Q. 1. Is it possible to design a rectangular park of perimeter 80 m and area 400 sq. m.?
Q. 2. Find a cubic polynomial with the sum, sum of product of its zeroes factor two at a time and the product of its zeros as 2, -7, -14 respectively.
Q. 3. Which term of the A.P 121,117,113……… is its first negative term?
Q. 4. Find the length of the median of ∆ ABC passing through B having vertices at A (5, 1), B (1, 5) and C (-3,-1).
Q. 5. Determine the ration in which the line y – x + 2 = 0, divides the line joining (3,-1) and (8, 9). Also find the points of trisection.
Q. 6. The angle of elevation of a cloud from a point 200 m above a lake is 30 and the angle of depression of it’s reflection of the cloud of the lake is 60.find the height of the cloud. Also find the distance of cloud from the point of observation.
Q. 7. A rocket is in the shape of a circular cylinder closed at the lower end and a cone of the same radius is attached at the top. The Radius of the cylinder is 2.5 m, its height is 21 m and slant height of the cone is 8 m. calculate the total surface area of the rocket.
Q. 8. A cone of radius 10 cm is divided into two parts by drawing a plane through the mid point of its axis, parallel to its base. Compare the volume of the two parts.
Q. 9. Draw the ‘Less than’ and ‘More than’ Ogive of the following Data and find the median. Verify your answer mathematically.
Marks |
0-5 |
5-10 |
10-15 |
15-20 |
20-25 |
25-30 |
30-35 |
35-40 |
No. of Students |
7 |
10 |
20 |
13 |
12 |
10 |
14 |
9 |
Q. 10. Cards numbered 13, 14, 15…………60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the numbered drawn on the card is (a) Divisible by 5 (b) a number which is a perfect square.
Q. 11. State and prove the BPT theorem.
Q. 12. In acute triangle ABC acute angle at B. If AD∟BC prove that AC2 = AB2 + BC2 – 2BC.BD
13. Find the sum of all 3 digit numbers which leave remainder 2, when divided by 3.
Q. 14. Draw the graphs of the equations x – y +1 = 0 and 3x+ 2y – 12=0.Determine the coordinates of the vertices of the triangle formed by these lines and the X axes and shade the triangular region.
Q. 15. An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm. Find the area between the two consecutive ribs of the umbrella.
Q. 16. Prove:
1 _ _ 1____ = 1 _ _ 1____
Sec A – tan A Cos A Cos A Sec A + tan A
Q. 17. Determine the value(s) of p for which 4x2 - 3px + 9 = 0 has real roots.
Q. 18. Write the relation between mean, mode and median.
Q. 1. Find the sum of all natural no. between 100 and 200 which are divisible by 4.
Q. 2. The length of minute hand of clock is 14 cm. Find the area swept by minute hand in 5 minutes.
Q. 3. A pole is 5 m high fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60 and the angle of depression of the point A from the top of the tower is 45. Find the height of the tower.
Q. 4. Two places A and B are 120 Km. apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction they meet in 6 hrs, if they move in opposite direction they meet in 1 hr and 12 minutes. Find the speed of cars. Use cross multiplication method for solving the equation.
Q. 5. Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360. Find the age of Rohan.
Q. 6. The mean of the following frequency distribution is 62.8 and sum of all frequencies is 50. Find f1 and f2
Group |
0-20 |
20-40 |
40-60 |
60-80 |
80-100 |
100-120 |
Total |
f |
5 |
f1 |
10 |
f2 |
7 |
8 |
50 |
Q. 7. What is the largest no. that divides 626,3127 and 15628 and leaves remainder of 1,2 and 3 respectively.
Q. 8. By applying division algorithm, prove that the polynomial p(x) = x2+3x+1 is a factor of the polynomial q(x) = 3x4+5x3-7x2+2x+2.
Q. 9. If tan (A-B) = 1/√3 and tan (A+B) = √3 find A and B.
Q. 10. A right circular cylinder is 15 cm high and it’s base diameter is 14 cm. It is melted and recast into a sphere of diameter 7 cm. Find the number of spheres so obtained.
Q. 11. A letter is chosen at random from the word ABHAYAAS.Find the probability that the letter chosen is i) Vowel ii) Consonant.
Q. 12. A bag contains 35 balls out of which x are blue.
Q. 13. For what value of K are the points (1, 5), (k, 1) and (4, 11) are collinear.
Q. 14. Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the coordinate of the fourth vertex.
Q. 15. The sum of the 4th and 8th terms of an A.P is 24 and sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Q. 16. How many silver coins 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm x 10 cm x 3.5 cm.
