NDA Mathematics 13 April 2025
DEFENCE 2025 Previous Year
3 hDuration
300Total Marks
120Questions
1Sections
Instructions
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Paper Structure
Mathematics
Mathematics
Q1.
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The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?
Q2.
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**Passage:**
Consider the following for the two (02) items that follow:
The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical tubers are given as $\Sigma X = 200, \Sigma Y = 250, \Sigma X^2 = 900$ and $\Sigma Y^2 = 1400$
---
Which one of the following is correct?
Q3.
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The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?
Q4.
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What is the arithmetic mean of 8^(2),9^(2),10^(2),...,15^(2)?
Q5.
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**Passage:**
Consider the following for the two (02) items that follow:
The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical tubers are given as $\Sigma X = 200$, \Sigma Y = 250, \Sigma X^2 = 900 and \Sigma Y^2 = 1400$
---
Which one of the following statements is correct?
Q6.
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**Passage:**
Consider the following for the four (04) items that follow:
The frequency distribution of height of students of a class is given below:
Height (in cm
Number of Students
160-162
12
162-164
15
164-166
24
166-168
13
---
The height which occurs most frequently in the class is
Q7.
mcq single
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**Passage:**
Consider the following for the four (04) items that follow:
The frequency distribution of height of students of a class is given below:
Height (in cm
Number of Students
160-162
12
162-164
15
164-166
24
166-168
13
---
What is the height of the class?
Q8.
mcq single
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**Passage:**
Consider the following for the four (04) items that follow:
The frequency distribution of height of students of a class is given below:
Height (in cm
Number of Students
160-162
12
162-164
15
164-166
24
166-168
13
---
What is the total number of students whose height is less than or equal to 165 cm?
Q9.
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**Passage:**
Consider the following for the four (04) items that follow:
The frequency distribution of height of students of a class is given below:
Height (in cm
Number of Students
160-162
12
162-164
15
164-166
24
166-168
13
---
The most appropriate graphical representation of the given frequency distribution is
Q10.
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**Passage:**
Consider the following for the two (02) items that follow:
Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}
---
Consider the following statements:
I. f is one-one function.
II. f is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?
Q11.
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**Passage:**
Consider the following for the two (02) items that follow :
Let the function f(x) = x^(2)- 1
---
What is $\lim_{x \to 1} \{f \circ f(x)\}$ equal to?
Q12.
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**Passage:**
Consider the following for the two (02) items that follow: Let the function f(x)=sin[x], where [⋅] is the greatest integer function and g(x)=∣x∣.
---
What $\lim_{x \to 0} {f(x) g(x)}$ is equal to?
Q13.
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**Passage:**
Consider the following for the two (02) items that follow:
Let the function f(x) = x ^(2) + 9
---
What is $\lim_{x \to 0} \frac{\sqrt{f(x)} - 3}{\sqrt{f(x)+7} - 4}$ equal to?
Q14.
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**Passage:**
Consider the following for the two (02) items that follow:
$\text{Let } f(x)= \begin{cases} x^3, & x^2 < 1 \\ x^2, & x^2 \ge 1 \end{cases} \\$
---
What is $\lim_{x \to 0} f'(x)$ equal to?
Q15.
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**Passage:**
Consider the following for the two (02) items that follow:
$\text{Let } f(x)= \begin{cases} x^3, & x^2 < 1 \\ x^2, & x^2 \ge 1 \end{cases} \\$
---
Consider the following statements:
I. The function is continuous at x=−1.
II. The function is differentiable at x=1.
Which of the statements given above is/are correct?
Q16.
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**Passage:**
Consider the following for the two (02) items that follow: Let the function f(x)=sin[x], where [⋅] is the greatest integer function and g(x)=∣x∣.
---
What is $\lim_{x \to 0} \frac{f(x)}{g(x)}$ equal to?
Q17.
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If p, 1, q are in AP and p, 2, q are in GP, then which of the following statements is/are correct?
I. p, 4, q are in HP.
II. (1/p), (1/4), (1/q) are in AP.
Select the answer using the code given below.
Q18.
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If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?
Q19.
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The sum of the first k terms of a series S is 3k^(2)+5k. Which one of the following is correct?
Q20.
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The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r≠1 is the common ratio, then what is the number of possible real values of r?
Q21.
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Let $\vec{a},\vec{b} ,(\vec{a}\times\vec{b})$ be unit vectors. What is $\vec{a}.\vec{b}$ equal to?
