Jay's Mathematics Classes

 📝NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES EXERCISE 3.1 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. Solution: Let the present age of the Aftab be `x` and the daughter's age be `y`. Seven years ago Aftab's age `= (x -7)` Daughter's age `= (y - 7)` `(x - 7) = 7(y - 7)` `⇒ x - 7 = 7y -49` `⇒ x - 7y = - 49 + 7` `⇒ x- 7y = - 42` Three years from now Aftab's age `= (x +3)` Daughter's age `= (y + 3)` `(x + 3) = 3(y + 3)` `⇒ x + 3 = 3y +9` `⇒ x - 3y = 9 -3` `⇒ x - 3y = 6` Algebraic representation: ` x- 7y = - 42;  x - 3y = 6` Table ` x- 7y = - 42` Table `x - 3y = 6` Graphical represe...

 NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers EXERCISE 1.1 2. Show that any positive odd integer is of form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. Solution Let `a` be the positive integer and `b` = 6 Applying Euclid's division lemma `a = 6q + r, 0 ≤ r < 6` Case I  If   `r = 0` then `a = 6q` Case II   If  `r = 1` then `a = 6q +1` Case III   If  `r = 2` then `a = 6q +2` Case IV   If   `r = 3` then `a = 6q + 3` Case V If   `r = 4` then `a = 6q + 4` Case VI  If   `r = 5` then `a = 6q + 5` `therefore` Case II `a = 6q +1`, Case IV `a = 6q + 3` , Case VI   `a = 6q + 5` are odd integers.  4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form `3m` or `3m + 1` for some integer `m.` Solution Let `a` be the positive integer and `b = 3` Applying Euclid's division lemma `a = 3q + r , 0 ≤ r < 3` Case I...

 Heredity and Evolution  Questions 1. Mustard was growing in two fields- A and B. While Field A produced brown coloured seeds, field B produced yellow coloured seeds. It was observed that in field A, the offsprings showed only the parental trait for consecutive generations, whereas in field B, the majority of the offsprings showed a variation in the progeny. What are the probable reasons for these? Ans:  In field A, the reason for the parental trait in consecutive generations of the offsprings is self-pollination.  In field B, variation is seen to occur because of recombination of genes as cross - pollination is taking place. 2. In an asexually reproducing species, if a trait X exists in 5% of a population and trait Y exists in 70% of the same population, which of the two trait is likely to have arisen earlier? Give reason. Ans:  Trait Y which exists in 70% (larger fraction) of the population, is likely to have arisen earlier because in asexual reproduction, ide...

 Circles  1. The tangent at a point C of a circle and a diameter AB when extended intersect at P.  If `angle`PCA=110º , find `angle`CBA [see Fig. ]. 2. In Fig. O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB. 3. In Fig. common tangents AB and CD to two circles intersect at E. Prove that AB = CD. 4. In Fig, tangents `PQ` and `PR` are drawn to a circle such that `angleRPQ = 30°`. A chord `RS` is drawn parallel to the tangent `PQ.` Find the `angleRQS.` Ans:  Given  PR and PQ are the tangents drawn from P.  ∠RPQ =  30° Hence, PR = PQ (Tangents drawn from an external point are equal)  ∴  `anglePRQ = anglePQR` In `trianglePQR` `anglePRQ + anglePQR + angleRPQ = 180°` 2`anglePQR = 150°` `therefore anglePQR = 75°` `anglePQR = angleRSQ` (Alternate Segment Theorem) Given `RS∥ PQ` `therefore anglePQR = angleSRQ = 75° ` (Alternat...

Magnetic Effects of Electric Current Question  Multiple Choice Questions 1. Choose the incorrect statement from the following regarding magnetic lines of field (a) The direction of the magnetic field at a point is taken to be the direction in which the north pole of a magnetic compass needle points (b) Magnetic field lines are closed curves (c) If magnetic field lines are parallel and equidistant, they represent zero-field strength (d) Relative strength of the magnetic field is shown by the degree of closeness of the field lines 2. If the key in the arrangement is taken out (the circuit is made open) and magnetic field lines are drawn over the horizontal plane ABCD, the lines are (a) concentric circles (b) elliptical in shape (c) straight lines parallel to each other (d) concentric circles near the point O but of elliptical shapes as we go away from it. Ans: (c) 3. A constant current flows in a horizontal wire in the plane of the paper from east to west as shown in Figure. The dire...

 How do Organisms Reproduce? How do we know that two different individual organisms belong to the same species? Usually, we say this because they look similar to each other. Thus, reproducing organisms create new individuals that look very much like themselves. Do Organisms Create Exact Copies of Themselves? Organisms look similar because their body designs are similar. If body designs are to be similar, the blueprints for these designs should be similar. Thus, reproduction at its most basic level will involve making copies of the blueprints of body design. The chromosomes in the nucleus of a cell contain information for the inheritance of features from parents to next generation in the form of DNA (Deoxyribo Nucleic Acid) molecules. The DNA in the cell nucleus is the information source for making proteins. If the information is changed, different proteins will be made. Different proteins will eventually lead to altered body designs. The Importance of DNA Copying In Reproduction Th...