Q. 17. Prove:
Sin A _ _ Cos A____ ____ = 1
Sec A + tan A-1 Cosec A +CotA -1
Q. 18. Name the type of triangle formed by the points (2,-2) (14,10) and (11,13)
Q. 1. Prove that √2 is irrational.
Q. 2. Divide 2x4 + x3 -14x2-19x-6 by x2 +3x +2 and verify the division logarithms.
Q. 3. For what value of k, the following pair of linear equations has infinite many solutions
10x +5y-(k-5) = 0,, 20x + 10y –k = 0
Q. 4. The sum of a two digit no. and no. obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
Q. 5. Solve the following quadratic equation : ax2 + (4a2 – 3b)x-12ab = 0
Q. 6. The sum of n terms of A.P. is 5n2- 3n.Find the A.P it’s nth term and find its 10th term.
Q. 7. State and prove Pythagoras Theorem.
Q. 8. In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9AD2 = 7AB2.
Q. 9. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).
Q. 10. Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are (0,-1), (2, 1) and (0, 3).Find the ratio of the triangle formed to area of the given triangle.
Q. 11. Evaluate : (Sin225 + Sin265) +√3(tan 5 tan 15 tan 30 tan 75 tan 85)
Q. 12. Prove : (1 + cot θ - cosec θ)(1+ tan θ + sec θ) = 2
Q. 13. From a point on a bridge across a river, the angles of depression of the banks on opposite sides of rivers are 30 and 45 respectively. If the bridge is at a height of 3 meter from the banks. Find the width of the river.
Q. 14. Draw a pair of tangents to a circle of radius 4 cm and which are inclined to each other at 60º.
Q. 15. Water in a canal 30dm wide and 12m deep is flowing velocity of 10 km/hr. How much area will it irrigate if 8 cm of standing water is required for irrigation?
Q. 16. A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the circles, it is just immersed as shown in figure .What friction of water flows over?
Q. 17. Draw both type of Olive Curve on the same graph paper and then determine the median
Marks |
50-60 |
60-70 |
70-80 |
80-90 |
90-100 |
Students | 4 |
8 |
12 |
6 |
6 |
Q. 18. Two dices are thrown simultaneously. Find the probability of getting:
Q. 19. What is the distance between two parallel tangents of a circle of radius 4 cm?
Q. 20. Find the area of quadrant of a circle whose circumference is 49 cm.
Q. 1. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting
Q. 2. Gulab jamun cotains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulag jaunts each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Q. 3. A person standing on the bank of the river observes that the angle of elevation of the top of a tree standing on opposite bank is 60º. When he moves 40 meters away from the bank, he finds the angle of elevation to be 30º. Find the height of the tree and width of the river.
Q. 4. Find the ratio in which in which the line segment joining the points A (3,-6) and B (5, 3) is divided by X axis. Also find the point of intersection.
Q. 5. If 3 time the 7th term of an equal to 5 times the 9th term shows that 12th term of A.P.
Q. 6. Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
Q. 7. Find all the zeros of the polynomial x3 + 3x2 – 4x –12, if one of its zeroes is -3.
Q. 8. Solve for x and y : 99x + 101 y = 499, 101x + 99y = 501.
Q. 9. A takes 3 hours more than B to walk a distance of 30 km. But if A doubles his pace, he is ahead of B by 1½ hours. Find the speed of walking.
Q. 10. The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hrs.30 minutes. Find the speed of the stream.
Q. 11. The sum of the areas of two squares is 640 sq m. If the difference in their perimeter be 64 m, find the sides of the two squares.
Q. 12. By reduction of Rs 1 per kg in price of sugar. Ritika can buy one kg. Sugar more for Rs.56. Find the original price of sugar.
Q. 13. State and prove converse of Pythagoras Theorem.
Q. 14. Prove
Cosec A + Cot A = 1+ 2 Cot2A + 2 Cosec A Cot A
Cosec A – Cot A
Q. 15. The area of an equilateral triangle is 49√3 cm2. taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in circle.
Q. 16. A cone of radius 10 cm is divided in to two parts by drawing a plane through the mid points its axis parallel to its base.Compare the volumes of the two parts.
Q. 17. If the median of the data listed below is 28.5 total of f 100, find x and y:
Marks |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
Students |
3 |
X |
20 |
10 |
5 |
y |