Q22.
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The position vectors of three points A, B and C respectively, where $\vec{a} ,\vec{b} $ and $\vec{c} $ respectively, where $\vec{c} = (\cos^2 \theta)\vec{a}+(\sin^2 \theta)\vec{b}$. What is $(\vec{a} \times \vec{b}) + (\vec{b} \times \vec{c}) + (\vec{c} \times \vec{a})$ equal to?
Q23.
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A line makes angles α, β and γ with the positive directions of the coordinate axes. If $\vec{a}=(\sin^2 \alpha)\hat{i} + (\sin^2 \beta)\hat{j} + (\sin^2 \gamma)\hat{k} \text{ and } \vec{b} = \hat{i} + \hat{j} + \hat{k}$ , then what is $\vec{a}.\vec{b}$ equal to?
Q24.
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Consider the following statements with respect to a vector d = (a × b) × c:
I. d is coplanar with a and b.
II. d is perpendicular to c.
Which of the statements given above is/are correct?
Q25.
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The position vectors of three points A, B and C are a
, b and c respectively such that $\vec{3a}-\vec{4b}+\vec{c}=\vec{0}$ What is AB:BC equal to?
Q26.
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If k is a root of x^(2)−4x+1=0, then what is tan^(−1)k+tan^(−1)$\frac{1}{k}$ equal to?
Q27.
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**Passage:**
Consider the following for the two (02) items that follow:
Let $y = \sin^{-1} \left( x - \frac{4x^3}{27} \right).$
---
What is y equal to?
Q28.
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**Passage:**
Consider the following for the two (02) items that follow:
Let $y = \sin^{-1} \left( x - \frac{4x^3}{27} \right).$
---
What is $\frac{dy}{dx}$ euqal to ?
Q29.
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If tan^(−1)k+tan^(−1 )$\frac{1}{2}$=$\frac{π}{2} $, then what is the value of k?
Q30.
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**Passage:**
Consider the following for the two (02) items that follow:
Let X be a random variable following binomial distribution with parameters n = 6 and p = k Further, 9P(X = 4) = P(X = 2) .
---
What is the value of P * (X = 3) ^ 0
Q31.
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**Passage:**
Consider the following for the two (02) items that follow:
A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
---
What is the probability that the committee includes exactly 3 gentlemen?
Q32.
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Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?
Q33.
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**Passage:**
Consider the following for the two (02) items that follow:
A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
---
What is the probability that the committee includes at least 2 ladies?
Q34.
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**Passage:**
Consider the following for the two (02) items that follow:
The probabilities that A, B and C become managers are 3/10 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively.
---
What is the probability that the bonus scheme will be introduced?
Q35.
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If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?
Q36.
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**Passage:**
Consider the following for the two (02) items that follow:
Let X be a random variable following binomial distribution with parameters n = 6 and p = k Further, 9P(X = 4) = P(X = 2) .
---
What is the value of k?
Q37.
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The probability of a man hitting a target is 1/5. If the man fires 7 times, then what is the probability that he hits the target at least twice?
Q38.
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If P(A)=1/3, P(B)=1/2 and P(A∩B)=1/4, then what is the value of P(A|B^(C))?
Q39.
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**Passage:**
Consider the following for the two (02) items that follow:
The probabilities that A, B and C become managers are 3/10 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively.
---
If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?
Q40.
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If P(A)=1/3, P(B)=1/2 and P(A∩B)=1/4, then what is the value of P(A^(C)∩B^(C))?
Q41.
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A man at M, standing 100 m away from the base (P) of a chimney of height 50 m, observes the angle of elevation of the highest point (Q) of the smoke to be 45^(∘). The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?
Q42.
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**Passage:**
Consider the following for the two (02) items that follow:
The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b
---
What is MN equal to?
Q43.
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**Passage:**
Consider the following for the two (02) items that follow:
The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b
---
What is PN equal to?
Q44.
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If p and q are real numbers between 0 and 1 such that the points (p,1), (1,q) and (0,0) form an equilateral triangle, then what is (p+q) equal to?
Q45.
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Under what condition will the lines m^(2)x+ny−1=0 and n^(2)x−my+2=0 be perpendicular?
Q46.
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ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1,2) and that of D are (−2,6), then what is the equation of BC?
Q47.
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Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance $\sqrt{2}$ units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?
