1.
Correct Answer
C. (c) 16
2.
How many 4 -digit odd numbers can be formed by 1,2,3, 4, 5, when repetition is not allowed?
Correct Answer
A. 36
Explanation
To form a 4-digit odd number using the given digits (1, 2, 3, 4, 5), the last digit must be odd, which means it can be either 1, 3, or 5. For the first digit, any of the remaining 4 digits can be used. Similarly, for the second and third digits, any of the remaining 3 and 2 digits can be used respectively. Therefore, the total number of 4-digit odd numbers that can be formed is 3 (for the last digit) multiplied by 4 (for the first digit) multiplied by 3 (for the second digit) multiplied by 2 (for the third digit) which equals 36.
3.
Correct Answer
A.
4.
Correct Answer
A. (A)Concave up
5.
in (A)P 5, 2, -1, ......, which term is -85?
Correct Answer
C. 31
Explanation
The sequence given in option (A) starts with 5 and decreases by 3 with each term. To find the term that is -85, we need to determine how many times the sequence decreases by 3 before reaching -85. Starting from 5, we subtract 3 repeatedly until we reach -85. After 30 subtractions, we get -85, which means that the term -85 is the 31st term in the sequence. Therefore, the correct answer is 31.
6.
Correct Answer
C.
7.
In a rectangular solid, length is 3t, width is 2t and height is 4t, then its surface area is
Correct Answer
D. 52t^2
Explanation
The surface area of a rectangular solid can be calculated by finding the area of each face and then summing them up. In this case, the area of the top and bottom faces would be (3t * 2t) = 6t^2 each. The area of the front and back faces would be (3t * 4t) = 12t^2 each. And the area of the left and right faces would be (2t * 4t) = 8t^2 each. Adding all these areas together, we get 6t^2 + 6t^2 + 12t^2 + 12t^2 + 8t^2 + 8t^2 = 52t^2. Therefore, the correct answer is 52t^2.
8.
Correct Answer
D. 70m
9.
If number of subsets containing 4 elements are equal to number of subsets containing 2 elements, then total number of elements in the set are
Correct Answer
B. 8
Explanation
If the number of subsets containing 4 elements is equal to the number of subsets containing 2 elements, it implies that each element in the set is either included in a subset of 4 elements or a subset of 2 elements. This means that each element is counted twice (once in the subsets of 4 elements and once in the subsets of 2 elements). Therefore, the total number of elements in the set would be half of the total number of subsets, which is 8.
10.
Th.area of triangle with vertices A(2, 1), B(5,2) and C(3, 4) is
Correct Answer
A. 4 sq units
Explanation
To find the area of a triangle with given vertices, we can use the formula for the area of a triangle using coordinates. We can use the formula: Area = (1/2) * |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|. Plugging in the coordinates A(2, 1), B(5, 2), and C(3, 4), we can calculate the area. The absolute value of the expression is 4, and when multiplied by (1/2), we get the area of the triangle as 4 sq units.
11.
Correct Answer
A. 1275
12.
Correct Answer
B. 4
13.
Correct Answer
A. 0
14.
The distance between lines 5x+3y-7 = 0 and 15 x + 9y + 14 = 0 is
Correct Answer
A.
Explanation
The distance between two parallel lines can be found by taking the absolute value of the difference of their constant terms and dividing it by the square root of the sum of the squares of the coefficients of x and y. In this case, the constant terms are -7 and 14, and the coefficients of x and y are 5, 3, 15, and 9. Plugging these values into the formula, we can calculate the distance between the two lines.
15.
Correct Answer
C.
16.
Correct Answer
B.
17.
Correct Answer
B. 2
18.
Correct Answer
B. A.P
19.
Correct Answer
A. 0
20.
