28278 + Interview Questions in Maths in Class 12

1.	If the lines (x-2)/(1)=(y-4)/(4)=(z-6)/(k)and (x+1)/(3)=(y+3)/(5)=(z+5)/(7) are coplanar, then the value of k is
Answer» 7 3 -3 -7 Answer :A

Discussion

2.	An electronic assembly consists of two sub-systems, say, A and B. From previous -testing procedures, the following probabilities are assumed to be known. P(A fails)= 0.2 (B fails alone) = 0.15P(A and B fail)= 0.15 Evaluate the following probabilities i. P(A fails\|B has failed) ii. P(A fails alone)
Answer» ANSWER :i. `(1)/(2)`, II. 0.05

Discussion

3.	Find the eqation of the plane passing through (a,b,c) and parallel to the plane vecr.(hati+hatj+hatk)=2
Answer» Answer :`hati+hatj+hatk` is a vector normal to the given plane. Since the required plane and the given plane are PARALLEL, this vector will be a vector noraml to the required plane also. `therefore` The DIRECTION ratios of the normal to the required plane are 1,1,1. Hence, the required equation is 1(x-a)+1(y-b)+1(z-c)=0 x-a+y-b+z=0 i.e., x+y+z=a+b+c

Discussion

4.	Evaluate int_(0)^(pi) sin^(3) theta(1+2 cos theta) (1+cos theta)^(2)d theta
Answer» ANSWER :`8/3`

Discussion

5.	The vertex A of a triangle lies on the lines x+y=1 and 2x+3y=6 . If the orthocentre of the triangle is O ((3)/(7),(22)/(7)) then the equation of OA in the normal form is
Answer» x cos`alpha+ysinalpha=7, alpha=tan^(-1)(1)/(7)` `x cos alpha+ysin alpha = (13)/(SQRT(17)), alpha= tan^(-1)((1)/(4))` `XCOS alpha + ysin alpha = (13)/(4), alpha = tan^(-1) ((13)/(sqrt(17)))` `x cos alpha+ysin alpha= (13)/(sqrt(17)), alpha = tan^(-1)(4)` Answer :D

Discussion

6.	How many 5-digits numbers form from the digits { 0, 1 ,……..9 } have ?
Answer» Strictly INCREASING digits Strictly increasing or DECREASING digits Increasing digits Increasing or decreasing digits Solution :(i) 252, (II) 512, (iii) 2002, (IV) 3994

Discussion

7.	A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2,11)} Is f a function from A to B ? Give reason for your answer.
Answer» SOLUTION :N/A

Discussion

8.	Evaluate (i) int_(0)^(1) (dx)/(e^(x)+e^(-x))
Answer» ANSWER :`TAN^(-1) (E) - pi/4`

Discussion

9.	For all x gt 0
Answer» `(2x)/(5) GT LOG (1+x)` ` x gt log (1+x)` `x LT log (1+x)` `x=log (1+x)` Answer :B

Discussion

10.	Solve as directed : 2(3x-1) lt 7x + 1 lt 3 (2x +1) for real values.
Answer» SOLUTION :2(3x-1) `lt` 7x + 1 `lt` 3 (2x +1) `6X-2 lt 7x +1 lt 6x + 3` ` -2 lt x+1 lt 3 `rArr -3 lt x lt 2` If x `in` R the solution set is S = { x:x `in` R and `-3 lt x lt 2`} {-3,2}

Discussion

11.	If int (2^(x) 3^(x))/(5^(2x). 7^(x)) dx = (1)/(k) ((2^(x).3^(x))/(5^(2x).7^(x))) + cthen k =
Answer» `log2 - LOG 3 + 2 log 5 - log 7` `log 2 + log 3 + 2LOG 5 + log 7` `log 2 + log 3 - 2 log 5- log 7` `(1)/("log 2 + log 3 - 2 log 5 - log 7")` Answer :C

Discussion

12.	Find the angles between the lines (x-2)/2=(y-1)/5=(z+3)/-3and(x+2)/-1=(y-4)/8=(z-5)/4
Answer» ANSWER :The direction RATIOS of the two lines are respectively 2, 5, -3 and -1, 8, 4 `therefore costheta=(a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2)) = (2xx(1)+5xx8+(-3)xx4)/(sqrt(4+25+9)sqrt(1+64+16)) = (-2+40-12)/(sqrt38sqrt81) = (26)/(9sqrt36)rArrtheta = cos^(-)(26/(9sqrt38))`

