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In a school, students may bring breakfast, buy it, or may not eat breakfast. If 1/4 of the students bring breakfast, 1/7 don't eat breakfast, and 187 buy it, how many students bring breakfast?
If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
A shopkeeper has 100 kg of good grade rice and x kg of bad grade rice. He brought good and bad grade rice for Rs. 20 and Rs. 10 respectively. He can sell the good and bad grade rice at Rs. 30 and Rs. 13.5 respectively. Out of x kg, if he mixes y kg of bad grade rice with good grade, he will get a profit of 69 2/7% from total sale. If he mixes y/2 kg of bad grade rice with good grade, he will get a profit of 57.5%. What is the profit he would have got if he sold honestly? (in rupees)
Many breakfast cereals are fortified with vitamin supplements , some of these cereals provide 100 percent of the recommended daily requirement of vitamins. Nevertheless, a well -balanced breakfast, including a variety of foods is a better source of those vitamins than are such fortified breakfast cereals alone.
কোনো প্রকার কুঋণ সমন্বয় করার পূর্বে দেনাদারের পরিমাণ হচ্ছে ২০,৫০০ টাকা। কুঋণ ৫০০ টাকা, কুঋণ সঞ্চিতি ৫৫০ টাকা। দেনাদারের উপর ১০% কুঋণ সঞ্চিতি এবং ৫% বাট্টা সঞ্চিতি ধার্য করা হয়। বাট্টা সঞ্চিতির পরিমাণ কত? (The debtors balance appears at Tk. 20,500 prior to bad debt adjustment. Bad debt expense in Tk.500 and bad debt reserve is Tk. 550. A provision is created for bad debt is 10% and is made for a discount of 5%. What will be reserve for discount in taka?)
Consider the following statements:
1. In criminal proceedings good character of the accused is always relevant
2. In criminal proceedings bad character of the accused is always relevant
3. In a civil case evidence of character of any person concerned is always admissible
4. A previous conviction is relevant as evidence of bad character
Which of the statements given above are correct?
The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?
The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$        where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$   is the angular momentum. The Hamiltonian does not commute with
$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$     $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$     $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$     is simplified to :