CBSE ADDA

1. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).   [Hint: let the point be P(x, y, z). given points be A(1, 2, 3) and B(3, 2, - 1). Then PA = PB] ans: x – 2z = 0 2.Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10.  [Hint: let the point be P(x, y, z). given points be A(4, 0, 0) and B(-4, 0, 0). Then PA + PB = 10] 3.Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.  Ans: i) (-4/5, 1/5, 27/5) ii) (-8, 17, 3) 4.Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.  Ans : 1:2  5. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).  [hint: any point on YZ plane is of the form (0, y, z)] ans: 2:3  6. Find

You first read CBSE X Maths Constructions Solved Questions CONSTRUCTIONS Questions for self practice  1. Draw a line segment AB of length 4.4cm. Taking A as centre, draw a circle of radius 2cm and taking B as centre, draw another circle of radius 2.2cm. Construct tangents to each circle from the centre of the other circle. 2. Draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 90. 3. Construct a tangent to a circle of radius 2cm from a point on the concentric circle of radius 2.6cm and measure its length. Also, verify the measurements by actual calculations. (length of tangent =2.1cm) 4. Construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle. 5. Draw a line segment AB of length 8cm. taking A as center, draw a circle of radius 4cm and taking B as centre, draw another circ

                                            ir 1. The number of solutions of the pair of linear equations  x +  2 y –  8 = 0 and 2 x +  4 y =  16 is : (a) 0 (b) 1 (c) infinitely many (d) none of these 2. The graphical representation of the pair of equations  x +  2 y –  4 = 0 and 2 x +  4 y –  12 = 0 represents (a) intersecting lines (b) parallel lines (c) coincident lines (d) all of these 3. If a pair of linear equations is consistent, then the lines will be : (a) parallel (b) always coincident (c) intersecting or coincident (d) always intersecting 4. The condition so that the pair of linear equations  kx +  3 y +  1 = 0, 2 x + y +  3 = 0 has exactly one solution is : (a)  k =  6 (b)  k  ≠ 6 (c)  k =  3 (d)  k  ≠ 3 5. The lines representing the linear equations 2 x – y =  3 and 4 x – y =  5 : (a) intersect at a point   (b) are parallel (c) are coincident (d) intersect at exactly two points 6. The pair of linear equations 2 x +  5 y = – 11 and 5 x +  15 y

X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank for CBSE EXAMS 1. If radii of the two  concentric circles  are 15cm and 17cm , then find the length of each chord of one circle which is tangent to one other.  Ans. 16cm 2. If two tangents making an angle of 120 0   with each other , are drawn to a circle of radius 6cm, then find the angle between the two radii, which are drawn to the tangents.            Ans. 60 0 3. PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that  < QPT = 60  degree   then find <PRQ.                                Ans. 120 0   4. If a tangent PQ at a point P of a circle of radius 5cm meets a  line through  the centre O at a point Q such  that OQ = 12 cm then find the length of PQ.                            Ans. √119cm  5. From a point P, two tangents PA and PB are drawn to a  circle C (O,r) . If OP =2r ,then what is the type  of Triangle APB.                                  

CBSE ADDA Q . 1. Find a point on the x-axis which is equidistant from the points (7, 6) and (-3, 4). Q . 2. Show that the points A (1,2),B (5,4),C (3,8) and D (-1,6) are the vertices of a square. Q . 3. If A(6,-1), B(1,3) and C(k,8) are three points such that AB = BC, find the value of k. Q . 4. By distance formula, shoe that the points (1,-1), (5,2), (9,5), are collinear. Q . 5. Find the ratio in which the point P (m,6) divides the join of A(-4,3) and B(2,8). Also find the value of m. Q . 8. Show that the points (a, b + c), (b, c + a), (c, a + b), are collinear . Q . 9. Find the area of quadrilateral ABCD whose vertices are A (-5,7),B (-4,-5),C (-1,-6) and D(4,5). 10th Co-Ordinate Geometry Solved Problems-1 Download File 10th Co-Ordinate Geometry Solved Problems -2 Download File 10th Co-Ordinate Geometry Solved Problems-3 Download File 10th Co-Ordinate Geometry Solved Problems-4 Download File 10th Co-Ordinate Geometry Solved Problems-5 Downlo

CBSE Maths X Triangles – Criteria for Similarity of Triangles 10th math Converse of Thales theorem 10th math Triangles Thales theorem and angle bisector theorem 10th math SAS similarity of triangle 10th SSS similarity for two triangles are similar 10th AA- similarity for two triangles are similar class 10 similar-triangles study links

X Similar Triangle test paper MCQ's (JNV)  New Pattern Download File X Similar Triangle test paper(MCQ) Download File 10th Triangle Solved questions Download File JSUNIL TUTORIAL

CBSE ADDA Q . 1. Find a point on the x-axis which is equidistance from the points (7, 6) and (-3, 4). Q . 2. Show that the points A (1,2),B (5,4),C (3,8) and D (-1,6) are the vertices of a square. Q . 3. If A(6,-1), B(1,3) and C(k,8) are three points such that AB = BC, find the value of k. Q . 4. By distance formula, shoe that the points (1,-1), (5,2), (9,5), are collinear. Q . 5. Find the ratio in which the point P (m,6) divides the join of A(-4,3) and B(2,8). Also find the value of m. Q . 6. In what ratio is the line segment joining the points (-2,-3) and (3,7) divided by the y-axis . Also. find the coordinates of the points of division. Q . 7. Two vertices of a ABC are given by A(6,4) and (-2,2), and its centroid is G(3,4).Find the coordinates of the third vertex C of  triangle ABC. Q . 8. Show that the points (a, b + c), (b, c + a), (c, a + b), are collinear . . Q . 9. Find the area of quadrilateral ABCD whose vertices are A (-5,7),B (-4,-5),C (-1,-6) and D(4,5) For more prac