Discussion

13.	If the vectors 2hati-3hatj+4hatk and hati+2hatj-hatk and m hati - hatj+2hatk are coplanar, then the value of m is
Answer» `(5)/(8)` `(8)/(5)` `-(7)/(4)` `(2)/(3)` Solution :GIVEN vectors will be COPLANAR, if `\|(2, -3, 4),(1,2,-1),(m,-1,2)\|=0` `implies 2(4-1)+3(2 +m) +4(-1-2m)=0` `implies m=8/5`

Discussion

14.	Two circles intersect at the point P (2,3) and the line joining the other extermity of the two diameter through P makes an angle pi//6 with x-axis, then the equation of the common chord of the two circle is
Answer» `X + sqrt3 y - (2 + 3 sqrt3)=0` `x+ SQRT3Y - (2 sqrt3 +2) =0` `sqrt3 x +y - (2 sqrt3+3) =0` `sqrt3 + y-(2 + 3SQRT3) =0` ANSWER :C

Discussion

15.	Let pi_(1)and pi_(2) be two planes and angle be a line such thet pi_(1): x + 2y + 3z = 14 pi_(2) : 2x - y +3z = 27 angle : (x+1)/2=(y+1)/3=(z+1)/4 The line through P perpendicular to the plane pi_(1) passes through the point
Answer» `(1, 1, 1)` `(0, 1, 0)` `(0, 0, 0)` `(0, 0, 1)` ANSWER :C

Discussion

16.	The position vectors of two points A and B are respectively 6vec(a)+2vec(b) and vec(a)-3bar(b). If the point C divides AB internally in the ratio 3 : 2 then the position vector of C is ……………
Answer» `3vec(a)-VEC(B)` `3vec(a)+vec(b)` `vec(a)+vec(b)` `vec(a)-vec(b)` ANSWER :A

Discussion

17.	e_(1),e_(2) arerespectively the eccentricites of the hfyperbola x^(2)-y^(2) cosec^(2) theta=5 and the ellipsex^(2) cosect^(2) theta+y^(2)=5 if 0lt thetalt pi//2 and e_(1)=sqrt(7) then theta is equal to
Answer» `(pi)/(4)` `(pi)/(6)` `(pi)/(3)` NONE of these ANSWER :c

Discussion

18.	A rectangular sheet of tin 45 cm by 24 cm is to made into a box without top, by cutting-off square from each other corner and folding up the flaps. What should be the side of the square to be cut-off so that the volume of the box is maximum?
Answer» ANSWER :x=5 CM

Discussion

19.	Evaluate the following integrals int_(0)^(pi/4) (sin x + cos x)/(9+ 16 sin 2x) dx
Answer» ANSWER :`1/20 LOG 3`

Discussion

20.	If f (6-x ) =f (x), for all then 1/5 int _(2)^(3) x [f (x) + f (x+1)]dx is equal to :
Answer» `INT _(3) ^(4) f (X+z) DX` `int _(3 )^(4) f (x+1) dx` ` int _(1) ^(2) f (x+1) dx` `int _(1) ^(3) f (x) dx` Solution :`I =1/5 int _(2)^(3) x [ f (x) + f (x+1)]dx""…(i)` `I =1/5 int _(2)^(3) ( 5-x) [f (5-x) + f (6-x)]dx` II)` Adding (i) and (ii) `2I =5/5 int _(2)^(3) [f (x) + f(x+1) ]dx` `2I = int _(2)^(2) f (x) dx + int _(2) ^(3) f (x+1) dx` `2I = int _(2)^(3) f (x) dx + int _(2)^(3) f [6-x] dx` `2I = int _(2) ^(3) f (x) dx + int _(2)^(3) f (x) dx` `I = int _(2)^(3) f (x) dx implies I= int _(1) ^(2) f (x +1) dx`

Discussion

21.	Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -int_(alpha)^(beta) y(t) x'(t) dt , S = int_(alpha)^(beta) x (t) y' (t) dt S = (1)/(2) int_(alpha)^(beta) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area of the region bounded by the an arc of cycloid x = a (t - sin t) , y = a ( 1 - cost) and the x-axis
Answer» `pi a^(2)` `pi ` `3 pi a^(2)` `4 pi a^(2)` Answer :C

