1. The HCF of 30, 72, and 432 is

2. If the distance between the points (p, - 5) and (4, 10) is 17 units, then the value of p are

3.  If the pair of equations 3x + 4y - 8 = 0 and px +8y/3 = 15 has no solution, then the value of p is

4. The line segment joining the points P(3, -1) and Q(-6, 5) is trisected. The coordinates of point of trisection are

5. If C is the mid-point of PQ. P is (4, x), C is (y, -1) and Q is (-2, 4) then x and y, respectively are

Assertion-Reason Based Questions

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

6. Assertion (A) 5x² + 14x+10=0 has no real roots.

Reason (R) ax² + bx + c = 0 has no real roots if b² < 4ac.

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

7. Assertion(A) Zeroes of f(x) = x²-4x-5 are 5, -1.

Reason (R) The polynomial whose zeroes are 2+√3, 2-√3 is x² - 4x + 7.

8. If one of the zeroes of the polynomial f(x) = (k² +8)x² + 13x + 6k is reciprocal of the other, then the values of k are

9. HCF of two numbers is 11 and their LCM is 990. If one number is 22, then other number is

10. The following pair of linear equations, x = y and x–2 = y–2 are

11. The sum of first 15 terms of given AP is 97, 94, 91, 88,...

12. If (a, b) is the mid-point of line segment joining the points (6, 4) and (8,–6) then the values of a and b are

13. If a number x is added to twice its square, then the resultant is 21, then the quadratic representation of this statement is

14. If P is a point on Y-axis, whose ordinate is 3 and Q is a point (–5,2), then the distance PQ is

Assertion-Reason Based Questions

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

15. Assertion (A) The common difference of an AP, whose nth term is a _n = (3n+7), is 3.

Reason (R) The nth term of an AP is a _n = a+(n-1)d.

16. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 sec, B in 308 sec and C in 198 sec, all starting at the same point. After what time will they meet again at the starting point?

17. The sum of all natural numbers from 1 to 100, is

18. If one of the zeroes of a quadratic polynomial (k - 1)x² + kx + 1 is - 3, then the value of k is

19. What is the nature of roots of the quadratic equation 5y^2 – 4y+3 = 0?

20. The pair of linear equations 2x+ky–3=0, 6x+ 2/3y+7=0 has a unique solution, if

21. The point of intersection of the coordinate axes is

22. The value of k such that the quadratic polynomial x² - (k+6)x + 2(2k+1) has sum of the zeros as half of their product, is

Assertion-Reason Based Questions

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

23. Assertion (A) If mid-point of a line joining the points (6, -3) and (a, b) is (-3,5), then a and b are - 12 and 13, respectively.

Reason (R) A line is obtained by joining the points (x_1, y_1) and (x_2, y_2), then mid-point is given by[(x_1+x_2/2),(y_1+y_2/2)]

24. A tower stands near an airport. The angle of elevation θ of the tower from a point on the ground is such that its tangent is 5/12. The height of the tower, if the distance of the observer from the tower is 120 m is

25. The distance between A(-5,3) and B(-2,-1) is

1. What term of the AP 2, 5, 8, ...is 56?

2. If the 3rd and 7th terms of an AP are 17 and 27 respectively. Find the first term of the AP :

3. Find the nth term of an AP whose 6th and 8th terms are 12 and 22 respectively :

4. Find the sum of the AP 11, 13, 15, ..., 99 :

5. The ratio of the 7th to the 3rd terms of an AP is 12 : 5, find the ratio of the 13th to 4th term:

6. How many terms of the AP 1, 4, 7,......... are needed to  give the sum 925?

7. The 5th, 8th and 11th terms of a G.P. are a, b, c  respectively, then which one of the  following is true?

8. The 5th and 12th terms of a G.P. are 32 and 4096 f respectively. Find the nth term of the G.P. :

9. Find the 22nd term of the G.P. - 2, 2, -2, ...:

10. The A.M. of two positive numbers is 15 and their G.M. is 12. What is the smaller number?

11. The sum of 3 numbers in G.P. is 38 and their product is 1728. Find the greatest number :

12. The sum of first three terms of a G.P. is to the sum of the first six terms is 125 : 152. Find the common ratio of the G.P. :

13. The third term of a G.P. is 4. The product of first five terms is:

14. The sum of first three terms of a G.P. is 21 and sum of their squares is 189. Find the common ratio :

15. The sum of the first and the third terms of a G.P. is 15 and that of the 5th and the 7th terms is 240. Find the 9th term

16. The sum of four terms in G.P. is 312. The sum of first and fourth terms is 252. Find the product of second and third terms:

17. A bouncing tennis ball rebounds each time to a height equal to one half the height of the previous bounce. If it is dropped from a height of 16 m, find the total distance it has travelled when it hits the ground for the 10th time:

18. Find the sum to n terms of the series

7 + 77 + 777 + 7777 + ...

19. There are four numbers such that the first three of them form an Arithmetic Progression and the last three form a Geometric Progression. The sum of the first and the third is 2 and that of second and fourth is 26. What is the sum of first and fourth numbers?

20. In a set of four numbers, the first three are in G.P. and the last three are in AP with common difference 6. If the first number is the same as the fourth, find the third number :

21. 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, then find the maximum possible payment which he can receive, however long he may live :

22. Find the sum of the series 1/4 - 3/16 + 9/64 - 27/256 + ....

23. The sum of first two terms of a of a G.P. is 5 /3 and the sum to infinity of the series is 3. Find the first term:

24. A ball is dropped from a height of 96 ft and it rebounds 2/3 of the height it falls. If it continues to fall and rebound, find the total distance that the ball can travel before coming to rest.

25. Divide 20 into four parts which are in AP and such that the product of the first and fourth is to the product of the second and third in the ratio 2 : 3. Find the product of the first and fourth term of the AP :