NCERT 9 MATH SUBJECTIVE QUESCTION

Class IX Math Subjective question for Probability 1.   A coin is tossed 150 times and it is found that head comes 1115 times and tail 35 times. If a coin tossed at random, what is the probability of getting?       (i) A head                        (ii) a tail 2.   A bag-I contains four cards numbered 1, 3, 5 and 7 respectively. Another bag-II contains here cards numbered 2, 4 and 6 respectively. A card is drawn at random from each bag. Find the probability that the sum of two cards drawn is 9. 3.   A bag contains 7 white, 3 red and 4 black balls. A ball drawn at random. Find the probability that it is a red or a black ball. 4.   In a single throw of two dice, find the probability of getting a total of 8. 5.   One card is drawn from a well-shuffled deck of 52 cards. Find the ...

Class IX Math Subjective question for Surface area and volume 1.    The length, breadth and height of a cuboid are 15 cm, 10 cm and 20 cm respectively. Find its total surface area. 2.    Shanta had to make a model of a cylinderical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope, wha would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? take  ( Pi = 22/7 ) 3.    The height of a cone is 16 cm and its base radius is 12 cm. Find: (i) the curved surface area, (ii) total surface area of the cone. [Use �� = 3.14] 4.    If the slant height and the base radius of a cone are 10 cm and 8 cm respectively, then find         (i) curved surface area and         (ii) total surface area. [Take π = 3.14] 5...

Class IX Math Subjective question for Heron's formula 1.    Find the area of a triangle whose sides are 12 cm, 6 cm and 15 cm. 2.     Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 cm. 3.    A park in the shape of a quadrilateral ABCD has C = 90°. AB = 18 m, BC = 24 m, CD = 10 m and AD = 16 m. How much area does it occupy? 4.    Find the area of a triangle with base =20cm and height are 10 cm. 5.    Find the area of a triangle having perimeter 32cm. One side of its side is equal to 11cm and difference of the other two is 5cm. 6.    Perimeter of the rhombus is 100 m and its diagonal is 40m. Find the area of rhombus. 7.    Two parallel sides of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of trapezium. 8.    The perimeter of a triangular field is 135 cm and its side...

Class IX Math Subjective question for Circle 1.    Construct a ΔPQR in which PQ = 5.4 cm, ∠ Q = 60° and PR – PQ = 2.3 cm. 2.    Construct a ΔXYZ in which ∠ Y = 45°, ∠ Z = 75° and XY + YZ + ZX = 12 cm. 3.    Construct a ΔABC in which ∠ B = 60°, ∠ C = 45° and the perimeter of the triangle is 10 cm. 4.    Construct a ∠ ABC with perimeter 11 cm and each of its base angle is 45°. 5.    Construct a ∠ PQR whose perimeter is 12 cm and the lengths of whose sides are in the ratio 2 : 3 : 4. 6.    Construct a right-angled triangle whose be is 3.8 cm and hypotenuse is 5.6 cm. 7.    Construct a ∠ ABC in which ∠ B = 60° ∠ C = 30° and the length of the perpendicular from the vertex A is 5.3 cm. 8.    Construct an equilateral triangle whose perimeter is 16.2 cm. 9.    Construct an equilateral triangle if its altitude is 3.2 cm. 10.  ...

Class IX Math Sample Paper for Number Systems 1.   Find two rational numbers between 0.1 and 0.3 2.   Express   in the form of decimal. 3.   Simplify :  4.   Rationalize the denominator of  5.   Express   as a fraction in the simplest form. 6.   If   find the value of 7.   Simplify  8.   Find the value of x in  9.   If   find the value of  10.   What is the value of 

Q 1. Give the equivalent version of Euclid's fifth postulate in terms of parallel lines. Solution 'For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l'. Q 2. Define : (A) a square (B) Perpendicular lines Solution Square - A square is a rectangle with a pair of consecutive sides equal. Perpendicular lines - Two lines are perpendicular, if the angle between them is 90 o . Q 3. Write any three Euclid's postulates. Solution Any three of these five postulates Postulate 1: A straight line may be drawn from any one point to any other point. Postulate 2: A terminated line can be produced indefinitely. Postulate 3: A circle can be drawn with any centre and any radius. Postulate 4: All right angles are equal to one another. Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straig...

Q 1. If one of the angle of the triangle is  equal to the sum of the other two angles .Express this information into equivalent linear equation of two variables  and  also find the angles of triangle id  measure of one of the angle is 60 degree. Solution   Let  the first angle = x             Let the second angle=y             According to the given information, Third angle=x+y                         We know that sum of angles in  a triangle is equal to 180 degree.             So,             X+y+(x+y)=180             2x+2y=180       ...

Q 1. Which of the following points lie on x-axis? Which on y-axis? A(0,2), B(5,6), C(-3,0), D(0,-3), E(0,4), F(6,0), G(3,0) Solution If x-coordinate of a point is zero then it lies on y-axis and if y-coordinate is zero then it lies on x-axis.   Points on x-axis : C(-3,0), F(6,0), G(3,0) Points on y-axis : A(0,2), D(0,-3), E(0,4) Q 2. The perpendicular distance of a point from the x - axis is 4 units and the perpendicular distance from the y - axis is 5 units. Write the coordinates of such a point if it lies in the (i) I Quadrant (ii) II Quadrant (iiii) III Quadrant (iv) IV Quadrant Solution (i) In the first quadrant, the coordinates of the required point will be (5,4). (ii) In the second quadrant, the coordinates of the required point will be (-5,4). (iii) In the third quadrant, the coordinates of the required point will be (-5,-4). (iv) In the fourth quadrant, the coordinates of the required point will be (5,-4). Q 3. In which quadrant do the given points lie? ...

Q 1. Find the values of a and b so that (x + 1) and (x - 2) are factors of (x 3  + ax 2  + 2x + b). Solution If (x + 1) is a factor of x 3  + ax 2  + 2x + b then (-1) 3  + a(-1) 2  + 2(-1) + b = 0 -1 + a - 2 + b = 0 a + b = 3                   ...(1) If (x - 2) is a factor of x 3  + ax 2  + 2x+ b then (2) 3  + a(2) 2  + 2(2) + b = 0 4a + b = -12 ...(2) Subtracting (1) from (2), we get 3a = -15 Or, a = -5 Using in (1), we get -5 + b = 3 Or, b = 8 Hence, a = -5, b = 8. Q 2. Without actually calculating the cubes, find the value of 75 3  - 25 3  - 50 3 . Solution Let x = 75, y = -25, z = -50 x + y + z = 75 - 25 - 50 = 0 We know, if x + y + z = 0 then x 3  + y 3  + z 3  = 3xyz 75 3  - 25 3  - 50 3  = 3(75) (-25) (-50) = 281250 Q 3. Using factor theorem, show that (x + 1) is a factor of x 19  + 1. Solution Let f(x) = x...