Questions asked by Subha
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1*2*3*4*5*6.....upto 1000
Find the number of zeroes at the end?

Solve
#sin^1((ax)/c) + sin^1( (bx)/c) = sin^1( x )#where a²+b²=c² and c≠0 ?

If the roots of the equation #ax^2+2bx+c=0# are real and distinct then find the nature of the roots of the equation #(a+c)(ax^2+2bx+c) = 2(ac  b²)(x²+1)#?

If the roots of the equation #ax^2+2bx+c=0# are real and distinct then find the nature of the roots of the equation #(a+c)(ax^2+2bx+c) = 2(ac  b^2)(x^2+1)#?

Solve the following equation in natural numbers :
#x²+y²=1997(xy) #?

Is there any process to determine that a number given is prime number or not?

Which is more stable #cl# or chlorine free redical ?

Find all real matrices #A# , such that #A²= I(2)#
(#A# is a matrix of second order)?

Conversion
Methanol to tertiary butyl cyanide?

Find the number of real root and the number of imaginary root in the following equation
#e^x=x^2# =?

Find the number of four tuples (a,b,c,d) of positive integers satisfying all three equations
#a^3=b^2#,
#c^3=d^2#,
#ca=64# ?

Limit x tends to 0+ #sinx^sinx# ?

Is there any particle that have no mass?

What is the direction of null vector?

Is there any reason for why the O blood group is rear compared to other blood group?

#12^a = 18# & #24^b=16# then find the value of b in terms of a ?

Ortho,parabromoanisole + #NaNH_2# + Liquid #NH_3# =?
How do you predict the product?

If #x_1#,#x_2#,#x_3#,......,#x_n# are #n# real numbers satisfying #0<x_1<x_2<...<x_n<pi/2#, how do you prove that #tanx_1 < (sinx_1+sinx_2+...+sinx_n)/ (cosx_1+cosx_2+...+cosx_n) < tanx_n#?

If a,b,c are real numbers prove that
#(a+bc)^2#+#(b+ca)^2#+#(c+ab)^2)#>= ab+bc+ca ?

1 bromo 3 clorocyclobutane + Metallic sodium = ? ( the medium of reaction is dioxane )?

Why #D_2O# is hydrophobic in nature?

A circular loop of radius a , carrying a current I ,is placed in a 2D magnetic field. The centre of the loop coincides with the centre of the field. The strength of magnetic field at the periphery of loop is B. Find the magnetic force on the wire?

Find maxima of the following expression using calculus
#(2xsin2x)/x^2# ?

Prove that in every year, the 13 th day of some month occurs on a Friday?

#int_0^y e^t dt# + #int_0^x cos(t^2) dt#= 0
Then find the value of #e^y*dy/dx + cos(x^2)# ?

Why do two wires with current flowing in the same direction attract each other, and two wires with current flowing in opposite direction repel?

Find a vector perpendicular to the plane #2*xy+2z=5# ?

#(sin x)^4 / x + (cos x )^4 /y = 1/(x+y)#
Then prove that #(sin x)^12 /x^5 + (cos x)^12 /y^5 = 1/(x+y)^5# ?

Solve for x,y,z in integer.
#x+y+z=1# , #x^3+y^3+z^2=1#?

#int x/(1+x)(1+x^2)dx# ?

#x*y = a(y+√(y²x²))# then show that #x³*dy/dx=y²(y+√(y²x²))# ?

#(1x^4)^½ + (1y^4)^½ =k(x^2y^2)# then show that #dy/dx = x*√(1y^4)/y*√(1x^4)# ?

3,4dimethoxybenzaldehyde is treated with bromine.What will be the product/s ?

N,Ndimethylaniline is treated with #NaNO_2"/dil"HCL#.what will be the product/s?

#AA x,y,z in RR f(x+y+z) = f(x)f(y)f(z)!=0# & #f(2)=5 , f'(0)=2# then find the value of #f'(2)# ?

Why nightblooming flowers are generally white?

Among the red,green,brown algae that inhabit the sea , which is likely to be found in the deepest waters?

Is vegetative reproduction also a type of asexual reproduction? Is the term clone applicable to the offspring formed by vegetative reproduction?

In some plants,where flowering occurs more than once,what would you call the interflowering period"Juvenile" or "mature" ?

How to prepare pentabromobenzene from aniline?

What are matter waves ? I have not understand the topic clearly. Please help me.

What should be the major product if 2methylbuta1,3diene is treated with HBr ?

Find the components of the resultant force on it along&perpendicular to the string?

What will be product(s) if ethylene glycol is treated with fuming sulphuric acid & heat ?

Hunsdiecker reaction follows free radical mechanism. Though 1° radical is less stable, the yield of alkyl halide follows 1° > 2° > 3°. Why?

Silver salt of fatty acid treated with #I_2#/#C Cl_4#. If the ratio of silver salt & iodine is 1:1 then alkyl iodide is formed,if the ratio is 2:1 then ester is formed.Why?

Find all real functions f from #RR>RR# satisfying the relation #f(x²+yf(x))=xf(x+y)# ?

#int (1+sinx)/(sinx * (1+cosx))dx# ?

#int x^2/(xsinx+cosx)^2 dx# ?

#int (sin^8xcos^8x)/(12sin^2xcos^2x)dx#?

Let #RR# denoted the set of real numbers. Find all functions #f:RR>RR#,satisfying #abs(f(x)  f(y)) = 2 abs(xy)# for all #x,y# belongs to #RR#.?

#int (1x)/((1+x)*(x+x^2+x^3)^(1/2)dx#?

If electric field in a point is zero, is it possible that the potential of the point is also zero?

Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise)

The sides AB,BC,CA of a triangle ABC have 3,4,5 interior points respectively on them. Find the total number of triangles that can be constructed by using these points as vertices ?

Give an example which is continous everywhere but not differentiable at 3 points?

#int_0^pi max(sin(x),cos(x)) dx# =?

Consider the functional equation #f(xy)=f(x)/f(y)# . If #f'(0) = p# and #f'(5)=q# , then find #f'(5)# ?

Find the smallest integer that produces remainder of 2,4,6&1 when it is divided by 3,5,7&11 respectively?

Please help ?

Please help me to do this 2 problems?

In a bridge game of playing cards,4 players are distributed one card each by turn so that each player gets 13 cards. Find possible number ways?

How to differentiate a definite integral?

Show that #sum x/2^x = 2# summation running 0 to infinity ?

Find the number of squares in this picture?

D is matrix of order #n*n# such that #D=Diag[d_1,d_2,.....d_n]# find f(D)?

Prove that power set is a field?

Find the inflection point of the function #e^(x/2)# ?

Prove that in a real vector space #V# #c(alpha  beta ) = c*alpha  c*beta # where #c in RR ; alpha,beta in V# ?

For what value of #lamda# the following vectors will form a basis for #E^3#
#a_1 = (1,5,3) , a_2 = (4,0,lamda) , a_3 = (1,0,0) # ?

What can be said about differentiation of a constant with respect to a constant & differentiation of a variable with respect to a constant?

Show that,
#(1+cos theta + i*sin theta)^n + (1+cos theta  i*sin theta)^n = 2^(n+1) * (cos theta/2)^n * cos (n*theta/2)# ?