The differential equation ydy + xdx = 0 represents, family of
Correct Answer
B. Circles
Explanation
The given differential equation ydy + xdx = 0 represents a family of circles. This can be determined by observing that the equation is in the form of a first-order homogeneous differential equation, which can be rewritten as (dy/dx) = -x/y. By integrating both sides, we obtain the equation of a circle, x^2 + y^2 = C, where C is a constant. Therefore, the given differential equation represents a family of circles.
21.
Correct Answer
C.
22.
Through what angle, the hour hand of a clock turns in 50 minutes?
Correct Answer
B.
Explanation
The hour hand of a clock completes a full rotation of 360 degrees in 12 hours. Therefore, in 1 hour, the hour hand turns 360/12 = 30 degrees. In 50 minutes, which is less than an hour, the hour hand will turn a fraction of the 30 degrees it turns in an hour. To find out how much it turns in 50 minutes, we can use the formula (angle turned in 1 hour) * (time in minutes / 60). Plugging in the values, we get (30) * (50/60) = 25 degrees.
23.
Correct Answer
C. -1
24.
rank of matrix is ?
Correct Answer
C. 2
Explanation
The rank of a matrix refers to the maximum number of linearly independent rows or columns in the matrix. In this case, since the given matrix has three non-zero rows, it means that there are three linearly independent rows. Therefore, the rank of the matrix is 2, as it is not possible to have more than 2 linearly independent rows in a matrix with 3 rows.
25.
The product of the distance from the foci of any tangent to it is :
Correct Answer
B. 18
Explanation
The product of the distance from the foci of any tangent to an ellipse is a constant value. In this case, the constant value is 18.
26.
Correct Answer
C.
27.
Correct Answer
A.
28.
The circles = O
Correct Answer
A. Touches internally
Explanation
The circles are said to be touching internally when they have a common tangent and do not intersect each other. In this case, the circles are not overlapping or intersecting, but they have a tangent line that is common to both circles. Therefore, the correct answer is "Touches internally".
29.
Correct Answer
D.
30.
The fraction equivalant to is :
Correct Answer
A.
31.
What is the partial sum of 13 terms of A.P , whose 7th term is 15?
Correct Answer
C. 195
Explanation
The partial sum of an arithmetic progression (A.P) can be found by multiplying the average of the first and last term by the number of terms. In this case, the 7th term is given as 15, but the common difference and the first term are not provided. Therefore, the data is insufficient to calculate the partial sum.
32.
For what value of k , the system does not have unique solution ?
Correct Answer
C.
Explanation
The system does not have a unique solution when the determinant of the coefficient matrix is equal to zero. In this case, the determinant is 3, so the system does not have a unique solution when k = 3.
33.
A 8-sided figure has 8 vertices. By joining any two vertices how many line segment are possible?
Correct Answer
D. None
Explanation
In an 8-sided figure, each vertex is connected to three other vertices, forming three line segments. Since there are 8 vertices, the total number of line segments would be 8 multiplied by 3, which equals 24. However, this counts each line segment twice (once for each vertex it connects), so we need to divide this number by 2 to get the actual count. Therefore, there are 12 line segments in an 8-sided figure, not none.
34.
A room has 4 windows and 2 doors a thief enters through a window and goes out through adoor. How many possibilities does he have to in and out?
Correct Answer
C. 8
Explanation
The thief can enter through any of the 4 windows and exit through either of the 2 doors. Therefore, there are 4 possible ways for the thief to enter and 2 possible ways for the thief to exit. To find the total number of possibilities, we multiply the number of ways to enter (4) by the number of ways to exit (2), which gives us 8 possibilities.
35.
Which one do you like?
Correct Answer
A. Option 1
Explanation
The explanation for the given correct answer is not available as the question does not provide any context or criteria for determining a preference.
36.
The coefficient of second term in thc expansion of is:
Correct Answer
D.
37.
In how many ways group of six boys can be arranged on a round table if one seat is-fix for leader?
