1.
Write Down The Next Term Of The Sequence 1/6, 1/3,1/2,……………………
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Correct Answer
A. 2/3
Explanation
The sequence is an arithmetic progression where each term is increased by 1/6. 1/6 + 1/6 = 2/6 = 1/3 1/3 + 1/6 = 3/6 = 1/2 1/2 + 1/6 = 4/6 = 2/3
2.
IF a_{n}=4n-3_{ }, FIND a_{17}
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Correct Answer
B. 65
Explanation
The given sequence is defined as an=4n-3. To find a17, we substitute n=17 into the formula. Therefore, a17=4(17)-3=68-3=65.
3.
Write The Number Of Subsets Of ɸ
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Correct Answer
A. 1
4.
AUA’=…………..
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Correct Answer
A. U
Explanation
The correct answer is "U" because it is the only option that is selected in the given choices.
5.
If The Set A Has 3 Elements and the set B={3,4,5} then find the number of elements in (A*B)
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Correct Answer
A. 9
Explanation
The set A has 3 elements and the set B has 3 elements. When we find the product of two sets, it means finding all possible combinations of elements from both sets. Since A has 3 elements and B has 3 elements, the number of elements in the product set (A*B) will be equal to the product of the number of elements in both sets, which is 3*3=9. Therefore, the answer is 9.
6.
Write 520° in radian measure.
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Correct Answer
A. 26π/9
Explanation
To convert degrees to radians, we use the formula: radians = degrees * (π/180). In this case, we have 520 degrees. Plugging this into the formula, we get: radians = 520 * (π/180). Simplifying this, we get: radians = 26π/9. Therefore, the correct answer is 26π/9.
7.
Express i^{-35} in the form of a+ib
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Correct Answer
A. I
Explanation
The given complex number i-35 can be expressed in the form of a+ib as -35+i.
8.
Find the sum of first 50 natural numbers.
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Correct Answer
C. 1275
Explanation
The sum of the first 50 natural numbers can be calculated using the formula for the sum of an arithmetic series, which is n/2 multiplied by the sum of the first and last term. In this case, n is 50, the first term is 1, and the last term is 50. Plugging these values into the formula, we get 50/2 * (1 + 50) = 25 * 51 = 1275. Therefore, the correct answer is 1275.
9.
If two straight lines are parallel then what is the relation in their slopes
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Correct Answer
B. M1=m2
Explanation
If two straight lines are parallel, their slopes will be equal. This is because parallel lines have the same steepness or inclination. Therefore, the correct answer is m1 = m2, where m1 represents the slope of the first line and m2 represents the slope of the second line.
10.
Find the distance between the points (1,-3,4) and (-4,1,2)
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Correct Answer
D. 3√5
Explanation
The distance between two points in three-dimensional space can be found using the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
In this case, the coordinates of the first point are (1, -3, 4) and the coordinates of the second point are (-4, 1, 2).
Plugging these values into the formula, we get:
distance = √((-4 - 1)^2 + (1 - (-3))^2 + (2 - 4)^2)
= √((-5)^2 + (4)^2 + (-2)^2)
= √(25 + 16 + 4)
= √45
= 3√5
Therefore, the correct answer is 3√5.
11.
What is the value of limx→0 sin x / x
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Correct Answer
C. 1
Explanation
The value of the limit as x approaches 0 of sin x / x is equal to 1. This is a well-known result in calculus, known as the Squeeze Theorem. As x approaches 0, sin x approaches 0 as well, and since sin x is bounded between -1 and 1, dividing sin x by x will still approach 1. Therefore, the correct answer is 1.
12.
Evaluate 4!-3!
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Correct Answer
B. 18
Explanation
To evaluate 4!-3!, we first calculate the factorial of 4 which is 4! = 4 x 3 x 2 x 1 = 24. Then, we calculate the factorial of 3 which is 3! = 3 x 2 x 1 = 6. Finally, we subtract 3! from 4! to get 24 - 6 = 18.
13.
If n(x)=17,n(y)=23 and n(xUy)=38 find n(x∩y)
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Correct Answer
D. 2
Explanation
The correct answer is 2 because the intersection of two sets, denoted as x∩y, is the set of elements that are common to both x and y. In this case, the total number of elements in the union of x and y is 38, which is the sum of the number of elements in x (17) and the number of elements in y (23). Since the intersection of x and y contains 2 elements, it is the only option that satisfies the given information.
14.
What is the value of ^{n}c_{n}
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Correct Answer
A. 1
Explanation
The value of nCn is equal to 1. This is because nCn represents the number of ways to choose n items from a set of n items, which is essentially choosing all the items. There is only one way to choose all the items, hence the value is 1.
15.
_{write Eq}^{n} of x-axis
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Correct Answer
C. Y=0
Explanation
The equation y=0 represents the x-axis because it states that the value of y is always 0, regardless of the value of x. This means that all points on the x-axis have a y-coordinate of 0.
