Show that
Question: Show that $\left|\begin{array}{cc}\sin 10^{\circ} -\cos 10^{\circ} \\ \sin 80^{\circ} \cos 80^{\circ}\end{array}\right|=1$ Solution: Let $\Delta=\left|\begin{array}{cc}\sin 10^{\circ} -\cos 10^{\circ} \\ \sin 80^{\circ} \cos 80^{\circ}\end{array}\right|$ $\Rightarrow \Delta=\sin 10^{\circ} \cos 80^{\circ}+\cos 10^{\circ} \sin 80^{\circ}$ $=\sin 10^{\circ} \cos \left(90^{\circ}-10^{\circ}\right)+\cos 10^{\circ} \sin \left(90^{\circ}-10^{\circ}\right) \quad[\because \cos \theta=\sin (90-...
Read More →Solve the following equations
Question: Evaluate $\left|\begin{array}{ccc}2 3 7 \\ 13 17 5 \\ 15 20 12\end{array}\right|^{2}$ Solution: Let $A=\left|\begin{array}{ccc}2 3 7 \\ 13 17 5 \\ 15 20 12\end{array}\right|=2(204-100)-3(156-75)+7(260-255)$ $\Rightarrow A=2(104)-3(81)+7(5)$ $\Rightarrow A=208-243+35$ $\Rightarrow A=243-243=0$ $\therefore\left|\begin{array}{ccc}2 3 7 \\ 13 17 5 \\ 15 20 12\end{array}\right|=0$ $\Rightarrow\left|\begin{array}{ccc}2 3 7 \\ 13 17 5 \\ 15 20 12\end{array}\right|^{2}=0^{2}=0$ $\left[\because...
Read More →Evaluate the following determinants:
Question: Evaluate the following determinants: (i) $\left|\begin{array}{cc}x -7 \\ x 5 x+1\end{array}\right|$ (ii) $\left|\begin{array}{cc}\cos \theta -\sin \theta \\ \sin \theta \cos \theta\end{array}\right|$ (iii) $\left|\begin{array}{ll}\cos 15^{\circ} \sin 15^{\circ} \\ \sin 75^{\circ} \cos 75^{\circ}\end{array}\right|$ (iv) $\left|\begin{array}{cc}a+i b c+i d \\ -c+i d a-i b\end{array}\right|$ Solution: (i) $\Delta=x(5 x+1)+7 x=5 x^{2}+x+7 x$ $=5 x^{2}+8 x$ (ii) $\Delta=\cos ^{2} \theta-\le...
Read More →Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case:
Question: Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case:(i) $A=\left[\begin{array}{ll}5 20 \\ 0 -1\end{array}\right]$ (ii) $A=\left[\begin{array}{cc}-1 4 \\ 2 3\end{array}\right]$ (iii) $A=\left[\begin{array}{ccc}1 -3 2 \\ 4 -1 2 \\ 3 5 2\end{array}\right]$ (iv) $A=\left[\begin{array}{lll}1 a b c \\ 1 b c a \\ 1 c a b\end{array}\right]$ (v) $A=\left[\begin{array}{lll}0 2 6 \\ 1 5 0 \\ 3 7 1\end{array}\...
Read More →Why is AIDS considered to be a
Question: Why is AIDS considered to be a "syndrome" and not a disease? (CCE 2012) Solution: Syndrome is a group of symptoms, signs, physical and physiological disturbances that are due to a common cause. AIDS is also a complex of diseases and symptoms which develop due to failure of the body to fight off even minor infections. HIV that causes AIDS damages immune system of the patient by destroying T4 lymphocytes. As a result, even small cold leads to development of pneumonia, a minor gut infecti...
Read More →For what values of a and b if A = B, where
Question: For what values ofaandbifA=B, where $A=\left[\begin{array}{cc}a+4 3 b \\ 8 -6\end{array}\right], B=\left[\begin{array}{cc}2 a+2 b^{2}+2 \\ 8 b^{2}-5 b\end{array}\right]$ Disclaimer: There is a misprint in the question, $b^{2}-5 b$ should be written instead of $b^{2}-56$. Solution: As the given matricesAandB are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get $a+4=2 a+2 \quad 3 b=b^{2}+2$ $8=8 \quad-6=b^{2}-5 b$ On simplifying...