Discussion

22.	If f(x)=x^2 and g(x)= sinx thenf@g(x) is
Answer» SIN^2(X) sin(x^2) (x^2 )(SINX) sin(x^3) ANSWER :A

Discussion

23.	A determinant is chosen at random from the set of all 2 xx 2 determinants with elements -1, 0, 1 only. Find the probability that the determinant chosen is positive.
Answer» ANSWER :`(8)/(27)`

Discussion

24.	Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2z = 5.
Answer» ANSWER :ANGLE `theta=cos^(-1)(5SQRT3)/(21)`

Discussion

25.	Let pi_(1)and pi_(2) be two planes and angle be a line such thet pi_(1): x + 2y + 3z = 14 pi_(2) : 2x - y +3z = 27 angle : (x+1)/2=(y+1)/3=(z+1)/4 If the line in the last question meets the plane pi_(2) in the point Q then the co-ordinates of mid-point of P and Q is
Answer» `(1, 2, 3)` `(3, 6, 9) `(2, 3, 4)` `(2, 4, 6)` ANSWER :D

Discussion

26.	Evaluate the integrals by using substitution int_(0)^(2)(dx)/(x+4-x^(2))
Answer» ANSWER :`1/(SQRT17)LOG(21+5sqrt17)/4`

Discussion

27.	Let z_k=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","List II"),((P) " For each " z_k"there exists a " z_j" such that " z_k.z_j=1,1."True"),((Q)"There exists a "k in{1,2,....9}"such that "z_1.z=z_k" has no solution z in the set of complex numbers.",2. False),((R)(\|1-z_1\|\|1-z_2\|....\|1-z_9\|)/10 "equal ",3.1),((S)1-sum_(k=1)^9cos((2kpi)/(10))"equal" ,4.2):}
Answer» <P>`{:(P,Q,R,S),(1,2,4,3):}` `{:(P,Q,R,S),(2,1,3,4):}` `{:(P,Q,R,S),(1,2,3,4):}` `{:(P,Q,R,S),(2,1,4,3):}` ANSWER :C

Discussion

28.	Show that the lines vecr=(4veci+5vecj+6veck)+t(2veci+3vecj+4veck) and vecr=(2veci+3vecj+4veck)+s(3veci+4vecj+5veck) are coplanar. Find the equation of the plane in which they lie.
Answer» SOLUTION :N/A

Discussion

29.	The value of a for which the equations x^(3)+ax+1=0 and x^(4)+ax^(2)+1=0 have a common root is
Answer» -2 -1 1 2 Answer :A

Discussion

30.	Find the derivative of sin^(-1) [(2^(x+1).3^(x))/(1+ (36)^(x))] with respect to x.
Answer» ANSWER :`(2^(x+1).3^(x))/(1+ (36)^(2)) LOG 6`

Discussion

31.	The minimum value \|x-6\| + \|x+3\| + \|x-8\|+\|x-4\|+\|x-3\| is
Answer» 11 21 31 42 Answer :B

Discussion

32.	An A.P. consists of 23 terms. If the sum of the three terms Is the middle is 141 and the sum of the last three terms is 261, then the first is
Answer» 6 5 4 3 Answer :D

Discussion

33.	Integrate the following rational functions : int(1)/(sinx-sin2x)dx
Answer» ANSWER :`-(1)/(6)log\|1+cosx\|-(1)/(2)log\|1-cosx\|+(2)/(3)log\|1-2cosx\|+c`

Discussion

34.	Integrate the rational functions x/((x+1)(x+2))
Answer» ANSWER :`"LOG"((x+2)^(2))/(\|x+1\|)+C`

Discussion

35.	int cosh^(-1) ((x)/(3))dx =
Answer» `x " cosh"^(-1) ""(x)/(3) + sqrt(x^(2) - 9) + C ` `x " cosh"^(-1) ""(x)/(3) + sqrt(x^(2) - 3) + c ` `x " cosh"^(-1) ""(x)/(3) - sqrt(x^(2) - 9) + c ` `(1)/(2) x^(2) " cosh"^(-1) ""((x)/(3)) + sqrt(x^(2) - 9) + c ` ANSWER :C

