Maths-
General
Easy

Question

A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length

  1. m2 – n2    
  2. m (n + 1) n (n + 1)    
  3. 4m + n – 2    
  4. m2n2    

hintHint:

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length. We have to find the number of rectangles possible with odd side length.

The correct answer is: m2n2


    Now we have given that a rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having an edge length of one unit.
    There are 2n horizontal lines and 1 2 m vertical lines (numbered 1,2.......2n).
    Two horizontal lines, one with an even number and one with an odd number, as well as two vertical lines must be chosen in order to create the necessary rectangle.
    Then the number of rectangles will be:
    (1+3+5+......+(2m1))(1+3+5+......+(2n1))=m2n2
    So it is m2n2.

    Here we used the concept of number system and the rectangle, we can also solve it by permutation and combination. herefore, we get the number of rectangles possible with odd side length = m2n2.

    Related Questions to study

    General
    maths-

    nCr + 2nCr+1 + nCr+2 is equal to (2  less or equal thanless or equal than n)

    nCr + 2nCr+1 + nCr+2 is equal to (2  less or equal thanless or equal than n)

    maths-General
    General
    maths-

    The coefficient of x to the power of n in fraction numerator x plus 1 over denominator left parenthesis x minus 1 right parenthesis squared left parenthesis x minus 2 right parenthesis end fraction is

    The coefficient of x to the power of n in fraction numerator x plus 1 over denominator left parenthesis x minus 1 right parenthesis squared left parenthesis x minus 2 right parenthesis end fraction is

    maths-General
    General
    Maths-

    How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which not two S are adjacent ?

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is equals 7 cross times space C presuperscript 6 subscript 4 cross times C presuperscript 8 subscript 4.

    How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which not two S are adjacent ?

    Maths-General

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is equals 7 cross times space C presuperscript 6 subscript 4 cross times C presuperscript 8 subscript 4.

    parallel
    General
    Maths-

    The value of 50C4 + not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscriptis -

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is C presuperscript 56 subscript 4.

    The value of 50C4 + not stretchy sum subscript r equals 1 end subscript superscript 6 end superscript 56 minus r C subscript 3 end subscriptis -

    Maths-General

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is C presuperscript 56 subscript 4.

    General
    Maths-

    The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.

    The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

    Maths-General

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.

    General
    physics-

    A mass of 100 blank g strikes the wall with speed 5 blank m divided by s at an angle as shown in figure and it rebounds with the same speed. If the contact time is 2 cross times 10 to the power of negative 3 end exponent s e c, what is the force applied on the mass by the wall

    A mass of 100 blank g strikes the wall with speed 5 blank m divided by s at an angle as shown in figure and it rebounds with the same speed. If the contact time is 2 cross times 10 to the power of negative 3 end exponent s e c, what is the force applied on the mass by the wall

    physics-General
    parallel
    General
    maths-

    If the locus of the mid points of the chords of the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, drawn parallel to y equals m subscript 1 end subscript x is y equals m subscript 2 end subscript x then m subscript 1 end subscript m subscript 2 end subscript equals

    If the locus of the mid points of the chords of the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, drawn parallel to y equals m subscript 1 end subscript x is y equals m subscript 2 end subscript x then m subscript 1 end subscript m subscript 2 end subscript equals

    maths-General
    General
    Maths-

    If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is C presuperscript n plus 2 end presuperscript subscript r plus 1 end subscript.

    If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-

    Maths-General

    The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is C presuperscript n plus 2 end presuperscript subscript r plus 1 end subscript.

    General
    maths-

    The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

    The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

    maths-General
    parallel
    General
    physics-

    An intense stream of water of cross-sectional area A strikes a wall at an angle theta with the normal to the wall and returns back elastically. If the density of water is rho and its velocity is v,then the force exerted in the wall will be

    An intense stream of water of cross-sectional area A strikes a wall at an angle theta with the normal to the wall and returns back elastically. If the density of water is rho and its velocity is v,then the force exerted in the wall will be

    physics-General
    General
    physics-

    The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line O A will

    The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line O A will

    physics-General
    General
    physics-

    Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are vand 2 v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A

    Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are vand 2 v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A

    physics-General
    parallel
    General
    maths-

    In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is

    In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is

    maths-General
    General
    maths-

    The number of non-negative integral solutions of x + y + z  n, where n  N is -

    The number of non-negative integral solutions of x + y + z  n, where n  N is -

    maths-General
    General
    maths-

    Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

    Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

    maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.