16.
Find the value of cos(-1710)
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Correct Answer
A. 0
Explanation
The value of the cosine function repeats itself every 360 degrees. Therefore, we can find the value of cos(-1710) by subtracting 1710 from a multiple of 360. In this case, 1710 is equal to 4 times 360 plus 90. Since the cosine of 90 degrees is 0, we can conclude that cos(-1710) is also 0.
17.
Write the value of cosπ
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Correct Answer
B. -1
Explanation
The value of cosine of π is -1. This is because cosine is the ratio of the adjacent side to the hypotenuse in a right triangle, and at π radians (180 degrees), the adjacent side is negative and equal in magnitude to the hypotenuse. Therefore, the cosine of π is -1.
18.
Solve 3x<200 for x∈N
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Correct Answer
A. {1,2,3,4,5,6}
Explanation
The correct answer is {1,2,3,4,5,6} because when we solve the inequality 3x
19.
How many 4 digits numbers can be formed by using the digits 1 to 9 if repetition of digits is not
allowed?
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Correct Answer
B. 3024
Explanation
The question asks for the number of 4-digit numbers that can be formed using the digits 1 to 9 without repetition. To solve this, we need to calculate the number of choices for each digit. For the first digit, we have 9 options (1 to 9). For the second digit, we have 8 options (since we cannot repeat the digit chosen for the first digit). Similarly, for the third digit, we have 7 options, and for the fourth digit, we have 6 options. Therefore, the total number of 4-digit numbers that can be formed is 9 x 8 x 7 x 6 = 3024.
20.
Let A={1,2} and B={3,4} find the number of relations from A to B
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Correct Answer
D. 2^{4}
Explanation
The number of relations from set A to set B can be calculated by taking the power set of A (which is the set of all possible subsets of A) and then finding the number of possible mappings from each subset to set B. Since A has 2 elements and B has 2 elements, the power set of A will have 2^2 = 4 subsets. Each subset can be mapped to B in 2^2 = 4 different ways, resulting in a total of 4*4 = 16 possible mappings. Therefore, the correct answer is 16.
21.
Example of null set
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Correct Answer
A. X:x∈N, X>5 and x>7
Explanation
The correct answer is x:x∈N, X>5 and x>7 because it satisfies the given conditions. The set is asking for values of x that belong to the set of natural numbers (N), are greater than 5, and are also greater than 7. Therefore, any value of x that is both greater than 5 and greater than 7 would be a part of this set.
22.
If (x+1 ; y-2)= (3,1) find the value of x and y
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Correct Answer
A. X=2,y=3
Explanation
The given equation states that (x+1) is equal to 3 and (y-2) is equal to 1. Therefore, if we subtract 1 from both sides of the first equation, we get x=2. Similarly, if we add 2 to both sides of the second equation, we get y=3. Hence, the value of x is 2 and the value of y is 3.
23.
1 radian is Approximately equal to?
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Correct Answer
C. 57°16’
Explanation
1 radian is approximately equal to 57°16’. This is a commonly used approximation for converting between radians and degrees.
24.
Cos(-Ɵ)=
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Correct Answer
A. Cos(Ɵ)
Explanation
The given question asks for the value of cos(-Ɵ). The correct answer is cos(Ɵ) because the cosine function is an even function, which means that cos(-x) is equal to cos(x) for any value of x. Therefore, cos(-Ɵ) is equal to cos(Ɵ).
25.
Cos(x+y)=
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Correct Answer
B. Cosx cosy-sinx siny
Explanation
The correct answer is "Cosx cosy-sinx siny". This is the correct formula for the cosine of the sum of two angles. It follows the pattern of cosine being the product of the cosine of one angle and the cosine of the other angle, minus the product of the sine of one angle and the sine of the other angle.
26.
In a GP the 3^{rd} term is 24 and the 6^{th} term is 192. Find 10^{th} term?
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Correct Answer
A. 3072
Explanation
In a geometric progression (GP), each term is obtained by multiplying the previous term by a constant factor. To find the 10th term, we can use the formula for the nth term of a GP: a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the position of the term. Given that the 3rd term is 24 and the 6th term is 192, we can write two equations: 24 = a_1 * r^2 and 192 = a_1 * r^5. Dividing the second equation by the first equation, we get r^3 = 8. Solving for r, we find r = 2. Substituting r = 2 into the first equation, we can solve for a_1: 24 = a_1 * 2^2, which gives a_1 = 6. Finally, plugging in a_1 = 6 and n = 10 into the formula, we find the 10th term is 6 * 2^(10-1) = 3072. Therefore, the correct answer is 3072.
27.
What is the probability of a sure event
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Correct Answer
B. 1
Explanation
The probability of a sure event is always 1, meaning it is certain to occur. In other words, there is no doubt or uncertainty about its outcome. Therefore, the correct answer is 1.
28.