Q48.
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**Passage:**
Consider the following for the two (02) items that follow:
Let 2sinα + cosα = 2 where 0 < α < 90°
---
What is 2sin2α+cos2α equal to?
Q49.
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**Passage:**
Consider the following for the three (03) items that follow: Let p=sin35^(∘), q=sin25^(∘) and r=sin(−95^(∘)).
---
What is (pq+qr+rp) equal to?
Q50.
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**Passage:**
Consider the following for the three (03) items that follow: Let p=sin35^(∘), q=sin25^(∘) and r=sin(−95^(∘)).
---
What is (p+q+r) equal to?
Q51.
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**Passage:**
Consider the following for the three (03) items that follow:
Let p = tan 2α - tanα and q = cotα - cot 2α
---
What is tan^(2)α equal to?
Q52.
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**Passage:**
Consider the following for the two (02) items that follow:
Let 2sinα + cosα = 2 where 0 < α < 90°
---
What is tanα equal to?
Q53.
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**Passage:**
Consider the following for the three (03) items that follow:
Let p = tan 2α - tanα and q = cotα - cot 2α
---
What is (p/q) equal to?
Q54.
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**Passage:**
Consider the following for the two (02) items that follow: Let p=∣sinα−sin(α−90∘)∣.
---
What is the minimum value of p?
Q55.
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**Passage:**
Consider the following for the three (03) items that follow:
Let p = tan 2α - tanα and q = cotα - cot 2α
---
What is (p+q) equal to?
Q56.
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**Passage:**
Consider the following for the two (02) items that follow: Let p=∣sinα−sin(α−90∘)∣.
---
What is the maximum value of p?
Q57.
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**Passage:**
Consider the following for the three (03) items that follow: Let p=sin35^(∘), q=sin25^(∘) and r=sin(−95^(∘)).
---
What is (p^(2)+q^(2)+r^(2)) equal to?
Q58.
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**Passage:**
Consider the following for the two (02) items that follow:
The slope of the tangent to the curve y = f(x) at (x, f(x) ) is 4 for every real number x and the curve passes through the origin.
---
What is the nature of the curve?
Q59.
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**Passage:**
Consider the following for the two (02) items that follow:
Let the function f(x) = x ^(2) + 9
---
Consider the following statements:
I. f(x) is an increasing function.
II. f(x) has local maximum at x = 0
Which of the statements given above is/are correct?
Q60.
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**Passage:**
Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB+AC = 3 units.
---
What is the maximum area of the triangle?
Q61.
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**Passage:**
Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB+AC = 3 units.
---
What is ∠A equal to if the area of the triangle is maximum?
Q62.
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**Passage:**
Consider the following for the two (02) items that follow:
Let the curve f(x) = |x - 3|
---
What is the area bounded by the curve f(x) and y = 3?
Q63.
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**Passage:**
Consider the following for the two (02) items that follow :
Let the function f(x) = x^(2)- 1
---
What is the area bounded by the function f(x) and the x-axis?
Q64.
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**Passage:**
Consider the following for the two (02) items that follow:
The slope of the tangent to the curve y = f(x) at (x, f(x) ) is 4 for every real number x and the curve passes through the origin.
---
. What is the area bounded by the curve, the x-axis and the line x = 4?
Q65.
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If a line $\frac{x+1}{p} = \frac{y-1}{q} = \frac{z-2}{r}$ where p=2q=3r, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?
Q66.
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If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is cos(α+β)cos(α−β) equal to?
Q67.
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A(1,2,−1), B(2,5,−2) and C(4,4,−3) are three vertices of a rectangle. What is the area of the rectangle?
Q68.
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ABC is a triangle right-angled at B. If A(k,1,−1), B(2k,0,2) and C(2+2k,k,1) are the vertices of the triangle, then what is the value of k?
Q69.
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What is the equation of the plane passing through the point (1,1,1) and perpendicular to the line whose direction ratios are (3,2,1)?
Q70.
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A tangent to the parabola y^(2) = 4x is inclined at an angle 45° deg with the positive direction of x-axis. What is the point of contact of the tangent and the parabola?
Q71.
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If x=(1111)~2~, y=(1001)~2~ and z=(110)~2~, then what is x^(3)−y^(3)−z^(3)−3xyz equal to?
Q72.
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If the sum of binomial coefficients in the expansion of (x+y)^(n) is 256, then the greatest binomial coefficient occurs in which one of the following terms?
