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