a, b), (b, d), (c, a), (d, c)}. Write f ^{$-$ 1}. [NCERT EXEMPLAR]

Discussion

34.	Let S be the set of all points in (−π,π) at which the function, f(x) = min {sinx,cosx} is not differentiable. Then S is a subset of which of the following?
Answer» Let $S$ be the set of all points in $(- π, π)$ at which the function, $f (x)$ = min ${sin x, cos x}$ is not differentiable. Then $S$ is a subset of which of the following?

Discussion

35.	Range of the function f(x)=x2+1x2+1, is
Answer» Range of the function $f (x) = x^{2} + \frac{1}{x^{2} + 1}$ , is

Discussion

36.	Let the straight line 2x−y+1=0 touch the hyperbola x2a2−y216=1 at P(α,β). Then the value of 2a2+α−3β is equal to
Answer» Let the straight line $2 x - y + 1 = 0$ touch the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{16} = 1$ at $P (α, β) .$ Then the value of $2 a^{2} + α - 3 β$ is equal to

Discussion

37.	Let A and B be two sets defined as A={x:x∈W and −1≤2x+35≤3} and B={x:x∈Z and 0≤3−x7≤1}. If P=A−B and Q=B−A, then the value of n(P×Q) is
Answer» Let $A$ and $B$ be two sets defined as $A = {x : x \in W and - 1 \leq \frac{2 x + 3}{5} \leq 3}$ and $B = {x : x \in Z and 0 \leq \frac{3 - x}{7} \leq 1}$ . If $P = A - B$ and $Q = B - A$ , then the value of $n (P \times Q)$ is

Discussion

38.	19. ABCD is a trapezium in which AB\|\|CD & AD=BC. Show that *
Answer» 19. ABCD is a trapezium in which AB\|\|CD & AD=BC. Show that *

Discussion

39.	In the given figure, ABCD is a trapezium where AB\|\|DC and AD=BC. If ∠CBA=82°, then the measure of ∠ADC is equal to
Answer» In the given figure, $A B C D$ is a trapezium where $A B \| \| D C$ and $A D = B C$ . If $∠ C B A = 82 °$ , then the measure of $∠ A D C$ is equal to

Discussion

40.	The range of k for which both the roots of the quadratic equation (k+1)x2−3kx+4k=0 are greater than 1, is
Answer» The range of $k$ for which both the roots of the quadratic equation $(k + 1) x^{2} - 3 k x + 4 k = 0$ are greater than $1$ , is

Discussion

41.	The intergral ∫2x12+5x9(x5+x3+1)3dx is equal to :
Answer» The intergral $\int \frac{2 x^{12} + 5 x^{9}}{(x^{5} + x^{3} + 1)^{3}}$ dx is equal to :

Discussion

42.	55. What force should be applied on the wedge so thatblock over it does not move? (All surfaces aresmooth)m>F(1) F = (M+ m) g cot 0(2) F = (M+ m) g tan 0(3) F = (M+ m) g sin 0(4) F = (M+ m) g cos 0ntod b
Answer» 55. What force should be applied on the wedge so thatblock over it does not move? (All surfaces aresmooth)m>F(1) F = (M+ m) g cot 0(2) F = (M+ m) g tan 0(3) F = (M+ m) g sin 0(4) F = (M+ m) g cos 0ntod b

Discussion

43.	if cosA + sinA = square root of 2 multiplied by cosA, then show that cosA - sinA = square root of 2 multiplied by sinA
Answer» if cosA + sinA = square root of 2 multiplied by cosA, then show that cosA - sinA = square root of 2 multiplied by sinA

Discussion

44.	Let f(x)=∣∣∣∣cosx1012cosx1012cosx∣∣∣∣. If the value of f′(x)=αsin(βx), then the value of β−α is
Answer» Let $f (x) = ∣ ∣∣ ∣ \begin{matrix} cos x & 1 & 0 1 & 2 cos x & 1 0 & 1 & 2 cos x \end{matrix} ∣ ∣∣ ∣$ . If the value of $f^{'} (x) = α sin (β x),$ then the value of $β - α$ is

Discussion

45.	Two vectors have magnitudes 2 m and 3 m. The angle between them is 600. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.
Answer» Two vectors have magnitudes 2 m and 3 m. The angle between them is $60^{0}$ . Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.

45.

Two vectors have magnitudes 2 m and 3 m. The angle between them is 600. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.

