11 NCERT MATH SUBJECTIVE QUESTIONS

Q1. Write the coordinates of points in the Y-Z plane Solution The coordinates of points in the Y-Z plane are (0,y,z). Q2. A point is in the YZ plane. What is the value of the x-coordinate? Solution Since the point lies in the YZ plane the value of x-cordinate is zero. Q3. Find the locus of P if PA 2 + PB 2 = 2k 2 where A and B are the points (3,4,5) and (-1,3,-7). Solution Let P(x,y,z) be the point whose locus is to be found, NowPA 2 + PB 2 = 2k 2 .(x - 3) 2 + (y - 4) 2 + (z - 5) 2 + (x + 1) 2 + (y - 3) 2 + (z + 7) 2 =2k 2 x 2 - 6x + 9 + y 2 - 8y + 16 + z 2 - 10z + 25 + x 2 + 2x + 1 + y 2 - 6y + 9 + z 2 + 14z + 49 = 2k 2 2x 2 + 2y 2 + 2z 2 - 4x - 14y + 4z + 109 = 2k 2 . Q4. A point P is on the x-axis. What are its y-coordinate and z-coordinate? Solution The point lies on the x-axis hence the y and z co-ordinates are zero. The co-ordinates of P are (x,0,0). Q5. Write the coordinates of points in the X-Y plane. Solution Th...

Q1. The digits 1,2,3,....,9 are written in random order to form a 9 digit number.find the probability that this number will be divisible by 2? Solution These 9 digits can be arranged in 9! ways. for the number to be divisible by 2 it should be even i.e. the last digit should be either 2,4,6,8. which can be chosen in 4 ways then the remaining 8 digits can be arranged in 8! ways. So the required probability is= Q2. Out of 13 applicants for a job, there are 5 women and 8 men.It is desired to select 2 persons for the job. The probability that atleast one of the selected person will be woman? Solution The probability that none of the women will be selected=The probability of both men selected The probability of both men selected= The probability of atleast one woman will be selected=1- Q3. In a class 40% of the students offered Physics 20% offered Chemistry and 5%offered both.If a student is selected at random then find the probability that he has offered Physics or C...

Q1. A beam is supported at its ends by supports which are 14 cm apart. Since the load is concentrated at its centre, there is a deflection of 5 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 2 cm? Solution Q2. Find the centre and radius of the circle given by the equation (x + 5) 2 + (y + 1 ) 2 = 9 Solution Comparing to the standard equation of the circle (x - h) 2 + (y - k) 2 = r 2 . We have centre (-5,-1) and radius r = 3. Q3. Find the equation of the parabola with V(0,0) and focus (0,-2). Solution The vertex is the origin and the focus is (0,-2) which lies on the y - axis. Here a = -2, hence the parabola is of the form x 2 = -4ay.Hence the equation of the parabola is x 2 = -8y.Alert !  The negative sign is the formula x 2 = -4ay signifies that it is a downwoard parabola. Take a = 2, as the negative sigin is already considered in the formula. Q4. Find the equation of the parabo...

Q1. Define sequence and real sequence? Solution Sequence: A sequence is a function whose domain is the set of natural numbers.   Real Sequence: A real sequence is a function with domain N and the range a subset of the set of real numbers. Q2. Find the ratio of n th term of the sequence 2,4,8,16,32,64,..... to the n th term of the sequence 3,9,27,81,243,....? Solution   The sequence 2,4,8,16,32,64,.... follow the rule x n =2 n n=1,2,3,.... The sequence 3,9,27,81,243,.... follow the rule x n =3 n n=1,2,3,.... So the ratio is     Q3. A person is entitled to receive an annual payment which for each year is less by one tenth of what it was for the year before.If the first payment is 100 find the maximum possible payment which he can receive however long he may live? Solution Q4. Find the sum of the series 2 2 + 4 2 + 6 2 + 8 2 + … to n terms. Solution Q5. If m times the m th  term of an AP is n times the ...

Q1. I have four currency notes valued at Rs 50,100 and 2 notes of 500.In how many ways can I select the currency note ,so that only one type of note is selected each time? Solution We have 3 notes here, 50, 100 and 500.   So I can pick a 50 Rupee note, 100 Rupee note and a 500 Rupee note. So I have 3 selections here.   I can also pick all three at the same time. (50,100,500) This would count as one selection.   I can also choose two at a time   Hence, I can take either a 50 and a 100 rupee note, a 100 and a 500 rupee note, and a 50 and a 500 rupee note. Hence, there are 3 more cases here.   Total number of possible selections –3+3+1=7 Q2. In a class there are 27 boys and 15 girls.  The teacher wants to select a boys and a girl for the monitor ship of the class.  In how many ways can the teacher make this selection? Solution The teacher has to perform two jobs   First, he has to select a boy among 27 boys. Second, he has to sele...

Q1. List all the elements of the following setC = {x : x is a month of the year having 31 days starting with J} Solution There are three months starting with J: January, June and July. June has 30 days in it. So C = {January, July} Q2. Is the collection of all intelligent persons in India a set? Solution The collection of all intelligent persons in India is not well- defined, because the criterion for determining an intelligent person may vary. Hence, the given collection is not a set. Q3. In a pollution study of 1500 Indian rivers the following data were reported. 520 were polluted by sulphur compunds, 335 were polluted by phosphorous, 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compunds, 152 were polluted by sulphate and phosphate compounds only, 150 were polluted by phosphate and crude oil, and 28 were polluted by all 3 compounds. How many of the rivers were polluted by exactly one of the 3 impurities? Solution S=rive...