Discussion

36.	The order and degree of the differential equation y = x(dy)/(dx)-sqrt(1+((dy)/(dx))^(2))
Answer» (2,1) (2,2) (1,2) (1,1) ANSWER :C

Discussion

37.	Find \|veca-vecb\|, if two vectors vecaandvecb are such that \|veca\|=2,\|vecb\|=3andveca*vecb=4.
Answer» `sqrt3` `SQRT(15)` 1 `SQRT5` ANSWER :D

Discussion

38.	Find (dy)/(dx) in the following sin^(2)y+ cos xy= k
Answer» ANSWER :`(y.sin XY)/(sin2y- x.sin xy)`

Discussion

39.	Examine the continuity of the following functions at indicated points.f(x)={((x^2-a^2)/(x-a),if xnea atx=a),(a, ifx=a):}
Answer» Solution :`lim_(xtoa)f(X)=lim_(xtoa)(x^2-a^2)/(x-a)` `lim_(xtoa)((x-a)(x+a))/(x-a)` `lim_(xtoa)(x+a)=2a` Now f(a)=a Hence `lim_(xtoa)f(x)NEF(a)` So f(x)is not CONTINUOUS at x=a

Discussion

40.	A company manufactures two types of screws A and B. all the screws have to pass through a threading machine and a slotting machine. A box of type A screw requires 2min on the threading machine and 3 min on the slotting machine. A box of type B screw requires 8 min on the threading machine and 2 min on the slotting machine. In a week each machine is availbale for 60h. On selling these screws, the company gets a profit of 100 box on type A screw and 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.
Answer» Solution :Let the company manufactures x boxes of TYPES A SCREWS and y boxes of types B screws From the given INFORMATION, we have following correspondingconstraint table Thus, we see that objective function for maximum proft is Z=100x+170y Subject to constraints `2x+8y le 60 XX 60 ["time constraints for threading machine"]` `Rightarrow x+4y le 1800..(i) ` and `3x+2y le 60xx60["time constraint for slotting machine"]` `Rightarrow 3x+2y le 3600....(ii)` Also, `x ge 0, y ge 0 ["non negative contraints"] ...(iii)` `therefore "REQUIRED LPP is"` Maximise `Z=100x+170y` Subject to constraints `x+4y le 1800, 3x+2y le 3600, x ge 0, y le 0`,

Discussion

41.	Evaluate the following integral int (1)/(sqrt(sin^(3) x sin( x + alpha)))dx
Answer» ANSWER :`-(2)/(SINALPHA)SQRT(sinalphacotx+cosalpha)+C`

Discussion

42.	If the eccentric angle of the point of contact of common tangent on the hyperbola is (3pi)/4 then the number of distinct normals that can be drawn to the curve (y + 4)^(2)= 2 sqrt2 (x + 2 sqrt 2) from the point of contact is
Answer» 1 2 3 none of these SOLUTION :N/A

Discussion

43.	The value of .^(40)C_(0) xx .^(100)C_(40) - .^(40)C_(1) xx .^(99)C_(40) + .^(40)C_(2) xx .^(98)C_(40) "……." + .^(40)C_(40) xx .^(60)C_(40) is equal to "____".
Answer» SOLUTION :Given sum `=` Coefficient of `x^(40)` in `.^(40)C_(0)(1+x)^(100) - .^(40)C_(1)(1+x)^(99) + .^(40)C_(2)(1+x)^(96)+"….."+.^(40)C_(40)(1+x)^(60)` = Coefficient of `x^(40)` in `(1+x)^(60)(.^(40)C_(0)(1+x)^(40)-.^(40)C_(1)(1+x)^(39)+.^(40)C_(2)(1+x)^(38)+"....."+.^(40)C_(40))` `=` Coefficient of `x^(40)` in `(1+x)^(60)(1+x-1)^(40)` = Coefficient of `x^(40)` in `(1+x)^(60)x^(40)` `= 1`

Discussion

44.	Let C be a circle whose centre is on te x-axis. Suppose C touches the line 3x + 4y =5 at (1,1). If (alpha, beta) lies on the circle C, then \|3alpha + 4 beta-5\| cannot exceed
Answer» ANSWER :`12.50`