Answer»

Two vectors have magnitudes 2 m and 3 m. The angle between them is $60^{0}$ . Find

(a) the scalar product of the two vectors,

(b) the magnitude of their vector product.

Discussion

46.	Discuss the continuity of the following functions at the indicated point(s):(i) fx=x cos1x,x≠0 0 ,x=0at x=0(ii) fx=x2sin1x,x≠0 0 ,x=0at x=0(iii) fx=(x-a)sin1x-a,x≠a 0 ,x=aat x=a(iv) fx=ex-1log(1+2x), ifx≠a 7 , ifx=0at x=0(v) fx=1-xn1-x,x≠1n-1 ,x=1n∈Nat x=1(vi) fx=x2-1x-1, forx≠1 2 , forx=1at x=1(vii) fx=2x+x2x,x≠0 0 , x=0at x=0(viii) fx=x-asin1x-a, for x≠a0, for x=aat x=a
Answer» Discuss the continuity of the following functions at the indicated point(s): (i) $f (x) = \{\begin{cases} \|x\| \cos (\frac{1}{x}), & x \neq 0 \\ 0, & x = 0 \end{cases} at x = 0$ (ii) $f (x) = \{\begin{array}{l} x^{2} \sin (\frac{1}{x}), & x \neq 0 \\ 0, & x = 0 \end{array} at x = 0$ (iii) $f (x) = \{\begin{array}{l} (x - a) \sin (\frac{1}{x - a}), & x \neq a \\ 0, & x = a \end{array} at x = a$ (iv) $f (x) = \{\begin{array}{l} \frac{e^{x} - 1}{\log (1 + 2 x)}, if & x \neq a \\ 7, if & x = 0 \end{array} at x = 0$ (v) $f (x) = \{\begin{array}{l} \frac{1 - x^{n}}{1 - x}, & x \neq 1 \\ n - 1, & x = 1 \end{array} n \in N at x = 1$ (vi) $f (x) = \{\begin{cases} \frac{\|x^{2} - 1\|}{x - 1}, for & x \neq 1 \\ 2, for & x = 1 \end{cases} at x = 1$ (vii) $f (x) = \{\begin{array}{l} \frac{2 \|x\| + x^{2}}{x}, & x \neq 0 \\ 0, & x = 0 \end{array} at x = 0$ (viii) $f (x) = \{\begin{cases} \|x - a\| \sin (\frac{1}{x - a}), for x \neq a \\ 0, f o r x = a \end{cases} at x = a$

Discussion

47.	If a relation R defined on A={1,3,5,7}, then which of the following is/are void relation?
Answer» If a relation $R$ defined on $A = {1, 3, 5, 7}$ , then which of the following is/are void relation?

Discussion

48.	Find the smallest positive integer n, for which (1+i1−i)n=1.
Answer» Find the smallest positive integer n, for which ${(\frac{1 + i}{1 - i})}^{n} = 1.$

Discussion

49.	Let f(x)=−1+\|x−1\|,1≤x≤3 and g(x)=2−\|x+1\|,−2≤x≤2, then (fog)(x) is equal to
Answer» Let $f (x) = - 1 + \| x - 1 \|, 1 \leq x \leq 3$ and $g (x) = 2 - \| x + 1 \|, - 2 \leq x \leq 2$ , then (fog)(x) is equal to

Discussion

50.	The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is (A) (B) (C) (D) None of these
Answer» The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is (A) (B) (C) (D) None of these

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Prove that :sin^2 x . cos^2 y - cos^2 x . sin^2 y = sin^2 x - sin^2 y

If vectors A--&gt;= cos wt i^ + sin wt j^ and B--&gt; = cos wt /2^i + sin wt/2 j^ are functions of time, then value of t at which they are orthogonal to each other is:

How to do wavy curve method

The number of six digit numbers, all digits of which are odd, is __________.

Sum of integers from 1 to 100 that are divisible by 2 is a, by 5 is b and by both 2 and 5 is c. Find the sum of integers which are divisible 2 or 5.

