Correct the following statements:
Question: Correct the following statements: (a)Surgical methods of contraception prevent gamete formation. (b)All sexually transmitted diseases are completely curable. (c)Oral pills are very popular contraceptives among the rural women. (d)In E. T. techniques, embryos are always transferred into the uterus. Solution: (a)Surgical methods of contraception prevent gamete formation. Correction Surgical methods of contraception prevent the flow of gamete during intercourse. (b)All sexually transmitte...
Read More →State True/False with explanation
Question: State True/False with explanation (a)Abortions could happen spontaneously too. (True/False) (b)Infertility is defined as the inability to produce a viable offspring and is always due to abnormalities/defects in the female partner. (True/False) (c)Complete lactation could help as a natural method of contraception. (True/False) (d)Creating awareness about sex related aspects is an effective method to improve reproductive health of the people. (True/False) Solution: (a)Abortions could hap...
Read More →Show that the function defined by is a continuous function.
Question: Show that the function defined by $f(x)=|\cos x|$ is a continuous function. Solution: The given function is $f(x)=|\cos x|$ Thisfunctionfis defined for every real number andfcan be written as the composition of two functions as, $f=g \circ h$, where $g(x)=|x|$ and $h(x)=\cos x$ $[\because(g o h)(x)=g(h(x))=g(\cos x)=|\cos x|=f(x)]$ It has to be first proved that $g(x)=|x|$ and $h(x)=\cos x$ are continuous functions. $g(x)=|x|$ can be written as $g(x)= \begin{cases}-x, \text { if } x0 \...
Read More →What are the measures one has to take to prevent from contracting STDs?
Question: What are the measures one has to take to prevent from contracting STDs? Solution: Sexually transmitted diseases (STDs) get transferred from one individual to the other through sexual contact. Adolescents and young adults are at the greatest risk of acquiring these sexually transmitted diseases. Hence, creating awareness among the adolescents regarding its after-effects can prevent them from contracting STDs. The use of contraceptives, such as condoms, etc. while intercourse, can preven...
Read More →Suggest some methods to assist infertile couples to have children.
Question: Suggest some methods to assist infertile couples to have children. Solution: Infertility is the inability of a couple to produce a baby even after unprotected intercourse. It might be due to abnormalities present in either male or female, or might be even both the partners. The techniques used to assist infertile couples to have children are as follows. (a)Test tube babies Thisinvolves in-vitro fertilization where the sperms meet the egg outside the body of a female. The zygote, hence ...
Read More →Amniocentesis for sex determination is banned in our country.
Question: Amniocentesis for sex determination is banned in our country. Is this ban necessary? Comment. Solution: Amniocentesis is a pre-natal diagnostic technique that is used to determine the sex and metabolic disorders of the developing foetus in the mothers uterus through the observation of the chromosomal patterns. This method was developed so as to determine any kind of genetic disorder present in the foetus. However, unfortunately, this technique is being misused to detect the sex of the ...
Read More →Reduce the following equations into intercept form and find their intercepts on the axes.
Question: Reduce the following equations into intercept form and find their intercepts on the axes. (i) $3 x+2 y-12=0$ (ii) $4 x-3 y=6$ (iii) $3 y+2=0$. Solution: (i) The given equation is 3x+ 2y 12 = 0. It can be written as $3 x+2 y=12$ $\frac{3 x}{12}+\frac{2 y}{12}=1$ i.e., $\frac{x}{4}+\frac{y}{6}=1$ $\ldots(1)$ This equation is of the form $\frac{x}{a}+\frac{y}{b}=1$, where $a=4$ and $b=6$. (ii) The given equation is 4x 3y= 6. It can be written as $\frac{4 x}{6}-\frac{3 y}{6}=1$ $\frac{2 x}...
Read More →Removal of gonads cannot be considered as a contraceptive option. Why?
Question: Removal of gonads cannot be considered as a contraceptive option. Why? Solution: Contraceptive devices are used to prevent unwanted pregnancy and to prevent the spreading of STDs. There are many methods, such as natural, barrier, oral, and surgical methods, that prevent unwanted pregnancy. However, the complete removal of gonads cannot be a contraceptive option because it will lead to infertility and unavailability of certain hormones that are required for normal functioning of accesso...
Read More →Is the use of contraceptives justified? Give reasons.
