Mathematics Basic Examination

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Questions and Answers

The decimal expansion of the rational number $\frac{33}{22\times 5}$ will terminate after

3 decimal places
2 decimal places
1 decimal place (correct)
5 decimal places

If one zero of the quadratic equation $x^2 + 3x + k = 0$ is 2, then the value of k is

5
-10 (correct)
10
-5

The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm, respectively. If PQ = 9 cm, then AB equals:

10 cm (correct)
6 cm
24 cm
15 cm

Given that a - 1, a + 3, 3a - 1 are in Arithmetic Progression. The value of 'a' is equal to

2 (C) Signup and view all the answers

If 'p' is the angle (in degree) of a sector of a circle of radius 'r' , the area of the sector is

$\frac{πr^2p}{360°}$ (C) Signup and view all the answers

If a pair of linear equations is consistent, then the corresponding lines will be:

intersecting or coincident (C) Signup and view all the answers

The distance between two parallel tangents of a circle of radius 3 cm is

6 cm (D) Signup and view all the answers

A tree casts a shadow of 4 m long on the ground, when the angle of elevation of the sun is 45°. The height of the tree (in metres) is

4 (D) Signup and view all the answers

The two roots of a quadratic equation are 2 and -1. The quadratic equation is

$x^2 - x - 2 = 0$ (B) Signup and view all the answers

If two cubes each of volume $8 cm^3 $ are joined end to end, then the surface area of the resulting cuboid is:

$64 cm^2$ (C) Signup and view all the answers

A bag contains 3 red balls, 5 white balls and 7 black balls. The probability that a ball drawn from the bag at random will be neither red nor black is

$\frac{5}{15}$ Signup and view all the answers

Median of a data is 53 and its mean is 54. Using empirical relationship between the three measures of central tendency, the mode is

52 Signup and view all the answers

The following figure represents the graphs of the equation x - y + 1 = 0 and 3x + 2y - 12 = 0. The area of the triangle formed by these lines and y - axis is

1 (C) Signup and view all the answers

P (1,1) is the mid-point of the line segment joining A and B. Find the coordinates of A, if the coordinates of B is (4,3).

( -2,-1 ) Signup and view all the answers

What is the nature of the roots of the quadratic equation $4x^2 - 12x - 9 = 0$?

Real and equal Signup and view all the answers

Find the perimeter of a protractor whose diameter is 7cm

22cm Signup and view all the answers

Find the area of the quadrant of a circle whose circumference is 44 cm.

77 sq cm Signup and view all the answers

The radii of the circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6cm. Find the slant height of the frustum in cm.

10 cm Signup and view all the answers

Given that ∆ABC ~ ∆QRP and ar (∆ABC): ar(∆QRP) = 9 : 4. Find the length of QR, if AB = 18 cm

12 cm Signup and view all the answers

Using Euclid's division algorithm find the HCF of 65 and 117.

13 Signup and view all the answers

Find the HCF and LCM of 48, 54 by applying the Fundamental theorem of arithmetic.

HCF = 6, LCM = 432 Signup and view all the answers

A and ẞ are the zeroes of $x^2 - 3x + p$. Find the value of p, if $2α + 3β = 15$.

p=18 Signup and view all the answers

Find the area of the triangle with vertices (1, 2), (-2, 3) and (-3, -4)

13.5 sq units Signup and view all the answers

Evaluate: $\frac{cos 70° + 4(sec^ 2 59° – cot^2 31°)}{3sin 20°} + \frac{2sin90°}{3}$

2 Signup and view all the answers

Cards marked with numbers 8, 9, 10, ....., 49 are placed in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card drawn is
(i) divisible by 7. (ii) a number which is a perfect square.

(i) 7/13, (ii) 2/13 Signup and view all the answers

Simon Tuffle was the umpire of cricket test match between India and Srilanka. There were two types of coins. Type (A): A fair coin Type (B): An unfair coin(having tail on both sides) i) The coin selected for toss was type A coin. Find the probability of getting a tail on type A.
ii) Find the probability of getting a tail on type B coin.

(i) \frac{1}{2}, (ii) 1 Signup and view all the answers

Flashcards

Terminating Decimal

A decimal representation that terminates after a finite number of digits.

Non-Terminating Non-Repeating Decimal

A decimal representation that continues infinitely without repeating.