1.
Euclid's Division Lemma states that for any two positive integers a and b, there exist unique integers q and r such that a=bq + r, where
Correct Answer
B. 0<=r<b
Explanation
The correct answer is 0
2.
In the given figure, the graph of the polynomial p(x) is shown. The number of zeroes of p(x) is
Correct Answer
C. 2
Explanation
From the graph, we can see that the polynomial p(x) intersects the x-axis at two points. These points correspond to the zeroes of the polynomial. Therefore, the number of zeroes of p(x) is 2.
3.
In a triangle ABC, it is given that DE|| BC. If AD=3 cm, DB= 2cm and DE=6cm, then BC=?
Correct Answer
B. 10cm
Explanation
In the given triangle ABC, DE is parallel to BC. According to the properties of parallel lines, the corresponding angles formed by DE and BC are equal. Therefore, triangle ADE and triangle ABC are similar triangles. By using the property of similar triangles, we can set up the following proportion: AD/AB = DE/BC. Plugging in the given values, we get 3/AB = 6/BC. Cross-multiplying and solving for BC, we find that BC = 10 cm.
4.
If sin3X= cos(X-2), where 3X and (X-2) are both acute angles, then X=?
Correct Answer
D. 23
Explanation
If sin3X = cos(X-2), then we can use the trigonometric identity sin^2θ + cos^2θ = 1 to rewrite the equation as sin^2(3X) + sin^2(X-2) = 1. Since 3X and (X-2) are both acute angles, their sine values will be positive. Therefore, we can rewrite the equation as 1 - cos^2(3X) + 1 - cos^2(X-2) = 1. Simplifying further, we get 2 - cos^2(3X) - cos^2(X-2) = 1. Rearranging the terms, we have cos^2(3X) + cos^2(X-2) = 1. This equation is only satisfied when both cos^2(3X) and cos^2(X-2) are equal to 0. Therefore, we can solve for X by finding the values that make cos^2(3X) and cos^2(X-2) equal to 0. The only value that satisfies this condition is X = 23.
5.
If tanX=(3)^{1\2 } , then
Correct Answer
D. 1/2
Explanation
If tanX = (√3), it means that the ratio of the length of the side opposite angle X to the length of the side adjacent to angle X in a right triangle is (√3). To find the value of X, we can use the inverse tangent function (tan^(-1)). tan^(-1)(√3) is equal to 60 degrees. Since the tangent function has a period of 180 degrees, tan(60 + 180n) = (√3) for any integer n. Therefore, X can be 60 degrees, 240 degrees, 420 degrees, etc. In degrees, 60 degrees is equal to π/3 radians. In radians, 240 degrees is equal to 4π/3 radians. In radians, 420 degrees is equal to 7π/3 radians. Therefore, the answer is 1/2.
6.
The decimal expansion of 49/40 will terminate after how many places of decimal
Correct Answer
C. 3
Explanation
The decimal expansion of 49/40 will terminate after 3 places of decimal. This is because when we divide 49 by 40, we get a quotient of 1 and a remainder of 9. The remainder 9 becomes the numerator of the next division, and when we divide 90 (obtained by appending a zero to the remainder) by 40, we get a quotient of 2 and a remainder of 10. Similarly, when we divide 100 (obtained by appending a zero to the remainder) by 40, we get a quotient of 2 and a remainder of 20. At this point, we can see that the remainder is repeating, indicating that the decimal expansion will terminate after 3 places.
7.
The pair of linear equations 6x-3y+10=0, 2x-y+9=0
Correct Answer
D. No solutions
Explanation
The given pair of linear equations 6x-3y+10=0 and 2x-y+9=0 cannot be solved simultaneously because the coefficients of x and y in the two equations do not match. Therefore, there is no common solution that satisfies both equations.
8.
For a given data with 60 observations the 'less than ogive' and the 'more than ogive' intersect at (18.5,30).The median of the data is
Correct Answer
D. 18.5
Explanation
The given information states that the 'less than ogive' and the 'more than ogive' intersect at the point (18.5,30). This means that 30 observations are less than 18.5 and 30 observations are greater than 18.5. Since there are 60 observations in total, the median, which is the middle value of the data, would be the value at the 30th observation. Therefore, the median of the data is 18.5.
9.
If mode= x(median) - y(mean), then
Correct Answer
B. X=3,y=2
Explanation
The given expression mode = x(median) - y(mean) indicates that the mode is equal to two times the median minus three times the mean. The correct answer x=3, y=2 means that the mode is equal to three times the median minus two times the mean.
10.
If the product of zeroes of the polynomial ax^{2}- 6x-6 is 4, then a=?
Correct Answer
D. -3/2
Explanation
The product of the zeroes of a quadratic polynomial is equal to the constant term divided by the coefficient of the highest power of x. In this case, the product of the zeroes is given as 4, so we can set up the equation -6/a = 4. Solving for a, we get a = -3/2.