Discussion

45.	If 8 le E le 42 kJ/mol then which type of bond formation is possible (where E is bond energy ) ?
Answer» IONIC BOND Covalent bond HYDROGEN bond Vander waal's FORCE

Discussion

46.	There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2). If the number of rectangles formed by these two sets of lines is 225, then the value of n is equals to
Answer» `4` `5` `6` `7` Solution :`(C )` `"^(N)C_(2)*^(n)C_(2)=225impliesn=6`

Discussion

47.	Solvethe equationfor x 3sin^(2)(x/(2))+cos^(2)(x/(2))+4sin(x/(2))cos(x/(2))-8sin(x/(2))=0
Answer» ANSWER :no SOLUTION

Discussion

48.	Area of the region bounded by two parabolas y=x^(2) and x=y^(2) is
Answer» ANSWER :`1/3`

Discussion

49.	If f(x) is continuous such that abs(f(x)) le 1, forall x in R " and " g(x)=(e^(f(x))-e^(-abs(f(x))))/(e^(f(x))+e^(-abs(f(x)))), then range of g(x) is
Answer» `[0,1]` `[0, (E ^(2)+1)/(e ^(2)-1)]` `[0, (e ^(2)-1)/(e ^(2)+1)]` `[ (e ^(2)+1)/(e ^(2)+1),0]` ANSWER :D

Discussion

50.	If \|z -1\| lt 2 \|z - 2\| then the locus of z = x + iy is
Answer» `X^(2) + y^(2) + 3x - 2 = 0` `3x^(2) + 3y^(2) - 14 x + 15 GT 0` `3x^(2) + 3y^(2) - 14 x + 15 lt 0` `3x^(2) + 3y^(2) - 14 x + 15 = 0` Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the lines (x-2)/(1)=(y-4)/(4)=(z-6)/(k)and (x+1)/(3)=(y+3)/(5)=(z+5)/(7) are coplanar, then the value of k is

An electronic assembly consists of two sub-systems, say, A and B. From previous -testing procedures, the following probabilities are assumed to be known. P(A fails)= 0.2 (B fails alone) = 0.15P(A and B fail)= 0.15 Evaluate the following probabilities i. P(A fails|B has failed) ii. P(A fails alone)

Find the eqation of the plane passing through (a,b,c) and parallel to the plane vecr.(hati+hatj+hatk)=2

Evaluate int_(0)^(pi) sin^(3) theta(1+2 cos theta) (1+cos theta)^(2)d theta

The vertex A of a triangle lies on the lines x+y=1 and 2x+3y=6 . If the orthocentre of the triangle is O ((3)/(7),(22)/(7)) then the equation of OA in the normal form is

How many 5-digits numbers form from the digits { 0, 1 ,……..9 } have ?

A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2,11)} Is f a function from A to B ? Give reason for your answer.

Evaluate (i) int_(0)^(1) (dx)/(e^(x)+e^(-x))

For all x gt 0

Solve as directed : 2(3x-1) lt 7x + 1 lt 3 (2x +1) for real values.

If int (2^(x) 3^(x))/(5^(2x). 7^(x)) dx = (1)/(k) ((2^(x).3^(x))/(5^(2x).7^(x))) + cthen k =

Find the angles between the lines (x-2)/2=(y-1)/5=(z+3)/-3and(x+2)/-1=(y-4)/8=(z-5)/4

If the vectors 2hati-3hatj+4hatk and hati+2hatj-hatk and m hati - hatj+2hatk are coplanar, then the value of m is

Two circles intersect at the point P (2,3) and the line joining the other extermity of the two diameter through P makes an angle pi//6 with x-axis, then the equation of the common chord of the two circle is

Let pi_(1)and pi_(2) be two planes and angle be a line such thet pi_(1): x + 2y + 3z = 14 pi_(2) : 2x - y +3z = 27 angle : (x+1)/2=(y+1)/3=(z+1)/4 The line through P perpendicular to the plane pi_(1) passes through the point

The position vectors of two points A and B are respectively 6vec(a)+2vec(b) and vec(a)-3bar(b). If the point C divides AB internally in the ratio 3 : 2 then the position vector of C is ……………

e_(1),e_(2) arerespectively the eccentricites of the hfyperbola x^(2)-y^(2) cosec^(2) theta=5 and the ellipsex^(2) cosect^(2) theta+y^(2)=5 if 0lt thetalt pi//2 and e_(1)=sqrt(7) then theta is equal to

A rectangular sheet of tin 45 cm by 24 cm is to made into a box without top, by cutting-off square from each other corner and folding up the flaps. What should be the side of the square to be cut-off so that the volume of the box is maximum?

