Maths

### Question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and reason (R) are true and Reason (R) is not a correct explanation of...

### Question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and reason (R) are true and Reason (R) is not a correct explanation of...

### If the median of the data 4, 7, x-1, x-3, 16, 25, written in ascending order, is 13 then x is equal to

(a) 13 (b) 14 (c) 15 (d) 16 Answer: (c) 15 Sol: Median of 6 numbers is the average of 3rd and 4th term. ∴ 13 = (????−1)+(????−3) 2 ⇒ 26 = 2x – 4 ⇒ 2x = 30 ⇒ x = 15 Thus, x is equal to...

### The mean of 20 numbers is 0. OF them, at the most, how many may be greater than zero?

(a) 0 (b) 1 (c) 10 (d) 19 Answer: (d) 19 Sol: It is given that mean of 20 numbers is zero. i.e., average of 20 numbers is zero. i.e., sum of 20 numbers is zero. Thus, at most, there can be 19...

### The median of the first 8 prime numbers is

(a) 7 (b) 9 (c) 11 (d) 13 Answer: (b) 9 Sol: First 8 prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. Median of 8 numbers is average of 4th and 5th terms.

### Look at the cumulative frequency distribution table given below:

Answer: (c) 13 Sol: Converting the given data into a frequency table, we get: Hence, the number of families having an income range of Rs. 20,000 – Rs. 25,000 is 13. The correct option is...

### The median and mode of a frequency distribution are 26 and 29 respectively. Then, the mean is

(a) 27.5 (b) 24.5 (c) 28.4 (d) 25.8 Answer: (b) 24.5 Sol: Mode = (3 × median) – (2 × mean) ⇒ (2 × mean) = (3 × median) – mode ⇒ (2 × mean) = 3 × 26 – 29 ⇒ (2 × mean) = 49 ⇒ Mean = 49 2 ∴ Mean = 24.5...

### The mean and mode of a frequency distribution are 28 and 16 respectively. The median is

(a) 22     (b) 23.5      (c) 24    (d) 24.5 Answer: (c) 24 Sol: Mode = (3 × median) – (2 × mean) ⇒ (3 × median) = (mode + 2 mean) ⇒ (3 × median) = 16 + 56 ⇒ (3 × median) = 72 ⇒ Median = 72 3 ∴...

### If the mean and median of a set of numbers are 8.9 and 9 respectively, then the mode will be

(a) 7.2 (b) 8.2 (c) 9.2 (d) 10.2 Answer: (c) 9.2 Sol: It is given that the mean and median are 8.9 and 9, respectively, ∴ Mode = (3 × Median) – (2 × Mean) ⇒ Mode = (3 × 9) – (2 × 8.9) = 27 – 17.8 =...

### if the ‘less than type’ ogive and ‘more than type’ ogive intersect each other at (20.5, 15.5) then the median of the given data is

(a) 5.5            (b) 15.5 (c) 20.5          (d) 36.0 Answer: (c) 20.5 Sol: The x- coordinate represents the median of the given data. Thus, median of the given data is 20.5.

### The relation between mean, mode and median is

(a) mode=(3 * mean) – (2 * median) (b) mode=(3 *median) – (2 *mean) (c) median=(3 * mean) – (2 * mode) (d) mean=(3 * median) – (2 *mode) Answer: (b) mode=(3 * median) – (2 *mean) Sol: mode=(3 *...

### While computing the mean of the groue data, we assume that the frequencies are

(a) evenly distributed over the classes (b) centred at the class marks of the classes (c) centred at the lower limits of the classes (d) centred at the upper limits of the classes Answer: (b)...

### In the formula for the following the mean of the grouped data, the i d ’s are the deviations from A of

(a) lower limits of the classes (b) upper limits of the classes (c) midpoints of the classes (d) none of these Answer: (c) midpoints of the classes Sol: The ???????? ′???? are the deviations from A...

### The abscissa of the point of intersection of the Less Than Type and of the More Than Type cumulative frequency curves of a grouped data gives its

(a) Mean          (b) Median (c) Mode          (d)None of these Answer: (b) Median Sol: The abscissa of the point of intersection of the ‘less than type’ and that of the ‘more than type’ cumulative...

### The cumulative frequency table is useful is determining the

(a) Mean (b) Median (c) Mode (d) all of these Answer: (b) Median Sol: The cumulative frequency table is useful in determining the median.

