Questions asked by Shwetank Mauria

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• Cube root of a number is equal to its own cube. What are all the possibilities for this number?
  
• Penny was looking at her clothes closet. The number of dresses she owned were 18 more than twice the number of suits. Together, the number of dresses and the number of suits totaled 51. What was the number of each that she owned?
  
• Solve the following?
  
• What is its volume of the card box, whose dimensions are given below?
  
• Simplify: #((-24)/(-4))-:2+3*(-5+1)^2#?
  
• Simplify #(2x^2+3x+4)(5x^2+7x+6)#?
  
• How can we find the sign, positive or negative, of #(8(-2)(14)(-3)(-38))/((-19)(-28)(-27))#, without determining numerical answer?
  
• If street lights are placed at most 132 feet apart, how many street lights will be needed for a street that is 4 miles long, assuming that there are lights at each side of the street?
  
• The length L of a rectangle is 9 feet shorter than 4 times its width W. What is the perimeter of the rectangle in terms of its width alone?
  
• Connie cracks open a piggy bank and finds $3.70 (370 cents), all in nickels and dimes. There are 7 more dimes than nickels. How many nickels does Connie have?
  
• The largest side of a right triangle is #a^2+b^2# and other side is #2ab#. What condition will make the third side to be the smallest side?
  
• How do you prove that sum of the squares on the sides of a rhombus is equal to the sum of squares on its diagonals?
  
• When a number is divided by #2#, #3#, #4#, #5# or #6#, we always get a remainder of #1#. But on dividing a number by #7#, we find the number is divisible? What is the smallest such number? What are other such numbers? and how to solve such problems?
  
• How do you prove that arithmetic mean, geometric mean and harmonic mean of two numbers are in geometric sequence?
  
• How do you prove Ptolemy's Theorem that in a cyclic quadrilateral, sum of the products of opposite pair of sides is equal to the product of the diagonals?
  
• Two circles having equal radii #r_1# and touching a line #l#on the same side of #l# are at a distance of #x# from each other. Third circle of radius #r_2# touches the two circles. How do we find the height of third circle from #l#?
  
• A parallelogram has an inscribed circle touching all its four sides. How do you prove that it is a rhombus?
  
• How do you prove that sum of infinite series #1+1/4+1/9+...............# is less than two?
  
• If sum of #p# terms of an arithmetic sequence is #q# and sum of #q# terms is #p#, then prove that sum #(p+q)# terms is #-(p+q)#. Also find the sum of first #(p-q)# terms (#p>q#)?
  
• How to prove the following? #cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3#
  
• If #5^(10x)=4900# and #2^(sqrty)=25#, what is the value of #((5^((x-1)))^5)/4^(-sqrty)#?
  
• If #a, b, c# are in H.P., show that #a/(b+c), b/(c+a), c/(a+b)# are also in H.P.?
  
• If #sinx+sin^2x=1# and #acos^12x+bcos^8x+c cos^6x-1=0#, then what is the value of #a^2+b^2+c^2#?
  
• Tangents are drawn from an external point #(x_1,y_1)# to the circle #x^2+y^2=a^2#. How do we find the angle between the two tangents?