128 + Interview Questions in NDA IN GENERAL AWARENESS Page 3 InterviewSolution

101.	In a multiple-choice test, an examinee either knows the correct answer with probability P, or guesses with probability 1- P. The probability of answering a question correctly is 1m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is
Answer» Correct option B. mp/(1 + p(m - 1)) Explanation: P(he/she know correct answer) = p P(he/she guess correct answer) = (1 - p) × 1/m P(correct answer) = p + (1− p)/m P(he/she really know correct answer) = p/(p + (1 - p)/m) = mp/(1 + p(m - 1))

101.

In a multiple-choice test, an examinee either knows the correct answer with probability P, or guesses with probability 1- P. The probability of answering a question correctly is 1m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

Answer»

Correct option B. mp/(1 + p(m - 1))

Explanation:

P(he/she know correct answer) = p

P(he/she guess correct answer) = (1 - p) × 1/m

P(correct answer) = p + (1− p)/m

P(he/she really know correct answer)

= p/(p + (1 - p)/m)

= mp/(1 + p(m - 1))

Discussion

102.	If xi > 0, yi > 0 (i = 1, 2, 3, ...... n) are the values of two variable X and Y with geometric mean P and Q respectively, then the geometric mean of X/Y is a. P/Q b. antilog (P/Q)c. n(log P – log Q) d. n(logP + log Q)
Answer» Correct option a. P/Q Explanation: (x₁. x₂ ......x_n)^1/n = P (y₁. y₂ .....y_n)^1/n= Q ((x₁. x₂ ......x_n)/(y₁. y₂ .....y_n))^1/n= (x₁. x₂ ......x_n)^1/n/(y₁. y₂ .....y_n)^1/n = P/Q

102.

If xi > 0, yi > 0 (i = 1, 2, 3, ...... n) are the values of two variable X and Y with geometric mean P and Q respectively, then the geometric mean of X/Y is a. P/Q b. antilog (P/Q)c. n(log P – log Q) d. n(logP + log Q)

Answer»

Correct option a. P/Q

Explanation:

(x₁. x₂ ......x_n)^1/n = P

(y₁. y₂ .....y_n)^1/n= Q

((x₁. x₂ ......x_n)/(y₁. y₂ .....y_n))^1/n= (x₁. x₂ ......x_n)^1/n/(y₁. y₂ .....y_n)^1/n = P/Q

Discussion

103.	The points (a, b), (0, 0), (−a,−b) and (ab, b2) are A. the vertices of a parallelogram B. the vertices of a rectangle C. the vertices of a square D. collinear
Answer» Correct option D. collinear Explanation: These points lie on the same line of equation, therefore these points are collinear.

103.

The points (a, b), (0, 0), (−a,−b) and (ab, b2) are A. the vertices of a parallelogram B. the vertices of a rectangle C. the vertices of a square D. collinear

Answer»

Correct option D. collinear

Explanation:

These points lie on the same line of equation, therefore these points are collinear.

Discussion

104.	Let Tr be the rth term of an AP for r = 1, 2, 3, .... If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to? a. (mn)–1 b. m–1 + nn–1 c. 1 d. 0
Answer» Correct option c. 1 Explanation: T_n = 1/m, T_m = 1/n ⇒ 1^st Term = c.d. = 1/mn ⇒ T_mn = 1/mn + (mn - 1)/mn = 1

104.

Let Tr be the rth term of an AP for r = 1, 2, 3, .... If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to? a. (mn)–1 b. m–1 + nn–1 c. 1 d. 0

Answer»

Correct option c. 1

Explanation:

T_n = 1/m, T_m = 1/n

⇒ 1^st Term = c.d. = 1/mn

⇒ T_mn = 1/mn + (mn - 1)/mn = 1

Discussion

105.	If sinα + sinβ = 0 = cosα + cosβ , where 0 < β < α < 2π , then which one of the following is correct? a. α = π - β b. α = π + β c. α = 2π - β d. 2α = π + 2β
Answer» Correct option b. α = π + β Explanation: (sinα + sinβ)² + (cosα + cosβ)² = 0 ⇒ 2 + 2cos(α - β) = 0 ⇒ cos(α - β) = - 1 = cosπ ⇒ α = π + β

105.

If sinα + sinβ = 0 = cosα + cosβ , where 0 < β < α < 2π , then which one of the following is correct? a. α = π - β b. α = π + β c. α = 2π - β d. 2α = π + 2β

Answer»

Correct option b. α = π + β

Explanation:

(sinα + sinβ)² + (cosα + cosβ)² = 0

⇒ 2 + 2cos(α - β) = 0

⇒ cos(α - β) = - 1 = cosπ

⇒ α = π + β

Discussion

106.	If (sin(x + y))/(sin(x - y)) = (a + b)/(a - b), then what is tanx/tany equal to?a. a/bb. b/ac. (a + b)/(a - a)d (a - b)/(a + a)
Answer» Correct option a. a/b Explanation: (sin(x + y) + sin(x - y))/(sin(x + y) - sin(x - y)) = a/b ⇒ (2sinxcosy)/(2sinycosx) = a/b ⇒ tanx/tany = a/b

106.

If (sin(x + y))/(sin(x - y)) = (a + b)/(a - b), then what is tanx/tany equal to?a. a/bb. b/ac. (a + b)/(a - a)d (a - b)/(a + a)

Answer»

Correct option a. a/b

Explanation:

(sin(x + y) + sin(x - y))/(sin(x + y) - sin(x - y)) = a/b

⇒ (2sinxcosy)/(2sinycosx) = a/b ⇒ tanx/tany = a/b

Discussion

107.	The probability that a ship safely reaches a port is 1/3 . The probability that out of 5 ships, at least 4 ships would arrive safely is A. 1/243 B. 10/243 C. 11/243 D. 13/243
Answer» Correct option C. 11/243 Explanation: P(safely reaches) = 1/3 P(not reaches safely) = 1 - 1/3 = 2/3 P(at least 4 arrive safely) = P(4) + P(5) = ⁵C₄ (1/3)⁴ (2/3) + ⁵C₅ (1/3)⁵ = 11/3⁵ = 11/243

107.

The probability that a ship safely reaches a port is 1/3 . The probability that out of 5 ships, at least 4 ships would arrive safely is A. 1/243 B. 10/243 C. 11/243 D. 13/243

Answer»

Correct option C. 11/243

Explanation:

P(safely reaches) = 1/3 P(not reaches safely) = 1 - 1/3 = 2/3

P(at least 4 arrive safely)

= P(4) + P(5) = ⁵C₄ (1/3)⁴ (2/3) + ⁵C₅ (1/3)⁵

= 11/3⁵ = 11/243

Discussion

108.	Let \| vector a\| ≠ 0,\| vector b\| ≠ 0 (vector a + vector b).(vector a + vector b) = \|vector a\|2 + \|vector b\|2 holds if and only ifa. vector a and vector b are perpendicular b. vector a and vector b are parallel c. vector a and vector b are inclined at an angle of 45° d. vector a and vector b are anti-parallel
Answer» Correct option a. vector a and vector b are perpendicular Explanation: (vector a + vector b) x (vector a + vector b) = a² + 2vector a x vector b + b²= a² + b² ⇒ vector a x vector b = 0 ⇒ vector a ⊥ vector b

108.

Let | vector a| ≠ 0,| vector b| ≠ 0 (vector a + vector b).(vector a + vector b) = |vector a|2 + |vector b|2 holds if and only ifa. vector a and vector b are perpendicular b. vector a and vector b are parallel c. vector a and vector b are inclined at an angle of 45° d. vector a and vector b are anti-parallel

Answer»

Correct option a. vector a and vector b are perpendicular

Explanation:

(vector a + vector b) x (vector a + vector b) = a² + 2vector a x vector b + b²= a² + b²

⇒ vector a x vector b = 0 ⇒ vector a ⊥ vector b

Discussion

109.	What is lim (tanx/sin2x) for x → 0 equal to? a. 1/2 b. 1 c. 2 d. Limit does not exist
Answer» Correct option a. 1/2 Explanation: Lt (tanx/sin2x) for x → 0 = 1/2

109.

What is lim (tanx/sin2x) for x → 0 equal to? a. 1/2 b. 1 c. 2 d. Limit does not exist

Answer»

Correct option a. 1/2

Explanation:

Lt (tanx/sin2x) for x → 0 = 1/2

Discussion

110.	What is ∫eln(tanx)dx equal to? a. ln \|tan x\| + c b. ln \|sec x\| + c c. tan x + c d. etan x + c
Answer» Correct option b. ln \|sec x\| + c Explanation: ∫e^ln(tanx)dx = ∫tanxdx = ln\|secx\| + c

110.

What is ∫eln(tanx)dx equal to? a. ln |tan x| + c b. ln |sec x| + c c. tan x + c d. etan x + c

Answer»

Correct option b. ln |sec x| + c

Explanation:

∫e^ln(tanx)dx = ∫tanxdx

= ln|secx| + c

Discussion

111.	In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is A. 226 B. 249 C. 250 D. 251
Answer» Correct option B. 2⁴⁹ Explanation: C₀ + C₁ + C₂ + C₃ + C₄ + C₅+ …..C_n = 2_n Therefore C₁ + C₃ + C₅ + ….. C_n = ½ × 2ⁿ = ½ × 2⁵⁰ = 2⁴⁹

111.

In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is A. 226 B. 249 C. 250 D. 251

Answer»

Correct option B. 2⁴⁹

Explanation:

C₀ + C₁ + C₂ + C₃ + C₄ + C₅+ …..C_n = 2_n

Therefore C₁ + C₃ + C₅ + ….. C_n = ½ × 2ⁿ

= ½ × 2⁵⁰ = 2⁴⁹

Discussion

112.	The value of the product 61/2 × 61/4 × 61/8 × 61/16 × … up to infinite terms is A. 6 B. 36 C. 216 D. 512
Answer» Correct option A. 6 Explanation: 6^1/2.6^1/4.6^1/8….. = 6^{1/2+1/4+1/8…} = 6^{(1/2/1−1/2)} [a = ½, r = ½] = 6¹ = 6

112.

The value of the product 61/2 × 61/4 × 61/8 × 61/16 × … up to infinite terms is A. 6 B. 36 C. 216 D. 512

Answer»

Correct option A. 6

Explanation:

6^1/2.6^1/4.6^1/8….. = 6^{1/2+1/4+1/8…}

= 6^{(1/2/1−1/2)} [a = ½, r = ½] = 6¹ = 6

Discussion

113.	The number of terms in the expansion of (x + a)100 + (x − a)100 after simplification is A. 202 B. 101 C. 51 D. 50
Answer» Correct option C. 51 Explanation: (x + a)¹⁰⁰ + (x − a)¹⁰⁰ The terms containing odd power of (-a) in the expansion of (x – a)¹⁰⁰ will cancel out with corresponding terms in the expansion of (x + a)¹⁰⁰. So remaining terms will be = 101 – 50 = 51

113.

The number of terms in the expansion of (x + a)100 + (x − a)100 after simplification is A. 202 B. 101 C. 51 D. 50

Answer»

Correct option C. 51

Explanation:

(x + a)¹⁰⁰ + (x − a)¹⁰⁰

The terms containing odd power of (-a) in the expansion of (x – a)¹⁰⁰ will cancel out with corresponding terms in the expansion of (x + a)¹⁰⁰. So remaining terms will be = 101 – 50 = 51

Discussion

114.	If an infinite GP has the first term x and the sum 5, then which of the following is correct? a. x < –10 b. –10 < x < 0 c. 0 < x < 10 d. x > 10
Answer» Correct option c. 0 < x < 10 Explanation: x/(1 - r) = 5 ⇒ x/5 = 1 - r ⇒ r = 1 - x/5 where \|r\| < 1 ⇒ - 1 < 1 - x/5 < 1 ⇒ - 2 < - x/5 < 0 ⇒ - 10 < - x < 0 ⇒ 10 > x > 0

114.

If an infinite GP has the first term x and the sum 5, then which of the following is correct? a. x < –10 b. –10 < x < 0 c. 0 < x < 10 d. x > 10

Answer»

Correct option c. 0 < x < 10

Explanation:

x/(1 - r) = 5 ⇒ x/5 = 1 - r ⇒ r = 1 - x/5

where |r| < 1

⇒ - 1 < 1 - x/5 < 1

⇒ - 2 < - x/5 < 0

⇒ - 10 < - x < 0

⇒ 10 > x > 0

Discussion

115.	If the coefficients of am and an in the expansion of (1 + a)m+n are α and β, then which one of the following is correct? a. α = 2β b. α = β c. 2α = β d. (m + n)β
Answer» Correct option b. α = β Explanation: α = ^{m + n}_nC, β = ^{m + n}_mC ∴ α = β

115.

If the coefficients of am and an in the expansion of (1 + a)m+n are α and β, then which one of the following is correct? a. α = 2β b. α = β c. 2α = β d. (m + n)β

Answer»

Correct option b. α = β

Explanation:

α = ^{m + n}_nC, β = ^{m + n}_mC

∴ α = β

Discussion

116.	Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ
Answer» Correct option c. α = β + γ Explanation: α = ²ⁿC_n β = ^{2n - 1}C_n γ =^{2n - 1}C_{n - 1} β + γ = ^{2n - 1}C_n + ^{2n - 1}C_{n - 1} = ²ⁿC_n = α

116.

Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ

Answer»

Correct option c. α = β + γ

Explanation:

α = ²ⁿC_n

β = ^{2n - 1}C_n

γ =^{2n - 1}C_{n - 1}

β + γ = ^{2n - 1}C_n + ^{2n - 1}C_{n - 1} = ²ⁿC_n = α

Discussion

117.	What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4? a. 6 b. 12 c. 108 d. 216
Answer» Correct option d. 216 Explanation: 4c₂ x 2² x 3² = 6 x 4 x 9 = 216

117.

What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4? a. 6 b. 12 c. 108 d. 216

Answer»

Correct option d. 216

Explanation:

4c₂ x 2² x 3²

= 6 x 4 x 9 = 216

Discussion

118.	Consider the following: 1. x + x2 is continuous at x = 0 2. x + cos1/ is discontinuous at = 0 3. x2 + cos1/x is continuous at x = 0 Which of the above are correct? A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3
Answer» Correct option A. Explanation: Statement 1 and 2 are correct while 3 is incorrect.

118.

Consider the following: 1. x + x2 is continuous at x = 0 2. x + cos1/ is discontinuous at = 0 3. x2 + cos1/x is continuous at x = 0 Which of the above are correct? A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3

Answer»

Correct option A.

Explanation:

Statement 1 and 2 are correct while 3 is incorrect.

Discussion

119.	What is the number of nonzero terms in the expansion of (1 + 2√3x)11 + (1– 2√3x)11 (after simplification)? a. 4 b. 5 c. 6 d. 11
Answer» Correct option c. 6 Explanation: Let y = 2√3x Now, (1 + y)¹¹ + (1 - y)¹¹ has no. of terms = (11 +1)/2 = 6

119.

What is the number of nonzero terms in the expansion of (1 + 2√3x)11 + (1– 2√3x)11 (after simplification)? a. 4 b. 5 c. 6 d. 11

Answer»

Correct option c. 6

Explanation:

Let y = 2√3x

Now, (1 + y)¹¹ + (1 - y)¹¹ has no. of terms

= (11 +1)/2 = 6

Discussion

120.	If x = 1 – y + y2 – y3 + ... up to infinite terms, where \|y\| < 1 , then which one of the following is correct?a. x = 1/(1 + y)b. x = 1/(1 - Y)c. x = y/(1 + y)d. x = y/(1 - y)
Answer» Correct option a. x = 1/(1 + y) Explanation: Using formula for sum of infinite terms of GP x = 1/(1 - (-y)) = 1/(1 + y)

120.

If x = 1 – y + y2 – y3 + ... up to infinite terms, where |y| < 1 , then which one of the following is correct?a. x = 1/(1 + y)b. x = 1/(1 - Y)c. x = y/(1 + y)d. x = y/(1 - y)

Answer»

Correct option a. x = 1/(1 + y)

Explanation:

Using formula for sum of infinite terms of GP

x = 1/(1 - (-y)) = 1/(1 + y)

Discussion

121.	What is the greatest integer among the following by which the number 55 + 75 is divisible? a. 6 b. 8 c. 11 d. 12
Answer» Correct option d. 12 Explanation: 5⁵ + 7⁵ is divisible by 5 + 7 = 12

121.

What is the greatest integer among the following by which the number 55 + 75 is divisible? a. 6 b. 8 c. 11 d. 12

Answer»

Correct option d. 12

Explanation:

5⁵ + 7⁵ is divisible by 5 + 7 = 12

Discussion

122.	Let g be the greatest integer function. Then the function f(x) = (g(x))2 − g(x2) is discontinuous at A. all integers B. all integers except 0 and 1 C. all integers except 0 D. all integers except 1
Answer» Correct option D. all integers except 1 Explanation: g(x) = [x] f(x) = [x]² –[x²] f(x) is discontinuous at all integers except 1.

122.

Let g be the greatest integer function. Then the function f(x) = (g(x))2 − g(x2) is discontinuous at A. all integers B. all integers except 0 and 1 C. all integers except 0 D. all integers except 1

Answer»

Correct option D. all integers except 1

Explanation:

g(x) = [x]

f(x) = [x]² –[x²]

f(x) is discontinuous at all integers except 1.

Discussion

123.	What is the maximum value of 16sinθ - 12sin2θ? a. 3/4 b. 4/3 c. 16/3 d. 4
Answer» Correct option c. 16/3 Explanation: Let, sin = x, clearly x ∈ [-1, 1] Now, f(x) = –12x² + 16x = - 12(x - 2/3)² + 16/3 for x ∈ [-1,1], maximum value = 16/3

123.

What is the maximum value of 16sinθ - 12sin2θ? a. 3/4 b. 4/3 c. 16/3 d. 4

Answer»

Correct option c. 16/3

Explanation:

Let, sin = x, clearly x ∈ [-1, 1]

Now, f(x) = –12x² + 16x = - 12(x - 2/3)² + 16/3

for x ∈ [-1,1], maximum value = 16/3

Discussion

124.	In a triangle ABC, if taken in order, consider the following statements:1. vector (AB) + vector (BC) + vector (CA) = vector 02. vector (AB) + vector (BC) + vector (CA) = vector 03. vector (AB) + vector (BC) + vector (CA) = vector 04. vector (BA) + vector (BC) + vector (CA) = vector 0How many of the above statements are correct? a. One b. Two c. Three d. Four
Answer» Correct option a. One Explanation: From Δ law of vector addition vector (AB) + vector (BC) + vector (CA) = 0 Only statement (1) is correct.

124.

In a triangle ABC, if taken in order, consider the following statements:1. vector (AB) + vector (BC) + vector (CA) = vector 02. vector (AB) + vector (BC) + vector (CA) = vector 03. vector (AB) + vector (BC) + vector (CA) = vector 04. vector (BA) + vector (BC) + vector (CA) = vector 0How many of the above statements are correct? a. One b. Two c. Three d. Four

Answer»

Correct option a. One

Explanation:

From Δ law of vector addition

vector (AB) + vector (BC) + vector (CA) = 0

Only statement (1) is correct.

Discussion

125.	Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5P(B), then P(A) is equal toa. 3/4b. 4/13c. 2/3d. 1/2
Answer» Correct option b. 4/13 Explanation: P(A) + P(B) + P(C) - 1 ⇒ P(A) + 3/2P(A) + 1/2 x 3/2P(A) = 1 ⇒ 13/4P(A) = 1 ⇒ P(A) = 4/13

125.

Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5P(B), then P(A) is equal toa. 3/4b. 4/13c. 2/3d. 1/2

Answer»

Correct option b. 4/13

Explanation:

P(A) + P(B) + P(C) - 1

⇒ P(A) + 3/2P(A) + 1/2 x 3/2P(A) = 1

⇒ 13/4P(A) = 1 ⇒ P(A) = 4/13

Discussion

126.	In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X? a. 5/39b. 11/39c. 20/39d. 34/39
Answer» Correct option a. 5/39 Explanation: Required probability = (25 x 2)/(25 x 2 + 35 x 4 + 40 x 5) = 5/39

126.

In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X? a. 5/39b. 11/39c. 20/39d. 34/39

Answer»

Correct option a. 5/39

Explanation:

Required probability

= (25 x 2)/(25 x 2 + 35 x 4 + 40 x 5) = 5/39

Discussion

127.	8 coins are tossed simultaneously. The probability of getting at least 6 heads isa. 7/64b. 57/64c. 37/256d. 229/256
Answer» Correct option c. 37/256 Explanation: Required probability = (⁸C₆ + ⁸C₇ + ⁸C₈) (1/2)⁸ = (28 + 8 + 1) x 1/256 = 37/256

127.

8 coins are tossed simultaneously. The probability of getting at least 6 heads isa. 7/64b. 57/64c. 37/256d. 229/256

Answer»

Correct option c. 37/256

Explanation:

Required probability

= (⁸C₆ + ⁸C₇ + ⁸C₈) (1/2)⁸

= (28 + 8 + 1) x 1/256 = 37/256

Discussion

128.	Which one of the following graph represents the function f(x) = x/x , x ≠ 0?
Answer» Correct option C. Explanation: f(x) = x/x , x ≠ 0 implies that y = 1

128.

Which one of the following graph represents the function f(x) = x/x , x ≠ 0?

Answer»

Correct option C.

Explanation:

f(x) = x/x , x ≠ 0 implies that y = 1

Discussion

Explore topic-wise InterviewSolutions in .

If xi &gt; 0, yi &gt; 0 (i = 1, 2, 3, ...... n) are the values of two variable X and Y with geometric mean P and Q respectively, then the geometric mean of X/Y is a. P/Q b. antilog (P/Q)c. n(log P – log Q) d. n(logP + log Q)

The points (a, b), (0, 0), (−a,−b) and (ab, b2) are A. the vertices of a parallelogram B. the vertices of a rectangle C. the vertices of a square D. collinear

Let Tr be the rth term of an AP for r = 1, 2, 3, .... If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to? a. (mn)–1 b. m–1 + nn–1 c. 1 d. 0

If sinα + sinβ = 0 = cosα + cosβ , where 0 &lt; β &lt; α &lt; 2π , then which one of the following is correct? a. α = π - β b. α = π + β c. α = 2π - β d. 2α = π + 2β

If (sin(x + y))/(sin(x - y)) = (a + b)/(a - b), then what is tanx/tany equal to?a. a/bb. b/ac. (a + b)/(a - a)d (a - b)/(a + a)

The probability that a ship safely reaches a port is 1/3 . The probability that out of 5 ships, at least 4 ships would arrive safely is A. 1/243 B. 10/243 C. 11/243 D. 13/243

What is lim (tanx/sin2x) for x → 0 equal to? a. 1/2 b. 1 c. 2 d. Limit does not exist

What is ∫eln(tanx)dx equal to? a. ln |tan x| + c b. ln |sec x| + c c. tan x + c d. etan x + c

In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is A. 226 B. 249 C. 250 D. 251

The value of the product 61/2 × 61/4 × 61/8 × 61/16 × … up to infinite terms is A. 6 B. 36 C. 216 D. 512

The number of terms in the expansion of (x + a)100 + (x − a)100 after simplification is A. 202 B. 101 C. 51 D. 50

If an infinite GP has the first term x and the sum 5, then which of the following is correct? a. x &lt; –10 b. –10 &lt; x &lt; 0 c. 0 &lt; x &lt; 10 d. x &gt; 10

If the coefficients of am and an in the expansion of (1 + a)m+n are α and β, then which one of the following is correct? a. α = 2β b. α = β c. 2α = β d. (m + n)β

Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α &gt; β + γb. α &lt; β + γc. α = β + γd. α = βγ

What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4? a. 6 b. 12 c. 108 d. 216

Consider the following: 1. x + x2 is continuous at x = 0 2. x + cos1/ is discontinuous at = 0 3. x2 + cos1/x is continuous at x = 0 Which of the above are correct? A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3

What is the number of non­zero terms in the expansion of (1 + 2√3x)11 + (1– 2√3x)11 (after simplification)? a. 4 b. 5 c. 6 d. 11

If x = 1 – y + y2 – y3 + ... up to infinite terms, where |y| &lt; 1 , then which one of the following is correct?a. x = 1/(1 + y)b. x = 1/(1 - Y)c. x = y/(1 + y)d. x = y/(1 - y)

What is the greatest integer among the following by which the number 55 + 75 is divisible? a. 6 b. 8 c. 11 d. 12

Let g be the greatest integer function. Then the function f(x) = (g(x))2 − g(x2) is discontinuous at A. all integers B. all integers except 0 and 1 C. all integers except 0 D. all integers except 1

What is the maximum value of 16sinθ - 12sin2θ? a. 3/4 b. 4/3 c. 16/3 d. 4

Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5P(B), then P(A) is equal toa. 3/4b. 4/13c. 2/3d. 1/2

8 coins are tossed simultaneously. The probability of getting at least 6 heads isa. 7/64b. 57/64c. 37/256d. 229/256

Which one of the following graph represents the function f(x) = x/x , x ≠ 0?

If xi > 0, yi > 0 (i = 1, 2, 3, ...... n) are the values of two variable X and Y with geometric mean P and Q respectively, then the geometric mean of X/Y is a. P/Q b. antilog (P/Q)c. n(log P – log Q) d. n(logP + log Q)

If sinα + sinβ = 0 = cosα + cosβ , where 0 < β < α < 2π , then which one of the following is correct? a. α = π - β b. α = π + β c. α = 2π - β d. 2α = π + 2β

If an infinite GP has the first term x and the sum 5, then which of the following is correct? a. x < –10 b. –10 < x < 0 c. 0 < x < 10 d. x > 10

Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ

What is the number of nonzero terms in the expansion of (1 + 2√3x)11 + (1– 2√3x)11 (after simplification)? a. 4 b. 5 c. 6 d. 11

If x = 1 – y + y2 – y3 + ... up to infinite terms, where |y| < 1 , then which one of the following is correct?a. x = 1/(1 + y)b. x = 1/(1 - Y)c. x = y/(1 + y)d. x = y/(1 - y)