1.
=
Correct Answer
B. Zero
Explanation
The given answer is zero because when any number is divided by infinity, the result tends to zero. As the value of the denominator (infinity) increases indefinitely, the value of the fraction decreases and approaches zero. Therefore, the correct answer is zero.
2.
=?
Correct Answer
C. 0
Explanation
The given sequence of numbers is 2, -2, 0, 1. The pattern in this sequence is that each number is the result of subtracting the previous number by 2. Starting with 2, subtracting 2 gives -2, subtracting 2 again gives 0, and subtracting 2 once more gives -2. Therefore, the next number in the sequence would be obtained by subtracting 2 from 0, resulting in 0.
3.
=?
Correct Answer
C. 2
4.
?
Correct Answer
A. Zero
Explanation
The given answer is "Zero" because it is the only number listed in the options. The other numbers (1, 2, -2) are not mentioned in the question or the options, so they cannot be considered as the correct answer.
5.
?
Correct Answer
D. 3/16
Explanation
The correct answer is 3/16. This can be determined by multiplying the numerators (3 * 3 = 9) and multiplying the denominators (4 * 5 = 20). Therefore, the fraction 3/4 is equivalent to 9/20, which simplifies to 3/16.
6.
A man is standing in front of a building at a distance 140 m. The angle of elevation with third floor is 45 degree and the measure of the angle of elevation of the top floor is 60 degree. The height of building is:
Correct Answer
C. 242
Explanation
The height of the building can be determined using trigonometry. Since we have the angle of elevation and the distance from the man to the building, we can use the tangent function. The tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the man to the building). By taking the tangent of 45 degrees and multiplying it by 140 m, we find the height of the building to be approximately 197 m. However, since we also have the angle of elevation to the top floor, we can use the same method with the tangent of 60 degrees. Multiplying this tangent by 140 m, we find the height of the building to be approximately 242 m.
7.
A perfect cubical die is rolled, the probability of getting an even number is which is less than 5 and greater than 1 is:
Correct Answer
A. 1/2
Explanation
The probability of getting an even number on a perfect cubical die is 3 out of 6, since there are 3 even numbers (2, 4, 6) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6). Simplifying this fraction gives us 1/2.
8.
A zip code contains 5 digits. How many different zip codes can be made with the digits 0-9 if no digit is used more than once and the first digit is not 0?
Correct Answer
D. 9 x 9 x 8 x 7 x 6
Explanation
The first digit of the zip code cannot be 0, so there are 9 options for the first digit. After choosing the first digit, there are 9 options remaining for the second digit. Similarly, there are 8 options for the third digit, 7 options for the fourth digit, and 6 options for the fifth digit. Therefore, the total number of different zip codes that can be made is 9 x 9 x 8 x 7 x 6.
9.
are the partial fractions of:
10.
Condition that roots of equation differ by unity is:
Correct Answer
A.
Explanation
The condition that the roots of an equation differ by unity is when the equation is of the form (x - a)(x - (a + 1)) = 0, where 'a' is any real number. In this case, the roots of the equation will be 'a' and 'a + 1', and they will differ by unity.
11.
Constant function cannot be parallel to:
Correct Answer
B. Y-axis
Explanation
A constant function is a function that has the same output for every input. In other words, it is a horizontal line on a graph. The y-axis is a vertical line on the graph, so it cannot be parallel to a horizontal line. Therefore, a constant function cannot be parallel to the y-axis.
12.
Eccentricity is equal to infinity for
Correct Answer
A. Two parallel lines
Explanation
Eccentricity is a measure of how "stretched out" or elongated a shape is. It is commonly used to describe the shape of an ellipse or a conic section. In the case of two parallel lines, they do not form any conic section and their shape is not stretched out or elongated. Therefore, the eccentricity of two parallel lines is equal to infinity.
13.
Equation (x+a)(x+b)(x+c)(x+d)=k is reduced to quadratic equation if
Correct Answer
B. A=c+d-b
Explanation
The equation (x+a)(x+b)(x+c)(x+d)=k can be reduced to a quadratic equation if a=c+d-b. This means that the coefficients of the x^3 and x terms cancel out, resulting in a quadratic equation. The answer a=c+d-b satisfies this condition and allows the equation to be simplified to a quadratic form.
14.
Equation has:
Correct Answer
C. No Solution
Explanation
The equation in question does not have a solution. This means that there are no values of the variables that can satisfy the equation and make it true.
15.
For , =?
Correct Answer
B.
16.
Identify the function of the Graph given below:
Correct Answer
B.
Explanation
The graph given below represents a linear function. This is evident from the straight line that connects the points on the graph. In a linear function, the output (y) is directly proportional to the input (x), and the graph appears as a straight line. The slope of the line represents the rate of change, and the y-intercept represents the initial value.
17.
Identity element in set of rational number w.r.t multiplication is
Correct Answer
B. 1
Explanation
The identity element in the set of rational numbers with respect to multiplication is 1. This means that when any rational number is multiplied by 1, the result is the original number. For example, if we multiply any rational number, say 3/4, by 1, we get 3/4 as the result. Therefore, 1 is the correct answer as it satisfies the definition of an identity element in the set of rational numbers with respect to multiplication.
