Q1. In an A P ,if d= -4 , n= 7, an = 4 then a is (a) 6 (b) 7 (c) 20 (d) 28
Q2.The zeroes of a polynomial 3×2 -2x-5 are (a) -1,5/3 (b) 1,5/3 (c) 0,-1 (d) 1,0
Q3.Find the length of tangent drawn to a circle with radius 7 cm from a point 25 cm away from the Centre. (a) 24 cm (b) 27 cm (c) 26 cm (d) 25 cm
Q4. 5.A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is (a) 2/3 (b) 1/6 (c) 1/3 (d) 11/30
Q5. The sum and product of the roots of 2x 2 – 5x + 4 = 0are in the ratio : (a) 5 : 2 (b) 5 : 4 (c) 10 : 4 (d) none of these
Q6. In a throw of two dice, the probability of getting a sum of 10 is : a ) 1/12 b) 1/36 c) 1/6 d ) ¼
Q7. The radii of bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. The ratio between the volume of cylinder to that of cone is (a) 8 : 9 (b) 9 : 8 (c) 5 : 7 (d) 7 : 5
Q8. CosecA /secA is- a ) tan A b ) cot A c ) sin A d) cosec A
Q9. If one root of the quadratic equation 4×2 – 2x + (k-4) = 0 be the reciprocal of the other, then k a) 8 b) -8 c)4 d) -4
Q10.If cos A = sinA , find A
(a) 30° (b) 45° (c) 60° (d) 90°
Q11.f α and β are the zeroes of the polynomial p(x)=kx2−30x+45k and α+β=αβ, then the value of k.
Q12..Show that root 3 is irrational Number
Q13. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Q14.A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Q15. In the given figure, ABC and AMP are two right triangles, right angled at B and M, respectively. Prove that △ABC ∼ △AMP. Q28. The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, -9). Radius of the circle is 5 2 cm.
Q16. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
Q17. If sin α=1/2 and cot β= 3 , then find the value of cosec α + cosec β.
Q18.Solve graphically: x-y+2=0 and 4x-y-4=0.Also find the area of the triangle thus formed.
Find the 20th term from the last term of the AP : 3, 8, 13, …., 253.
Q19. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
or
From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are 30 and 60 respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.
Q20.State and proof Basic Proportionality theorem.
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