Question: Is the use of contraceptives justified? Give reasons. Solution: Yes, the use of contraceptives is absolutely justified. The human population is increasing tremendously. Therefore, to regulate the population growth by regulating reproduction has become a necessary demand in the present times. Various contraceptive devices have been devised to reduce unwanted pregnancies, which help in bringing down the increased birth rate and hence, in checking population explosion....
Read More →Show that the function defined by f (x) = cos (x2) is a continuous function.
Question: Show that the function defined by $f(x)=\cos \left(x^{2}\right)$ is a continuous function. Solution: The given function is $f(x)=\cos \left(x^{2}\right)$ Thisfunctionfis defined for every real number andfcan be written as the composition of two functions as, $f=g \circ h$, where $g(x)=\cos x$ and $h(x)=x^{2}$ $\left[\because(g o h)(x)=g(h(x))=g\left(x^{2}\right)=\cos \left(x^{2}\right)=f(x)\right]$ It has to be first provedthatg(x) = cosxandh(x) =x2are continuous functions. It iseviden...
Read More →What are the suggested reasons for population explosion?
Question: What are the suggested reasons for population explosion? Solution: The human population is increasing day by day, leading to population explosion. It is because of the following two major reasons. (a)Decreased death rate (b)Increased birth rate and longevity The death rate has decreased in the past 50 years. The factor leading to decreased death rate and increased birth rate are control of diseases, awareness and spread of education, improvement in medical facilities, ensured food supp...
Read More →Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts.
Question: Reduce the following equations into slope-intercept form and find their slopes and they-intercepts. (i) $x+7 y=0$ (ii) $6 x+3 y-5=0$ (iii) $y=0$ Solution: (i) The given equation is $x+7 y=0$. It can be written as $y=-\frac{1}{7} x+0$ $\ldots(1)$ This equation is of the form $y=m x+c$, where $m=-\frac{1}{7}$ and $c=0$. Therefore, equation $(1)$ is in the slope-intercept form, where the slope and the $y$-intercept are $-\frac{1}{7}$ and 0 respectively. (ii) The given equation is $6 x+3 y...
Read More →Do you think that reproductive health in our country has improved in the past 50 years?
Question: Do you think that reproductive health in our country has improved in the past 50 years? If yes, mention some such areas of improvement. Solution: Yes, the reproductive health has tremendously improved in India in the last 50 years. The areas of improvement are as follows. (1)Massive child immunization programme, which has lead to a decrease in the infant mortality rate (2)Maternal and infant mortality rate, which has been decreased drastically due to better post natal care (3)Family pl...
Read More →Is sex education necessary in schools? Why?
Question: Is sex education necessary in schools? Why? Solution: Yes, introduction of sex education in schools is necessary. It would provide right information to young individuals at the right time about various aspects of reproductive health such as reproductive organs, puberty, and adolescence related changes, safe sexual practices, sexually transmitted diseases, etc. The young individual or adolescents are more susceptible in acquiring various sexually transmitted diseases. Hence, providing i...
Read More →Suggest the aspects of reproductive health which need to be given special attention in the present scenario.
Question: Suggest the aspects of reproductive health which need to be given special attention in the present scenario. Solution: Reproductive health is the total well being in all aspects of reproduction. The aspects which have to be given special attention in the present scenarios are (1)Counselling and creating awareness among people, especially the youth, about various aspects of reproductive health, such as sexually transmitted diseases, available contraceptive methods, case of pregnant moth...
Read More →By using the concept of equation of a line, prove that the three points (3, 0),
Question: By using the concept of equation of a line, prove that the three points (3, 0),(2, 2) and (8, 2) are collinear. Solution: In order to show that points (3, 0), (2, 2), and (8, 2) are collinear, it suffices to show that the line passing through points (3, 0) and (2, 2) also passes through point (8, 2). The equation of the line passing through points (3, 0) and (2, 2) is $(y-0)=\frac{(-2-0)}{(-2-3)}(x-3)$ $y=\frac{-2}{-5}(x-3)$ $5 y=2 x-6$ i.e., $2 x-5 y=6$ It is observed that at $x=8$ an...
Read More →Find the values of a and b such that the function defined by
Question: Find the values ofaandbsuch that the function defined by $f(x)= \begin{cases}5, \text { if } x \leq 2 \\ a x+b, \text { if } 2x10 \\ 21, \text { if } x \geq 10\end{cases}$ is a continuous function. Solution: The given function $f$ is $f(x)= \begin{cases}5, \text { if } x \leq 2 \\ a x+b, \text { if } 2x10 \\ 21, \text { if } x \geq 10\end{cases}$ It isevident that the given functionfis defined at all points of the real line. Iffis a continuous function, thenfis continuous at all real n...