Evaluate the following integrals int_(0)^(pi/4) (sin x + cos x)/(9+ 16 sin 2x) dx

If f (6-x ) =f (x), for all then 1/5 int _(2)^(3) x [f (x) + f (x+1)]dx is equal to :

If f(x)=x^2 and g(x)= sinx thenf@g(x) is

A determinant is chosen at random from the set of all 2 xx 2 determinants with elements -1, 0, 1 only. Find the probability that the determinant chosen is positive.

Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2z = 5.

Let pi_(1)and pi_(2) be two planes and angle be a line such thet pi_(1): x + 2y + 3z = 14 pi_(2) : 2x - y +3z = 27 angle : (x+1)/2=(y+1)/3=(z+1)/4 If the line in the last question meets the plane pi_(2) in the point Q then the co-ordinates of mid-point of P and Q is

Evaluate the integrals by using substitution int_(0)^(2)(dx)/(x+4-x^(2))

Show that the lines vecr=(4veci+5vecj+6veck)+t(2veci+3vecj+4veck) and vecr=(2veci+3vecj+4veck)+s(3veci+4vecj+5veck) are coplanar. Find the equation of the plane in which they lie.

The value of a for which the equations x^(3)+ax+1=0 and x^(4)+ax^(2)+1=0 have a common root is

Find the derivative of sin^(-1) [(2^(x+1).3^(x))/(1+ (36)^(x))] with respect to x.

The minimum value |x-6| + |x+3| + |x-8|+|x-4|+|x-3| is

An A.P. consists of 23 terms. If the sum of the three terms Is the middle is 141 and the sum of the last three terms is 261, then the first is

Integrate the following rational functions : int(1)/(sinx-sin2x)dx

Integrate the rational functions x/((x+1)(x+2))

int cosh^(-1) ((x)/(3))dx =

The order and degree of the differential equation y = x(dy)/(dx)-sqrt(1+((dy)/(dx))^(2))

Find |veca-vecb|, if two vectors vecaandvecb are such that |veca|=2,|vecb|=3andveca*vecb=4.

Find (dy)/(dx) in the following sin^(2)y+ cos xy= k

Examine the continuity of the following functions at indicated points.f(x)={((x^2-a^2)/(x-a),if xnea atx=a),(a, ifx=a):}

Evaluate the following integral int (1)/(sqrt(sin^(3) x sin( x + alpha)))dx

If the eccentric angle of the point of contact of common tangent on the hyperbola is (3pi)/4 then the number of distinct normals that can be drawn to the curve (y + 4)^(2)= 2 sqrt2 (x + 2 sqrt 2) from the point of contact is

The value of .^(40)C_(0) xx .^(100)C_(40) - .^(40)C_(1) xx .^(99)C_(40) + .^(40)C_(2) xx .^(98)C_(40) "……." + .^(40)C_(40) xx .^(60)C_(40) is equal to "____".

Let C be a circle whose centre is on te x-axis. Suppose C touches the line 3x + 4y =5 at (1,1). If (alpha, beta) lies on the circle C, then |3alpha + 4 beta-5| cannot exceed

If 8 le E le 42 kJ/mol then which type of bond formation is possible (where E is bond energy ) ?

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2). If the number of rectangles formed by these two sets of lines is 225, then the value of n is equals to

Solvethe equationfor x 3sin^(2)(x/(2))+cos^(2)(x/(2))+4sin(x/(2))cos(x/(2))-8sin(x/(2))=0

Area of the region bounded by two parabolas y=x^(2) and x=y^(2) is

If f(x) is continuous such that abs(f(x)) le 1, forall x in R " and " g(x)=(e^(f(x))-e^(-abs(f(x))))/(e^(f(x))+e^(-abs(f(x)))), then range of g(x) is

If |z -1| lt 2 |z - 2| then the locus of z = x + iy is