18.
If A and B are square matrices of same order, then if
Correct Answer
A.
Explanation
A and B are invertible matrices, then AB is also invertible. This is because if A and B are invertible, it means that they have inverses A^-1 and B^-1 respectively. Therefore, we can say that (AB)^-1 = B^-1 * A^-1, which implies that AB is also invertible.
19.
If a is a recurring decimal fraction, then 2a-3 is?
Correct Answer
B. Recurring
Explanation
If a is a recurring decimal fraction, then 2a-3 will also be a recurring decimal fraction. This is because when we multiply a recurring decimal fraction by a constant (in this case 2) and subtract a constant (in this case 3), the resulting decimal will still have repeating patterns. Therefore, the answer is recurring.
20.
If a set A has 3 elements and B has 6 elements such that then the number of elements in :
Correct Answer
A. 3
Explanation
If set A has 3 elements and set B has 6 elements, the number of elements in the intersection of A and B can be at most 3. This is because the intersection of two sets can never have more elements than the smaller of the two sets. Therefore, the correct answer is 3.
21.
If f(x) = |x| + [x] then f(-2.5) =?
Correct Answer
C. -0.5
Explanation
The function f(x) is defined as the absolute value of x plus the greatest integer less than or equal to x. To find f(-2.5), we first take the absolute value of -2.5, which is 2.5. Then, we take the greatest integer less than or equal to -2.5, which is -3. Adding these two values together, we get -0.5.
22.
If foci of an ellipse concide,then
Correct Answer
A. E=0
Explanation
When the foci of an ellipse coincide, it means that they merge into a single point. In an ellipse, the eccentricity (e) represents the shape of the ellipse. When e=0, it indicates a circle, which is a special case of an ellipse. Therefore, if the foci of an ellipse coincide, the eccentricity (e) must be equal to 0.
23.
If one root of the equation is double of the other:
Correct Answer
A.
Explanation
The equation has two roots, one of which is double the other. This means that if we let the smaller root be x, then the larger root would be 2x. Therefore, the equation can be written as (x)(2x) = 0. Simplifying this equation gives us 2x^2 = 0. The only way for this equation to be true is if x = 0, since any other value of x would result in a non-zero value for 2x^2. Therefore, the correct answer is x = 0.
24.
If the co-efficient of and in the expansion of are same then a = ?
Correct Answer
A. 8
Explanation
If the coefficients of x and y in the expansion of (x + y)^n are the same, it means that the powers of x and y are equal in each term of the expansion. In this case, the coefficient of x^1y^1 is 8, which means that n must be 2. Therefore, a = 2.
25.
If the middle term in the expansion of is 1120 then k=?
Correct Answer
C. -2
Explanation
The middle term in the expansion of a binomial expression is given by the formula (n+1)/2. In this case, the middle term is 1120, so we can set up the equation (n+1)/2 = 1120. Solving for n, we find that n = 2239. Since the exponent of the second term is negative, the value of k is -2.
26.
If the roots of the quadratic equation are real and distinct then
Correct Answer
C.
Explanation
If the roots of a quadratic equation are real and distinct, it means that the equation has two different solutions. This implies that the discriminant, which is the expression inside the square root in the quadratic formula, is positive. When the discriminant is positive, the quadratic equation will have two real and distinct roots. Therefore, the correct answer is that "None of Given" options are applicable.
27.
If the vectors and are perpendicular to each other then /,m,n have values:
Correct Answer
D. L=4,m=4,n=5
Explanation
If the vectors l=4, m=4, and n=5 are perpendicular to each other, it means that their dot product is equal to zero. The dot product of two vectors is calculated by multiplying their corresponding components and summing them up.
In this case, the dot product of the vectors (4, 4, 5) and (4, 4, 5) is calculated as follows:
(4 * 4) + (4 * 4) + (5 * 5) = 16 + 16 + 25 = 57
Since the dot product is not equal to zero, the given answer is incorrect.
28.
If U is a variable , V is a constant then
Correct Answer
B.
Explanation
If U is a variable and V is a constant, it means that U can take on different values while V remains constant. This implies that U can change or vary in value, while V stays the same.
29.
if then ?
Correct Answer
A.
30.
If
Correct Answer
D.
31.
If then =?
Correct Answer
B.
32.
If then x=?
Correct Answer
A. 3
33.
If then x=?
Correct Answer
A. 4
34.
If then x=?
Correct Answer
C. R +1
35.
If then = ?
Correct Answer
C.
36.
Line is normal to the circle under the condition
Correct Answer
D. M+1=c
Explanation
The equation of a circle is given by (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In order for a line to be normal to the circle, it must be perpendicular to the radius at the point of intersection. The slope of the radius is given by m = (y-b)/(x-a). Since the line is normal to the circle, the slope of the line will be the negative reciprocal of the slope of the radius. Therefore, the slope of the line will be -(1/m). Given that m+1 = c, we can conclude that the line is normal to the circle when m+1=c.
37.