Q73.
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If $k<(\sqrt{2}+1)^3<k+2,$ where k is a natural number, the value of k?
Q74.
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What is the number of rational terms in the expansion of $(\sqrt{3}+5^\frac{1}{4})^{12}$
Q75.
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If $z\ne0$ is a complex number, then what is amp(z)+amp(zˉ) equal to?
Q76.
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What is $ \left( \frac{\sqrt{3}+i}{\sqrt{3}-i} \right)^3 $ equal to?
Q77.
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. What is the distance between the two foci of the hyperbola 25x^(2) - 75y ^(2)= 225 ?
Q78.
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**Passage:**
Consider the following for the two (02) items that follow:
Let the function y = (1 - cos x)^(-1) where$x \ne 2n\pi$ and n is an integer
---
What is the range of the function?
Q79.
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**Passage:**
Consider the following for the two (02) items that follow:
A function f is such that f(xy) = f(x + y) for all real values of x and y, and f(5) = 10
---
What is f(20)+f(-20) equal to?
Q80.
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**Passage:**
Consider the following for the two (02) items that follow:
Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}
---
If f(x) = px + q then what is the value of (p + q) ?
Q81.
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**Passage:**
Consider the following for the two (02) items that follow:
The function f(x) satisfies $f(x), f \left( \frac{x}{y} \right) = \frac{f(x)}{f(y)}.$ for all positive real values of x and y, and f(2) = 3
---
What is f(1)f(4) equal to?
Q82.
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**Passage:**
Consider the following for the two (02) items that follow:
Let the curve f(x) = |x - 3|
---
What is the domain of the function (f(x))?
Q83.
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**Passage:**
Consider the following for the two (02) items that follow:
The function f(x) satisfies $f(x), f \left( \frac{x}{y} \right) = \frac{f(x)}{f(y)}.$ for all positive real values of x and y, and f(2) = 3
---
What is f(16) equal to?
Q84.
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**Passage:**
Consider the following for the two (02) items that follow:
A function f is such that f(xy) = f(x + y) for all real values of x and y, and f(5) = 10
---
What is f(0) equal to?
Q85.
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A square is inscribed in a circle x ^(2) + y^( 2 )+ 2x + 2y + 1 = 0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?
Q86.
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What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x+y=0 and x−y=0?
Q87.
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If one root of the equation x^(2)−kx+k=0 exceeds the other by $2\sqrt{3}$ then which one of the following is a value of k?
Q88.
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If 
$x+\frac{5}{y}=4$, and then $y+\frac{5}{x}= -4$ what is (x + y) equal to?
$x+\frac{5}{y}=4$, and then $y+\frac{5}{x}= -4$ what is (x + y) equal to?
Q89.
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If x^(2)− x +1 = 0, then what is $(x-\frac{1}{x})^2+(x-\frac{1}{x})^4+(x-\frac{1}{x})^8$
Q90.
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If any point on an ellipse is (3sin$\alpha$, 5cos$\alpha$), then what is the eccentricity of the ellipse?
Q91.
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**Passage:**
Consider the following for the two (02) items that follow:
Let (x+y)p+q=xpyq, where p,q are positive integers.
---
The derivative of y with respect to x
Q92.
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**Passage:**
Let $x = \sec \theta - \cos \theta \text{ and } y = \sec^4 \theta - \cos^4 \theta \\ $
---
What $\left[ \frac{x^2+4}{y^2+4} \frac{dy}{dx} \left( x^2+4 \frac{d^2y}{dx^2} - 16y \right) \right] $ equal to?
Q93.
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**Passage:**
Consider the following for the two (02) items that follow:
Let (x+y)p+q=xpyq, where p,q are positive integers.
---
If p+q=10, then what is $\frac{dy}{dx}$ equal to?
Q94.
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**Passage:**
Let $x = \sec \theta - \cos \theta \text{ and } y = \sec^4 \theta - \cos^4 \theta \\ $
---
What is $(\frac{dy}{dx})^2$ equal to?
Q95.
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In how many ways can the letters of the word DELHI be arranged, keeping the positions of vowels and consonants unchanged?
Q96.
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How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all the consonants come together in each word?
Q97.
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What is the number of selections of at most 3 things from 6 different things?
Q98.
mcq single
+2.5 / 0.83
How many sides are there in a polygon that has 20 diagonals?