### The medium of a frequency distribution is found graphically with the help of

(a) a histogram                        (b) a frequency curve (c) a frequency polygon          (d) ogives Answer: (d) ogives Sol: This because median of a frequency distribution is found graphically...

### The mode of frequency distribution is obtained graphically from

(a) a frequency curve (b) a frequency polygon (c) a histogram (d) an ogive Answer: (c) a histogram Sol: The mode of a frequency distribution can be obtained graphically from a histogram.

### Which of the following measures of central tendency is influence by extreme values?

(a) Mean         (b) Median (c) Mode         (d) None of these Answer: (a) Mean Sol: Mean is influenced by extreme values.

### Which of the following cannot be determined graphically?

(a) Mean             (b) Median (c) Mode             (d) None of these Answer: (a) Mean Sol: The mean cannot be determined graphically because the values cannot be summed.

### Which of the following is not a measure of central tendency?

(a) Mean          (b) Mode (c) Median       (d) Standard Deviation Answer: (d) Standard Deviation Sol: The standard deviation is a measure of dispersion. It is the action or process of distributing...

### The median of 19 observations is 30. Two more observation are made and the values of these are 8 and 32. Find the median of the 21 observations taken together. Hint Since 8 is less than 30 and 32 is more than 30, so the value of median (middle value) remains unchanged.

Sol: Since, 8 is less than 30 and 32 is more than 30, so the middle value remains unchanged Thus, the median of 21 observations taken together is 30.

### In a frequency distribution table with 12 classes, the class-width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?

Sol: Upper class boundary = Lowest class boundary + width × number of classes = 8.1 + 2.5×12 = 8.1 + 30 = 38.1 Thus, upper class boundary of the highest class is 38.1.

### Fill in the blanks. (i) A line intersecting a circle in two distinct points is called a ……… (ii) A circle can have parallel tangents at the most … (iii) The common point of a tangent to a circle and the circle is called the ……… (iv) A circle can have ….. tangents

Sol: A line intersecting a circle at two district points is called a secant A circle can have two parallel tangents at the most The common point of a tangent to a circle and the circle is called the...

### Which of the following statement is not true? (a) A line which intersect a circle in tow points, is called secant of the circle. (b)A line intersecting a circle at one point only, is called a tangent to the circle. (c) The point at which a line touches the circle, is called the point of contact. (d) A tangent to the circle can be drawn form a point inside the circle.

Answer: (d) A tangent to the circle can be drawn form a point inside the circle. Sol: A tangent to the circle can be drawn from a point Inside the circle. This statement is false because tangents...

### Which of the following statements is not true? (a) A tangent to a circle intersects the circle exactly at one point. (b) The point common to the circle and its tangent is called the point of contact. (c) The tangent at any point of a circle is perpendicular to the radius of the circle through the point of contact. (d) A straight line can meet a circle at one point only.

Answer: (d) A straight line can meet a circle at one point only. Sol: A straight be can meet a circle at one point only This statement is not true because a straight line that is not a tangent but a...

### Which of the following statements in not true? (a)If a point P lies inside a circle, not tangent can be drawn to the circle, passing through p. (b) If a point P lies on the circle, then one and only one tangent can be drawn to the circle at P. (c) If a point P lies outside the circle, then only two tangents can be drawn to the circle form P. (d) A circle can have more than two parallel tangents. parallel to a given line.

Answer: (d) A circle can have more than two parallel tangents. parallel to a given line. Sol: A circle can have more than two parallel tangents. parallel to a given line. This statement is false...

### Which of the following pairs of lines in a circle cannot be parallel? (a) two chords (b) a chord and tangent (c) two tangents (d) two diameters

Answer: (d) two diameters Sol: Two diameters cannot be parallel as they perpendicularly bisect each other.

### In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT =24 cm. If O is the centre of the circle, then length OP = ?

(a) 30 cm                     (b) 28 cm                    (c) 25 cm                     (d) 18 cm Answer: (c) 25 cm Sol: The tangent at any point of a circle is perpendicular to the radius at the...

### In the given figure, a cradle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14cm, BC = 8cm and CA=12 cm. Find the length AD, BE and CF.

BD = 5cm = BE Solving (3) and (4), we get and AD = 9cm