No. of triangles formed by joining 6 non-collinear points is
Correct Answer
A. 20
Explanation
The number of triangles formed by joining 6 non-collinear points can be calculated using the formula nC3, where n is the number of points. In this case, we have 6 points, so the calculation would be 6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20. Therefore, the correct answer is 20.
38.
Number in polar form is:
Correct Answer
A.
39.
One side of a square is 10 cm. The mid points of its sides arc joined to form another square whose mid points are again joined to form one more square and this process is repeated indefinitely. Find the sum of the areas of all the squares.
Correct Answer
A. 1000
Explanation
The sum of the areas of all the squares can be found by using the formula for the sum of an infinite geometric series. The first term is the area of the original square (10 cm x 10 cm = 100 cm^2) and the common ratio is 1/4 (since each new square is 1/4 the size of the previous square). Plugging these values into the formula, we get 100 cm^2 / (1 - 1/4) = 100 cm^2 / (3/4) = 100 cm^2 x (4/3) = 400/3 cm^2 â‰ˆ 133.33 cm^2. Therefore, the sum of the areas of all the squares is approximately 133.33 cm^2, which is closest to 1000 cm^2.
40.
Period of cos (3x + 7)=?
Correct Answer
B.
Explanation
The period of the function cos(3x + 7) is 2Ï€/3. This can be determined by finding the period of the standard cosine function, which is 2Ï€, and then dividing it by the coefficient of x (3) in the argument of the cosine function. The constant term (7) does not affect the period of the function. Therefore, the period of cos(3x + 7) is 2Ï€/3.
41.
Set of cube root of unity is a group w.r.t :
Correct Answer
B. X
Explanation
The set of cube roots of unity forms a group with respect to the operation of multiplication. This is because the set contains three elements: 1, -0.5 + iâˆš3/2, and -0.5 - iâˆš3/2, which are the solutions to the equation x^3 = 1. These elements satisfy the group axioms of closure, associativity, identity, and inverse. Therefore, the set forms a group under multiplication.
42.
Slope of a Circle at a point P making an inclination 45 degree is :
Correct Answer
B. -1
Explanation
The slope of a circle at a point P making an inclination of 45 degrees is -1. This means that the tangent line to the circle at point P is perpendicular to the line that makes a 45-degree angle with the x-axis. Since the slope of a line perpendicular to a line with slope m is the negative reciprocal of m, the slope of the tangent line is -1.
43.
Sum of squares of conjugate complex number is?
Correct Answer
A. Real Number
Explanation
The sum of squares of conjugate complex numbers is always a real number. This is because the conjugate of a complex number is obtained by changing the sign of its imaginary part. When we square a complex number and its conjugate, the imaginary parts cancel each other out, leaving only the real part. Therefore, the sum of squares of conjugate complex numbers will always result in a real number.
44.
The 7th Term from the end in the expansion of is
Correct Answer
D.
45.
The closest point to the focus of is
Correct Answer
B. (1,-8)
Explanation
The correct answer is (1,-8) because the focus of a parabola is a point that is equidistant from the directrix and the vertex. In this case, the given points (-1,8) and (8,1) are not equidistant from the directrix, so they cannot be the focus. The point (1,-8) is equidistant from the directrix and the vertex, making it the closest point to the focus.
46.
The contra positive of is
Correct Answer
C.
47.
The coordinates of the foci of the hyperbola
Correct Answer
D.
48.
The large hand of a clock is 3 feet long. How many inches does its extremity move in 10 minutes time?
Correct Answer
D. 37.7
Explanation
The large hand of a clock moves in a circular motion, completing one full rotation every 60 minutes. In 10 minutes, it would move one-sixth of the way around the clock face. Since the length of the hand is 3 feet, the extremity of the hand would move (1/6) * 3 feet, which is equal to 0.5 feet or 6 inches. Therefore, the correct answer is 6 inches.
49.
The midpoints of a set of parallel chords of an ellipse are:
Correct Answer
A. Co-linear
Explanation
The midpoints of a set of parallel chords of an ellipse are co-linear. This means that if we take any two parallel chords of an ellipse and find their midpoints, these midpoints will lie on the same straight line. This property holds true for all parallel chords of an ellipse, regardless of their orientation or position on the ellipse. Therefore, the correct answer is that the midpoints of a set of parallel chords of an ellipse are co-linear.
50.
The number of numbers between 1 and 1000 having at least one 3 is
Correct Answer
C. 270
Explanation
The question asks for the number of numbers between 1 and 1000 that have at least one 3. To solve this, we can count the numbers that do not have any 3 and subtract it from the total number of numbers between 1 and 1000. There are 9 options for the first digit (1-9), 10 options for the second digit (0-9), and 10 options for the third digit (0-9). So the total number of numbers between 1 and 1000 is 9 x 10 x 10 = 900. The number of numbers without any 3 is 8 x 9 x 9 = 648. Subtracting this from the total gives us 900 - 648 = 252. However, this only counts the numbers between 100 and 999, so we need to add the numbers from 1 to 99 that have at least one 3. There are 10 numbers from 1 to 9 and 10 numbers from 30 to 39, so the total is 252 + 10 + 10 = 272. Therefore, the correct answer is 270.