Read More →Give any four factors necessary
Question: Give any four factors necessary for a healthy person. (CCE 2012) Solution: 1. Environment, 1. A clean physical environment with the help of public health services, 2. A congenial social environment. 2. Personal Hygiene. Personal cleanliness prevents catching up of infectious diseases. 3. Nourishment. A proper balanced diet keeps the immune system strong. 4. Vaccination. Timely vaccination against major diseases protects oneself from catching those diseases. 5. Avoiding overcrowded area...
Read More →Becoming exposed to or infected
Question: Becoming exposed to or infected with a microbe does not necessarily mean developing noticeable disease. Explain. Solution: An infectious microbe is able to cause a disease only if the immune system of the person is unable to put proper defence against it. Many persons have strong immune system or have acquired immunity against the pathogen or the pathogen attack is less than the infective dose. In such cases, despite exposure to infective microbe, the person will not catch the disease....
Read More →Find the values of x and y if
Question: Find the values ofxandyif $\left[\begin{array}{cc}x+10 y^{2}+2 y \\ 0 -4\end{array}\right]=\left[\begin{array}{cc}3 x+4 3 \\ 0 y^{2}-5 y\end{array}\right]$ Solution: Here, $x+10=3 x+4 \quad[\because$ All the corresponding elements of the matrix are equal $]$ $\Rightarrow x-3 x=4-10$ $\Rightarrow-2 x=-6$ $\therefore x=3$ Also, $y^{2}+2 y=3$ $\Rightarrow y^{2}+2 y-3=0$ $\Rightarrow y^{2}+3 y-y-3=0$ $\Rightarrow y(y+3)-1(y+3)=0$ $\Rightarrow(y+3)(y-1)=0$ $\Rightarrow y+3=0$ or $y-1=0$ $\R...
Read More →Why are antibiotics not
Question: Why are antibiotics not effective for viral diseases? (CCE 2011, 2012) Solution: Antibiotics are effective against bacteria and some other non-viral pathogens as they block some of their biosynthetic pathways without affecting human beings. However, viruses do not have their own metabolic machinery. There are very few biochemical processes that can block viral multiplication. Antibiotics are not effective against them. They can be over-powered only by specific anti-viral drugs....
Read More →Why do some children fall ill
Question: Why do some children fall ill more frequently than others living in the same locality? Solution: Children fall ill more frequendy due to 1. Poor personal hygiene 2. Poor domestic hygiene 3. Playing over floor 4. Eating with unclean hands. 5. Lack of proper nutrition and balanced diet. All these make the immune system weak....
Read More →What precautions would you take to justify
Question: What precautions would you take to justify "prevention is better than cure". (CCE 2011, 2012) Solution: Prevention is always better than cure as a disease always causes some damage to the body, loss of working days, besides expenditure on medication. The important precautions for preventing diseases are 1. Hygienic environment 2. Personal hygiene 3. Proper nutrition 4. Clean food 5. Clean water 6. Regular exercise and 7. Relaxation: Every body should also be aware of diseases and their...
Read More →For what values of x and y are the following matrices equal?
Question: For what values ofxandyare the following matrices equal? $A=\left[\begin{array}{cc}2 x+1 2 y \\ 0 y^{2}-5 y\end{array}\right], B=\left[\begin{array}{cc}x+3 y^{2}+2 \\ 0 -6\end{array}\right]$ Solution: As the given matricesAandBare equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get $2 x+1=x+3 \quad 2 y=y^{2}+2$ $\begin{array}{ll}0=0 y^{2}-5 y=-6\end{array}$ On simplifying, we get $x=2$, but there is no common value of $y$ for which...
Read More →Why is immune system essential for our health?
Question: Why is immune system essential for our health? Solution: Immune system is body defence system against various types of pathogens. It has many componentsphagocytic cells, natural killer cells, T-lymphocytes and B-lymphocytes. B-lymphocytes produce antibodies against pathogens and their toxins. Immune system keeps the body healthy by killing infecting microbes....
Read More →For what values of x and y are the following matrices equal?
Question: For what values ofxandyare the following matrices equal? $A=\left[\begin{array}{cc}2 x+1 2 y \\ 0 y^{2}-5 y\end{array}\right], B=\left[\begin{array}{cc}x+3 y^{2}+2 \\ 0 -6\end{array}\right]$ Solution: As the given matricesAandBare equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get $2 x+1=x+3 \quad 2 y=y^{2}+2$ $\begin{array}{ll}0=0 y^{2}-5 y=-6\end{array}$ On simplifying, we get $x=2$, but there is no common value of $y$ for which...
Read More →What do you mean by disease symptoms?