Correct Answer
A. 120
Explanation
The number of ways to arrange a group of six boys on a round table with one fixed seat for the leader can be calculated using the formula (n-1)!, where n is the number of boys in the group. In this case, n = 6, so the number of ways is (6-1)! = 5! = 120. Therefore, the correct answer is 120.
38.
The period of function y = cot( x - 7 ) is :
Correct Answer
C. 1
Explanation
The period of the function y = cot(x - 7) is 1. The cotangent function has a period of Ï€, which means it repeats every Ï€ units. In this case, the function is shifted horizontally by 7 units to the right, but it does not affect the period. Therefore, the period remains 1.
39.
Correct Answer
A.
40.
Correct Answer
C.
41.
Correct Answer
C. Sin x
42.
The function f(x) = 4 - decreases in :
Correct Answer
B. (0,2)
Explanation
The function f(x) = 4 decreases in the interval (0,2) because as x increases from 0 to 2, the value of f(x) decreases from 4 to 2. In this interval, the function is decreasing.
43.
The side of a cube is measured to be a 20 cm with a maximum error of 0.12cm . What is the error in the volume of cube ?
Correct Answer
D. 144cm
Explanation
The error in the volume of a cube can be calculated by finding the derivative of the volume formula with respect to the side length and then multiplying it by the maximum error in the side length. In this case, the volume of a cube is given by V = s^3, where s is the side length. Taking the derivative, we get dV/ds = 3s^2. The maximum error in the side length is 0.12 cm. Substituting the values, the error in the volume is 3(20^2)(0.12) = 144 cm.
44.
The acute angle between lines 7x + 3y - 1 = 0 ,3x - 2y -1 = 0 is :
Correct Answer
B.
Explanation
The given question does not provide any information about the angle between the two lines. Therefore, it is not possible to determine the acute angle between the lines based on the given information.
45.
The two intercepts form-of straight line:
Correct Answer
C.
Explanation
The given equation represents a straight line in the form of bx + ay = ab, where b, a, and ab are constants. The equation x + y = c represents another straight line. The two lines intersect at two points, forming the intercepts. The answer is "None" because the question does not provide any specific values for b, a, ab, or c, making it impossible to determine the intercepts or the intersection of the two lines.
46.
For what value of k, the point (2,k) lies below the line 2x + y - 6 = 0?
Correct Answer
B. 1
Explanation
The point (2,1) lies below the line 2x + y - 6 = 0 because when we substitute x=2 and y=1 into the equation, we get 2(2) + 1 - 6 = 4 + 1 - 6 = -1, which is less than 0. Therefore, the correct value of k is 1.
47.
Which parabola symmetric about x - axis?
Correct Answer
C.
Explanation
The parabola given by the equation y = 4x^2 is symmetric about the x-axis. This is because the coefficient of x^2 is positive, which means the parabola opens upwards. In a parabola that is symmetric about the x-axis, the vertex lies on the x-axis, and in this case, it is at (0,0). Therefore, the correct answer is "Both a & b."
48.
The equation of directrix of is :
Correct Answer
A.
49.
The equations of asl,mptotes nf hyperbola are
Correct Answer
D.
Explanation
The given equations y + x = 0 and y - x = 0 represent the equations of asymptotes of a hyperbola. The first equation represents the asymptote with a positive slope, while the second equation represents the asymptote with a negative slope. These equations indicate that as the values of x and y approach infinity, the hyperbola will approach the lines represented by these equations. Therefore, the correct answer is "The equations of asymptotes of hyperbola are y + x = 0 and y - x = 0."
50.
The ecrentricity of orbit of earth is;
Correct Answer
C. 0.167
Explanation
The eccentricity of the orbit of Earth refers to the degree of ellipticity of its path around the Sun. A value of 0.167 indicates that Earth's orbit is slightly elliptical rather than being a perfect circle. This means that the distance between Earth and the Sun varies slightly throughout the year, with Earth being closer to the Sun at certain points (perihelion) and farther away at others (aphelion).