CBSE ADDA Q. 1. Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive terms of an AP. Q. 2. If mth term of A.P. is , and nth term is , show that the mnth terms is 1. Q. 3. A circle is completely divided into n sectors in such a way that the angles of the sectors are in arithmetic progression. If the smallest-of these angles is 8° and the largest 72°, calculate n and the angle in the fourth sector. Q. 4. Which term of AP: 3, 10, 17 ... will be 84 more than its 13th term? Q. 5. If 9th term of an AP is zero, prove that 29th term is double the 19th term. Q. 6. Find a, b such that 27, a, b - 6 are in A.P. Q. 7. For what value of n, the nth terms of the sequences 3, 10, 17,... and 63, 65, 67,... are equal. Q. 8. If m times the mth term of an AP is equal to n times its nth term show that the (m + n)th term of the AP is zero. Q. 9. A person buys National Savings Certificates of value exceeding the last year's purchase by Rs.500. After 10 years he finds the t

CBSE ADDA Q. 1. Which term of the AP 21, 18, 15, ………… is – 81 ? Also any term 0? Q. 2. Is 68 a term of the AP 7, 10, 13, ………? Q. 3. The 10th term of an AP is 52 and 16th term is 82. Find the 32nd term. Q. 4. Find the sum of a + b, a – b, a – 3b,…….. to 22 terms. Q. 5. Find the sum of first 15 terms of an AP, whose nth term is 9 – 5n. Q. 6. If 6 times the 6th term is equal to 9 times the 9th term of an AP find its 15th term. Q. 7. Which term of AP 5, 13, 21, ………. Will be 72 less than its 17th term? Q. 8. If 1/x + 2 , 1/ x +3 , 1/ x + 5 are in AP then find x. Q. 9. Which term of the AP 32, 29, 26, ………. Is its first negative term? Q. 10. If the sum of first 20 terms of an AP is one third of the sum of next 20 terms. If first term is 1 , then find the sum of first 30 terms. Q. 11. Find the sum of all the three digits numbers each of which leaves the remainder 3 when divided by 5. Q. 12. If mth and nth terms of an AP are 1/n and 1/m respectively, t

CBSE Board 2014  SA-1 Original  papers of mathematics for Class 10th conducted in different CBSE schools 10th SA-1 Original  Maths Paper 2014_2015-1 10th SA-1 Original Maths Paper 2014_2015-2 10th SA-1 Original Maths Paper 2014_2015-3                Download Files

10 th  Polynomials Ch-02-Mathematics [Key points]  Check point [Formative Assessment] Þ   Any algebraic expression having non zero integral power (whole number) is called polynomial. Þ  If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). Þ  A polynomial of degree 1 is called a linear polynomial. For example, 2x – 3, √3x+1,y +√3 Þ  A polynomial of degree 2 is called a quadratic polynomial. The name ‘quadratic’ has been derived from the word ‘quadrate’, which means ‘square’.       2x 2  +  3x + 2 ,y 2  + 2 Þ  Any quadratic polynomial in x is of the form ax 2  + bx + c, where a, b, c are real numbers and a ≠ 0. Þ  A polynomial of degree 3 is called a cubic polynomial e.g. 2 –  x 3 ,  x 3 , √2  x 3 . Þ  General form of a cubic polynomial is  ax 3  + bx 2  + c x + d, where, a, b, c, d are real numbers and a ≠ 0. Þ  If p(x) is a polynomial in x, and if k is any real number, then the value obtained by

10th Triangle (Similarity) Practice Questions For SA-1 By JSUNIL Similar figures: “Two similar figures have the same shape but not necessarily the same sizes are called similar figures. “ This verifies that congruent figures are similar but the similar figures need not be congruent. Conditions for similarity of polygon: Two polygons of the same number of sides are similar, if (i) Their corresponding angles are equal and (ii) Their corresponding sides are in the same ratio (or proportion). Note: The same ratio of the corresponding sides is referred to as the scale factor (or the Representative Fraction) for the polygons. Equiangular triangles: If corresponding angles of two triangles are equal, then they are known as equiangular triangles. A famous Greek mathematician Thales gave an important truth relating to two equiangular triangles which is as follows: “The ratio of any two corresponding sides in two equiangular triangles is always the same.” Q. The Basic Proportionalit

X Polynomial MCQ Assignments in Mathematics Class X (Term I) 1. If α,β are zeroes of the polynomial f ( x ) = x 2 + px + q, then polynomial having 1/α and 1/β as its zeroes is (a) x 2 + qx + p (b) x 2 – px + q (c) qx 2 + px + 1 (d) px 2 + qx + 1 2. If α and β are zeroes of x 2 – 4 x + 1, then 1/α + 1/β – αβ is (a) 3 (b) 5 (c) –5 (d) –3 3. The quadratic polynomial having zeroes as 1 and –2 is : (a) x 2 – x + 2 (b) x 2 – x – 2 (c) x 2 + x – 2 (d) x 2 + x + 2 4. If α, β are zeroes of x 2 – 6x + k, what is the value of k if 3α+2β=20 ? (a)–16 (b) 8 (c) 2 (d) –8 5. If one zero of 2x 2 – 3x + k is reciprocal to the other, then the value of k is (a) 2 (b) −23 (c) −32 (d) –3 6. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is (a) x 2 + 3x – 2 (b) x 2 – 2x + 3 (c) x 2 – 3x + 2 (d) x 2 – 3x – 2 7. If (x