Question: What do you mean by disease symptoms? Explain giving two examples. Solution: Symptoms: They are manitestations or evidences of the presence of diseases. Symptoms are in the form of structural and functional changes in the body or body parts. They indicate that there is something wrong in the body, e.g. wound with pus, cough, cold, loose motions, pain in abdomen, headache, fever. Symptoms do not give any exact cause of the disease. For instance, headache is due to some dozen different d...
Read More →The sales figure of two car dealers during January 2013 showed that dealer A sold 5 deluxe,
Question: The sales figure of two car dealers during January 2013 showed that dealerAsold 5 deluxe, 3 premium and 4 standard cars, while dealerBsold 7 deluxe, 2 premium and 3 standard cars. Total sales over the 2 month period of January-February revealed that dealerAsold 8 deluxe 7 premium and 6 standard cars. In the same 2 month period, dealerB sold 10 deluxe, 5 premium and 7 standard cars. Write 2 3 matrices summarizing sales data for January and 2-month period for each dealer. Solution: Accor...
Read More →What is disease?
Question: What is disease? How many types of diseases have you studied? Give examples. (CCE 2011) Solution: Disease. It is a condition of derangement or disturbed functioning of the body or its part. Types of Diseases: 1. On the Basis of Duration. Acute and chronic. 2. On the Basis of Period of Occurrence. Congenital and acquired. 3. On the Basis of Causal Agent. Infectious and non-infectious. Infectious or communicable diseases can be contagious or non-contagious. Non-infectious disease may be ...
Read More →Given an example of
Question: Given an example of (i) a row matrix which is also a column matrix, (ii) a diagonal matrix which is not scalar, (iii) a triangular matrix Solution: (i) [6] This is a matrix that contains only one element. (ii) $\left[\begin{array}{lll}1 0 0 \\ 0 2 0 \\ 0 0 3\end{array}\right]$ For a diagonal matrix which is not scalar, all elements except those in the leading diagonal should be zero and the elements in the diagonal should not be equal. (iii) $\left[\begin{array}{lll}1 2 3 \\ 0 5 4 \\ 0...
Read More →Explain giving reasons:
Question: Explain giving reasons: 1. Balanced diet is necessary for maintaining healthy body. 2. Health of an organism depends upon the surrounding environmental conditions. 3. Our surrounding area should be free of stagnant water. (CCE 2012) 4. Social harmony and good economic conditions are necessary for good health. Solution: 1. Balanced diet provides all the nutrients for metabolic activities of the organism. 2. Environment contributes the immediate, second level and third level of causes. 3...
Read More →Name any two groups of microorganisms
Question: Name any two groups of microorganisms from which antibiotics could be extracted. Solution: Bacteria, Fungi....
Read More →Classify the following diseases as infectious and non-infectious:
Question: Classify the following diseases as infectious and non-infectious: 1. AIDS 2. Tuberculosis 3. Cholera 4. High blood pressure 5. Heart disease 6. Pneumonia 7. Cancer. Solution: 1. AIDS-infectious, 2. Tuberculosis-infectious, 3. Cholera-infectious, 4. High Blood Pressure-non-infectious. 5. Heart Disease-non-infectious. 6. Pneumonia-infectious, 7. Cancer-non-infectious....
Read More →Solve the following equations
Question: If $\left[\begin{array}{cc}x y 4 \\ z+6 x+y\end{array}\right]=\left[\begin{array}{cc}8 w \\ 0 6\end{array}\right]$, then find the values of $x, y, z$ and $w$. Solution: As the given matrices are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get $x y=8 \quad 4=w$ $z+6=0 \quad x+y=6$ On simplifying, we get $x=2, y=4, z=-6, w=4 \quad$ or $\quad x=4, y=2, z=-6, w=4$ Hence, the values of $x, y, z$ and $w$ is $2,4,-6,4$ or $4,2,-6,4$....
Read More →Fill in the blanks:
Question: Fill in the blanks: disease continues for many days and causes .. on body. .. disease continues for a few days and causes no long term effect on body. .. is defined as physical, mental and social well being and comfort. Common cold is disease. Many skin diseases are caused by . . Solution: 1. Chronic, long-term effect 2. Acute 3. Health 4. Infectious (communicable) 5. Fungi....
Read More →(a) Who discovered vaccine for the first time.
Question: (a) Who discovered vaccine for the first time. (b) Name two diseases which can be prevented by using vaccines. Solution: (a) Edward Jenner (b) Pertussis, diphtheria, tuberculosis, polio....
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