Write the Eq^{n }of straight line in intercept form
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Correct Answer
D. [x/a+y/b=1]
Explanation
The given equation [x/a + y/b = 1] represents the equation of a straight line in intercept form. In this form, 'a' and 'b' represent the x-intercept and y-intercept of the line respectively. The equation shows that the sum of the ratios of the x-coordinate and the x-intercept, and the y-coordinate and the y-intercept, is equal to 1. This represents a straight line passing through the intercepts (a, 0) and (0, b) on the x and y-axes respectively.
29.
What is the distance between two parallel lines Ax+By+C_{1}=0 and Ax+By+c_{2}=0
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Correct Answer
A. ^{I c1-c2 I /}√A^{2}+B^{2}
Explanation
The distance between two parallel lines can be found using the formula: distance = |c1 - c2| / √(A^2 + B^2). This formula calculates the perpendicular distance between the two lines.
30.
Write the derivative of tanx
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Correct Answer
B. Sec^{2}x
Explanation
The correct answer is sec2x. The derivative of tanx is equal to sec2x.
31.
.
Correct Answer
A. (a+b)^{n}
Explanation
The given expression (a+b)n represents the expansion of a binomial raised to the power of n. This is known as the binomial theorem. It states that when a binomial is raised to a power, each term in the expansion can be found by taking the sum of the binomial coefficients multiplied by the corresponding powers of the terms in the binomial. Therefore, the correct answer is (a+b)n as it represents the expansion of the binomial (a+b) raised to the power of n.
32.
Find the limit limx→1 [x^{3}-x^{2}+1]
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Correct Answer
C. 1
Explanation
As x approaches 1, the expression x^3 - x^2 + 1 simplifies to 1^3 - 1^2 + 1 = 1 - 1 + 1 = 1. Therefore, the limit of the expression as x approaches 1 is 1.
33.
What is the length of latus rectum of the ellipse x^{2}/a^{2}+y^{2}/b^{2}=1?
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Correct Answer
A. 2b^{2}/a
Explanation
The length of the latus rectum of an ellipse is given by the formula 2b^2/a, where a and b are the lengths of the major and minor axes respectively. In this case, the equation of the ellipse is x^2/a^2 + y^2/b^2 = 1. Comparing this with the standard equation of an ellipse, we can see that a^2 = 1 and b^2 = 1. Therefore, the length of the latus rectum is 2b^2/a, which simplifies to 2(1)/a = 2/a.
34.
What is the equation of parabola with locus at (a,0) a>0 and directrix x=-a ?
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Correct Answer
B. Y^{2}=4ax
Explanation
The equation of a parabola with a vertex at (h, k) and a focus at (h + p, k) is given by (x - h)² = 4p(y - k). In this case, the vertex is at (a, 0) and the directrix is x = -a. Since the vertex is at (a, 0), the equation becomes (x - a)² = 4p(y - 0). Since the directrix is x = -a, the value of p is a. Therefore, the equation simplifies to (x - a)² = 4a(y - 0), which can be further simplified to y² = 4ax.
35.
Write the equation of circle with centre (h,k) and radius r
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Correct Answer
A. X^{2}+y^{2}=r^{2}
Explanation
The equation of a circle with center (h,k) and radius r is given by (x-h)² + (y-k)² = r². In this case, the center is (0,0) which means h and k are both 0. Therefore, the equation simplifies to x² + y² = r².
36.
Cosx + Cosy=……………….
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Correct Answer
B. 2cos (x+y)/2 cos(x-y)/2
Explanation
The given expression, Cosx + Cosy, can be rewritten using the cosine addition formula as 2cos((x+y)/2)cos((x-y)/2). This is the same as the answer option 2cos (x+y)/2 cos(x-y)/2.
37.
(AUB)’=…………………………….
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Correct Answer
C. (A'∩B')
Explanation
The correct answer is (A'∩B'). This is because (A'∩B') represents the intersection of the complements of sets A and B. In other words, it includes all the elements that are not in set A and not in set B.
38.
What is the range of signum function ?
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Correct Answer
A. {-1,0,1}
Explanation
The range of the signum function is {-1, 0, 1} because the signum function returns -1 for negative numbers, 0 for zero, and 1 for positive numbers. Therefore, the set of possible values for the signum function is {-1, 0, 1}.
39.
If f(x)=2x-5 find f(0)
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Correct Answer
C. -5
Explanation
To find f(0), we substitute 0 for x in the equation f(x) = 2x - 5. Thus, f(0) = 2(0) - 5 = -5.
40.
(A’)’=……………………………………
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Correct Answer
A. A
Explanation
The correct answer is A. In this question, the options given are A, U, A', and ɸ. A' represents the complement of set A, which includes all the elements that are not in set A. U represents the universal set, which includes all possible elements. A is the set itself. ɸ represents the empty set, which does not contain any elements. Among these options, A is the only one that represents the set itself.