Read More →What do you think is the significance of reproductive health in a society?
Question: What do you think is the significance of reproductive health in a society? Solution: Reproductive health is the total well being in all aspects of reproduction. It includes physical, emotional, behavioural, and social well being. Sexually transmitted diseases such as AIDS, gonorrhoea, etc. are transferred from one individual to another through sexual contact. It can also lead to unwanted pregnancies. Hence, it is necessary to create awareness among people, especially the youth, regardi...
Read More →Point R (h, k) divides a line segment between the axes in the ratio 1:2.
Question: Point R (h, k) divides a line segment between the axes in the ratio 1:2.Find equation of the line. Solution: Let AB be the line segment between the axes such that point R (h,k) divides AB in the ratio 1: 2. Let the respective coordinates of A and B be (x, 0) and (0,y). Since point R (h,k) divides AB in the ratio 1: 2, according to the section formula, $(h, k)=\left(\frac{1 \times 0+2 \times x}{1+2}, \frac{1 \times y+2 \times 0}{1+2}\right)$ $\Rightarrow(h, k)=\left(\frac{2 x}{3}, \frac...
Read More →How many eggs do you think were released by the ovary of a female dog
Question: How many eggs do you think were released by the ovary of a female dog which gave birth to 6 puppies? Solution: Dogs and rodents are polyovulatory species. In these species, more than one ovum is released from the ovary at the time of ovulation. Hence, six eggs were released by the ovary of a female dog to produce six puppies....
Read More →P (a, b) is the mid-point of a line segment between axes.
Question: P (a, b) is the mid-point of a line segment between axes.Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$ Solution: Let AB be the line segment between the axes and let P (a,b) be its mid-point. Let the coordinates of A and B be (0,y) and (x, 0) respectively. Since P (a,b) is the mid-point of AB, $\left(\frac{0+x}{2}, \frac{y+0}{2}\right)=(a, b)$ $\Rightarrow\left(\frac{x}{2}, \frac{y}{2}\right)=(a, b)$ $\Rightarrow \frac{x}{2}=a$ and $\frac{y}{2}=b$ $\therefore x=2 a$ and ...
Read More →Find the values of k so that the function f is continuous at the indicated point.
Question: Find the values ofkso that the functionfis continuous at the indicated point. $f(x)=\left\{\begin{array}{l}k x+1, \text { if } x \leq 5 \\ 3 x-5, \text { if } x5\end{array} \quad\right.$ at $x=5$ Solution: The given function $f$ is $f(x)=\left\{\begin{array}{l}k x+1, \text { if } x \leq 5 \\ 3 x-5, \text { if } x5\end{array}\right.$ The given functionfis continuous atx= 5, iffis defined atx= 5 and if the value offatx= 5 equals the limit offatx= 5 It is evident that $f$ is defined at $x...
Read More →Find the values of k so that the function f is continuous at the indicated point.
Question: Find the values ofkso that the functionfis continuous at the indicated point. $f(x)=\left\{\begin{array}{l}k x+1, \text { if } x \leq \pi \\ \cos x, \text { if } x\pi\end{array} \quad\right.$ at $x=\pi$ Solution: The given function is $f(x)= \begin{cases}k x+1, \text { if } x \leq \pi \\ \cos x, \text { if } x\pi\end{cases}$ The given functionfis continuous atx=p, iffis defined atx=pand if the value offatx=pequals the limit offatx=p It is evident that $f$ is defined at $x=\mathrm{p}$ a...
Read More →The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre.
Question: The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre? Solution: The relationship between selling price and demand is linear. Assuming selling price per litre along thex-axis and demand along they-axis, we have two points i.e., (14, 980) and (16, 1220) in the XY plane that satisfy t...
Read More →The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C.
Question: The length $L$ (in centimetre) of a copper rod is a linear function of its Celsius temperature $C$. In an experiment, if $L=124.942$ when $C=20$ and $L=125.134$ when $C=110$, express $L$ in terms of $C$. Solution: It is given that when C = 20, the value of L is 124.942, whereas when C = 110, the value of L is 125.134. Accordingly, points (20, 124.942) and (110, 125.134) satisfy the linear relation between L and C. Now, assuming C along thex-axis and L along they-axis, we have two point...
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