7。e® cos 3x

mx-n/5 + nx+m/7 + nx = m/8Find the value of x

Find the equation of the striaght lines passing through the following pair of points: (i) (0, 0) and (2, - 2) (ii) (a, b) and ( a + c sin α, b + c cos α) (iii) (0, - a) and (b, 0) (iv) (a, b) and (a + b, a - b) (v) (at1, a/t1) and (at2, a/t2) (vi) (a cos α, a sin α) and (a cos β, a sin β)

Middle point of the chord of the circle x2+y2=25 intercepted on the line x−2y=2 is

A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0,0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

The value of ∫sin(7x2)sin(3x2)dx is(where C is constant of integration)

Calculate the mean deviation about the median of the following frequency distribution : xi57911131517fi246810128

The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

20. If a + b + c = 15 and a2 + b2 + c2 = 83, find the value of a3 + b3 + c3 3abc.

If the focus of the parabola x2−ky+3=0 is (0,2), then the value(s) of k is/are

The number of words that can be made by re-arranging the letters of the word Apurba so that vowels and consonants are alternate is

To divide a line segment AB in the ratio 5:7, first ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is(a) 8(b) 10(c) 11(d) 12

Construct a 2 × 2 matrix A = [aij] whose elements aij are given by aij=-3i+j2, if i≠ji+j2, if i=j

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = – 16y

If the equation ax2+2hxy+by2=0 has one line as the bisector of angle between the coordinate axes, then

The number of solutions of sin5x−cos5x=1cos x−1sin x (where sin x≠cos x) is

The value of cos10°-sin10° is

(→a×→b)(→c×→d)+(→b.→c)(→a.→d) is equal to

If the value of limx→0tan3x−sin3xx5 is α, then 2α=

If an angle A of a △ ABC satisfies 5cosA+3=0, then the roots of the quadratic equation, 9x2+27x+20=0 are:

XOZ -plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

If a,b,c be positive, then minimum value of b+ca + c+ab + a+bc is ___

Consider an equilateral triangle having vertices at the points A(2√3eiπ/2),B(2√3e−iπ/6) and C(2√3e−i5π/6). Let P be any point on its incircle. then AP2+BP2+CP2=

The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

Let 2[x+14]∫0{x2}dx={x}∫0[x+14] dx, where [⋅] and {⋅} denote the greatest integer and fractional part of x respectively. If [x]+14=λ{x}, λ∈R, then the value of λ is

If tan−1(x2+3|x|−4)+cot−1(4π+sin−1(sin14))=π2, then the value of sin−1(sin2|x|) is equal to

Let A = {a, b, c, d} and f : A → A be given by f = {(a, b), (b, d), (c, a), (d, c)}. Write f -1. [NCERT EXEMPLAR]

Let S be the set of all points in (−π,π) at which the function, f(x) = min {sinx,cosx} is not differentiable. Then S is a subset of which of the following?

Range of the function f(x)=x2+1x2+1, is

Let the straight line 2x−y+1=0 touch the hyperbola x2a2−y216=1 at P(α,β). Then the value of 2a2+α−3β is equal to

Let A and B be two sets defined as A={x:x∈W and −1≤2x+35≤3} and B={x:x∈Z and 0≤3−x7≤1}. If P=A−B and Q=B−A, then the value of n(P×Q) is

19. ABCD is a trapezium in which AB||CD & AD=BC. Show that *

In the given figure, ABCD is a trapezium where AB||DC and AD=BC. If ∠CBA=82°, then the measure of ∠ADC is equal to

The range of k for which both the roots of the quadratic equation (k+1)x2−3kx+4k=0 are greater than 1, is

The intergral ∫2x12+5x9(x5+x3+1)3dx is equal to :

55. What force should be applied on the wedge so thatblock over it does not move? (All surfaces aresmooth)m>F(1) F = (M+ m) g cot 0(2) F = (M+ m) g tan 0(3) F = (M+ m) g sin 0(4) F = (M+ m) g cos 0ntod b

if cosA + sinA = square root of 2 multiplied by cosA, then show that cosA - sinA = square root of 2 multiplied by sinA

Let f(x)=∣∣∣∣cosx1012cosx1012cosx∣∣∣∣. If the value of f′(x)=αsin(βx), then the value of β−α is

Two vectors have magnitudes 2 m and 3 m. The angle between them is 600. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.

If a relation R defined on A={1,3,5,7}, then which of the following is/are void relation?

Find the smallest positive integer n, for which (1+i1−i)n=1.

Let f(x)=−1+|x−1|,1≤x≤3 and g(x)=2−|x+1|,−2≤x≤2, then (fog)(x) is equal to

The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is (A) (B) (C) (D) None of these

If vectors A-->= cos wt i^ + sin wt j^ and B--> = cos wt /2^i + sin wt/2 j^ are functions of time, then value of t at which they are orthogonal to each other is: