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2019 29 questions

Q62019 · 12 Apr 2019 · Shift 1
If $e^{y} + x y = e$ , the ordered pair $(\frac{d y}{d x}, \frac{d ^{2} y}{d x ^{2}})$ at $x = 0$ is equal to :
1. A. $(\frac{1}{e}, - \frac{1}{e ^{2}})$
2. B. $(- \frac{1}{e}, \frac{1}{e ^{2}})$
3. C. $(- \frac{1}{e}, - \frac{1}{e ^{2}})$
4. D. $(\frac{1}{e}, \frac{1}{e ^{2}})$
Show answer
Answer: B
Q62019 · 12 Apr 2019 · Shift 2
A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :
1. A.(1, 5)
2. B.( 2, 3)
3. C.(3, 5)
4. D.(3, 10)
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Answer: D
Q112019 · 12 Apr 2019 · Shift 2
A value of $α$ such that $\int_{α}^{α + 1} \frac{d x}{( x + α ) ( x + α + 1 )} = lo g_{e} (\frac{9}{8})$ is :
1. A.2
2. B.-2
3. C. $\frac{1}{2}$
4. D. $- \frac{1}{2}$
Show answer
Answer: B
Q222019 · 12 Apr 2019 · Shift 2
The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to :
1. A. $p \land q$
2. B. $q \Rightarrow\sim p$
3. C. $p \lor q$
4. D. $(\sim p) \Rightarrow q$
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Answer: A
Q232019 · 12 Apr 2019 · Shift 2
If $^{20} C_{1} + (2^{2})^{20} C_{2} + (3^{2})^{20} C_{3} + \dots + (2 0^{2})^{20} C_{20} = A (2^{β})$ , then the ordered pair $(A, β)$ is equal to :
1. A. $(420, 19)$
2. B. $(420, 18)$
3. C. $(380, 18)$
4. D. $(380, 19)$
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Answer: B
Q22019 · 10 Apr 2019 · Shift 1
All the pairs (x, y) that satisfy the inequality $2^{s i n^{2} x - 2 s i n x + 5} \cdot \frac{1}{4 ^{s i n^{2} y}} \leq 1$ also satisfy the equation
1. A. $sin x = ∣ sin y ∣$
2. B. $sin x = 2 sin y$
3. C. $2 sin x = sin y$
4. D. $2∣ sin x ∣ = 3 sin y$
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Answer: A
Q62019 · 10 Apr 2019 · Shift 1
If the length of the perpendicular from the point $(β, 0, β)$ $(β \neq = 0)$ to the line, $\frac{x}{1} = \frac{y - 1}{0} = \frac{z + 1}{- 1}$ is $\frac{3}{2}$ , then $β$ is equal to :
1. A.2
2. B.1
3. C.-2
4. D.-1
Show answer
Answer: D
Q102019 · 10 Apr 2019 · Shift 1
If $lim_{x \to 1} \frac{x ^{4} - 1}{x - 1} = lim_{x \to k} \frac{x ^{3} - k ^{3}}{x ^{2} - k ^{2}}$ , then k is :
1. A. $\frac{3}{2}$
2. B. $\frac{8}{3}$
3. C. $\frac{4}{3}$
4. D. $\frac{3}{8}$
Show answer
Answer: B
Q172019 · 10 Apr 2019 · Shift 2
Lines are drawn parallel to the line $4 x - 3 y + 2 = 0$ , at a distance $\frac{3}{5}$ from the origin. Then which one of the following points lies on any of these lines ?
1. A. $(\frac{1}{4}, - \frac{1}{3})$
2. B. $(- \frac{1}{4}, \frac{2}{3})$
3. C. $(- \frac{1}{4}, - \frac{2}{3})$
4. D. $(\frac{1}{4}, \frac{1}{3})$
Show answer
Answer: B
Q232019 · 10 Apr 2019 · Shift 2
The sum $1 + \frac{1 ^{3} + 2 ^{3}}{1 + 2} + \frac{1 ^{3} + 2 ^{3} + 3 ^{3}}{1 + 2 + 3} + \dots + \frac{1 ^{3} + 2 ^{3} + 3 ^{3} + \dots + 1 5 ^{3}}{1 + 2 + 3 + \dots + 15} - \frac{1}{2} (1 + 2 + 3 + \dots + 15)$ is equal to :
1. A.620
2. B.1240
3. C.1860
4. D.660
Show answer
Answer: A
Q202019 · 9 Apr 2019 · Shift 1
If $[1011] [1021] [1031] \dots [10 n - 1 1] = [10781]$ , then the inverse of $[10 n 1]$ is
1. A. $[11201]$
2. B. $[11301]$
3. C. $[10 - 13 1]$
4. D. $[10 - 12 1]$
Show answer
Answer: C
Q292019 · 9 Apr 2019 · Shift 1
Let $S = {θ \in [- 2 π, 2 π] : 2 cos^{2} θ + 3 sin θ = 0}$ . Then the sum of the elements of S is
1. A. $π$
2. B. $2 π$
3. C. $\frac{13 π}{6}$
4. D. $\frac{5 π}{3}$
Show answer
Answer: B
Q82019 · 9 Apr 2019 · Shift 2
If the two lines $x + (a - 1) y = 1$ and $2 x + a^{2} y = 1$ $(a \in R - {0, 1})$ are perpendicular, then the distance of their point of intersection from the origin is :
1. A. $\frac{2}{5}$
2. B. $\frac{2}{5}$
3. C. $\frac{2}{5}$
4. D. $\frac{2}{5}$
Show answer
Answer: D
Q102019 · 9 Apr 2019 · Shift 2
The vertices B and C of a $Δ ABC$ lie on the line, $\frac{x + 2}{3} = \frac{y - 1}{0} = \frac{z}{4}$ such that $BC = 5 units$ . Then the area (in sq. units) of this triangle, given that the point $A (1, - 1, 2)$ , is :
1. A.6
2. B. $517$
3. C. $34$
4. D. $234$
Show answer
Answer: C
Q162019 · 9 Apr 2019 · Shift 2
Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-
1. A.13.5
2. B.13
3. C.12.8
4. D.13.9
Show answer
Answer: D
Q262019 · 9 Apr 2019 · Shift 2
Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of $1 5^{\circ}$ with ground. Then the distance (in m) between the poles, is :-
1. A. $5 (2 + 3)$
2. B. $\frac{5}{2} (2 + 3)$
3. C. $10 (3 - 1)$
4. D. $5 (3 + 1)$
Show answer
Answer: A
Q122019 · 8 Apr 2019 · Shift 2
If a point R(4, y, z) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10), then the distance of R from the origin is :
1. A. $214$
2. B. $53$
3. C. $221$
4. D.6
Show answer
Answer: A
Q132019 · 8 Apr 2019 · Shift 2
If $z = \frac{3}{2} + \frac{i}{2} (i = - 1)$ , then $(1 + i z + z^{5} + i z^{8})^{9}$ is equal to :
1. A.1
2. B.−1
3. C.0
4. D. $(- 1 + 2 i)^{9}$
Show answer
Answer: B
Q182019 · 8 Apr 2019 · Shift 2
Suppose that the points (h,k), (1,2) and (−3,4) lie on the line $L_{1}$ . If a line $L_{2}$ passing through the points (h,k) and (4,3) is perpendicular to $L_{1}$ , then $\frac{k}{h}$ equals :
1. A. $\frac{1}{3}$
2. B.3
3. C.0
4. D. $- \frac{1}{7}$
Show answer
Answer: A
Q222019 · 8 Apr 2019 · Shift 2
The sum $k = 1 \sum 20 k \frac{1}{2 ^{k}}$ is equal to
1. A. $2 - \frac{11}{2 ^{19}}$
2. B. $2 - \frac{3}{2 ^{17}}$
3. C. $1 - \frac{11}{2 ^{20}}$
4. D. $2 - \frac{21}{2 ^{20}}$
Show answer
Answer: A
Q42019 · 12 Jan 2019 · Shift 1
If $\frac{z - α}{z + α}$ ( $α \in R$ ) is a purely imaginary number and $∣ z ∣ = 2$ , then a value of $α$ is :
1. A. $\frac{1}{2}$
2. B. $2$
3. C.2
4. D.1
Show answer
Answer: C
Q122019 · 12 Jan 2019 · Shift 1
For $x > 1$ , if $(2 x)^{2 y} = 4 e^{2 x - 2 y}$ , then $(1 + lo g_{e} 2 x)^{2} \frac{d y}{d x}$ is equal to :
1. A. $\frac{x l o g _{e} 2 x - l o g _{e} 2}{x}$
2. B. $lo g_{e} 2 x$
3. C. $x lo g_{e} 2 x$
4. D. $\frac{x l o g _{e} 2 x + l o g _{e} 2}{x}$
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Answer: A
Q252019 · 12 Jan 2019 · Shift 1
Let $S_{k} = \frac{1 + 2 + 3 + \dots + k}{k}$ . If $S_{1}^{2} + S_{2}^{2} + \dots + S_{10}^{2} = \frac{5}{12} A$ , then A is equal to :
1. A.283
2. B.156
3. C.301
4. D.303
Show answer
Answer: D
Q122019 · 11 Jan 2019 · Shift 2
Let $f (x) = \frac{x}{a ^{2} + x ^{2}} - \frac{d - x}{b ^{2} + ( d - x ) ^{2}}$ , $x \in R$ , where a, b and d are non-zero real constants. Then :
1. A.f is an increasing function of x
2. B.f is neither increasing nor decreasing function of x
3. C.f ' is not a continuous function of x
4. D.f is a decreasing function of x
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Answer: A
Q212019 · 11 Jan 2019 · Shift 2
If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :
1. A.5x + 3y – 11 = 0
2. B.5x – 3y + 1 = 0
3. C.3x – 5y + 7 = 0
4. D.3x + 5y – 13 = 0
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Answer: B