Q99.
mcq single
+2.5 / 0.83
If the number of selections of r as well as (n+r) things from 5n different things are equal, then what is the value of r?
Q100.
mcq single
+2.5 / 0.83
What is the number of positive integer solutions of x+y+z=5?
Q101.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the two (02) items that follow:
Let f(x) = [x^(2)] where [.] is the greatest integer function.
---
What $\int_{\sqrt{2}}^{\sqrt{3}} f(x) dx$ equal to?
Q102.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the two (02) items that follow:
Let f(x) = [x^(2)] where [.] is the greatest integer function.
---
$\int_{\sqrt{2}}^{2} f(x) dx$ is equal to ?
Q103.
mcq single
+2.5 / 0.83
If $A=\begin{bmatrix}x&y&z\\y&z&x\\z&x&y\end{bmatrix}$
where x,y,z are integers, is an orthogonal matrix, then what is A^(2) equal to?
Q104.
mcq single
+2.5 / 0.83
If $A=\begin{bmatrix}1&2&2 \\ 2&1&2\\2&2&1\end{bmatrix}$ then what is A^(2)−4A equal to?
Q105.
mcq single
+2.5 / 0.83
If
$A = \begin{bmatrix} y & z & x \\ z & x & y \\ x & y & z \end{bmatrix} $
where x,y,z are integers, is an orthogonal matrix, then what is the value of x^(2)+y^(2)+z^(2)?
Q106.
mcq single
+2.5 / 0.83
If $f(\theta) = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$ then what is (f(π))^(2) equal to?
Q107.
mcq single
+2.5 / 0.83
If
$\begin{bmatrix} x & 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix}$
then which one of the following is a value of x?
Q108.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB=3cm, BC=5cm and CA=7cm.
---
What is the area of the triangle?
Q109.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB=3cm, BC=5cm and CA=7cm.
---
What is ∠B equal to?
Q110.
mcq single
+2.5 / 0.83
The vertices of a triangle are A(1, 1),B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?
Q111.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the three (03) items that follow: The sides of a triangle ABC are AB=3cm, BC=5cm and CA=7cm.
---
Consider the following statements:
I. The triangle is obtuse-angled triangle.
II. The sum of acute angles of the triangle is also acute.
Which of the statements given above is/are correct?
Q112.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the two (02) items that follow:
In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3: 1.
---
Consider the following statements:
I. The triangle is right-angled.
II. One of the sides of the triangle is 3 times the other.
III. The angles A, C and B of the triangle are in AP.
Which of the statements given above is/are correct?
Q113.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the two (02) items that follow:
In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3: 1.
---
One of the angles of the triangle is
Q114.
mcq single
+2.5 / 0.83
. Consider the following statements in respect of the determinant
$ \Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix} $
I. Δ is positive if k>0.
II. Δ is negative if k<0.
III. Δ is zero if k=0.
How many of the statements given above are correct?
Q115.
mcq single
+2.5 / 0.83
Consider the following in respect of a non-singular matrix M:
I. ∣M^(2)∣=∣M∣^(2)
II. ∣M∣=∣M^(−1)∣
III. ∣M∣=∣M^(T)∣
How many of the above are correct?
Q116.
mcq single
+2.5 / 0.83
If A^(2)+B^(2)+C^(2)=0, then what is the value of the following?
$\begin{vmatrix} 1& cosC& cosB\\ cosC&1&cosA \\ cosB&cosA&1 \end{vmatrix} $
Q117.
mcq single
+2.5 / 0.83
If $\Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} $
and A, B, C, D, G are the cofactors of the elements a, b, c, d, g respectively, then what is bB+cC−dD−gG equal to?
Q118.
mcq single
+2.5 / 0.83
If ω is a non-real cube root of unity, then what is a root of the following equation?$ \begin{vmatrix} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{vmatrix} = 0 $
Q119.
mcq single
+2.5 / 0.83
If $ \begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i -1 \\ -1 &-1 -i & 1 \end{vmatrix} = A + iB $
where i= $\sqrt{-1}$ , then what is A+B equal to?
Q120.
mcq single
+2.5 / 0.83
**Passage:**
Consider the following for the two (02) items that follow:
Let the function y = (1 - cos x)^(-1) where$x \ne 2n\pi$ and n is an integer
---
What is ∫ydx equal to?
where c is the constant of integration.