IIT Ramaiah SAT April 29 2018 Question Paper

IIT Ramaiah SAT April 29 2018 - Question 1

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In a circle of radius 2018 having centre at $$O$$, $$OPQR$$ is a rectangle with $$Q$$ on the circumference of the circle. $$P$$, $$R$$ points inside the circle such that $$PQ = 504$$. Then $$PR =$$

A

2018

B

504

C

252

D

$$\sqrt{1008}$$

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IIT Ramaiah SAT April 29 2018 - Question 2

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The cost of a jug and a glass is Rs. 110. If the cost of the jug is Rs. 100 more than that of the glass then the cost of the glass in rupees is

A

10

B

8

C

9

D

5

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IIT Ramaiah SAT April 29 2018 - Question 3

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If $$y = ax^2 + bx + c$$, $$a \ne 0$$, then $$y = a\left(x + \frac{b}{2a}\right)^2 + \frac{4ac - b^2}{4a}$$

A

If $$a$$ is positive then minimum value of $$y$$ is $$\frac{4ac - b^2}{4a}$$

B

If $$a$$ is positive then maximum value of $$y$$ is $$\frac{4ac - b^2}{4a}$$

C

If $$a$$ is negative then minimum value of $$y$$ is $$\frac{4ac - b^2}{4a}$$

D

If $$a$$ is negative then maximum value of $$y$$ is $$\frac{4ac - b^2}{4a}$$

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IIT Ramaiah SAT April 29 2018 - Question 4

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In a quadrilateral $$ABCD$$, $$p$$, $$q$$ are the lengths of the perpendiculars drawn from the vertices $$B$$ and $$D$$ onto the diagonal $$AC$$. If $$AC = r$$, then the area of the quadrilateral $$ABCD$$ is

A

$$pqr$$

B

$$\frac{pqr}{2}$$

C

$$(p + q)r$$

D

$$\frac{(p + q)r}{2}$$

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IIT Ramaiah SAT April 29 2018 - Question 5

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Two circles having centers at $$A(x_1, y_1)$$, $$B(x_2, y_2)$$ having radii 5, 3 respectively are touching each other at a point $$P(x_3, y_3)$$. Then $$\left|\sum (x_1 y_2 - x_2 y_1)\right| =$$

A

5

B

0

C

3

D

15

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IIT Ramaiah SAT April 29 2018 - Question 6

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A factor of $$\sum a^2 b + \sum ab^2 + 3abc$$ is ($$a$$, $$b$$, $$c$$ are real numbers)

A

$$\sum a^2$$

B

$$\sum a$$

C

$$\sum ab$$

D

$$\sum ab^2$$

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IIT Ramaiah SAT April 29 2018 - Question 7

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$$D$$, $$E$$, $$F$$ are the mid points of the sides $$BC$$, $$CA$$ and $$AB$$ of a triangle $$ABC$$.

A

$$DE \parallel AB$$

B

$$EF = \frac{1}{2}BC$$

C

Area of triangle $$DEF = \frac{1}{3}$$(Area of triangle $$ABC$$)

D

Area of triangle $$DEF = \frac{1}{4}$$(Area of triangle $$ABC$$)

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IIT Ramaiah SAT April 29 2018 - Question 8

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Statement 1 - Given any two real numbers $$p$$, $$q$$ there always exist two real numbers $$a$$ and $$b$$ such that $$a + b = p$$ and $$ab = q$$.<br>Statement 2 - There exist two real numbers $$a$$, $$b$$ such that $$a + b = 3$$ and $$ab = -400$$.

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 9

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$$\sqrt{x - a} + \sqrt{x - 5} = 0$$ then $$a$$ is a solution of

A

$$x^2 - 6x + 5 = 0$$

B

$$x^2 - 7x + 10 = 0$$

C

$$x^2 - x + 1 > 0$$

D

$$x^2 + x + 1 > 0$$

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IIT Ramaiah SAT April 29 2018 - Question 10

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In a triangle $$ABC$$, $$D$$, $$E$$ are points on the line segments $$AB$$ and $$AC$$ respectively. $$DE$$ is parallel to $$BC$$. If $$\frac{AB}{AC} = \frac{6}{7}$$ and $$\frac{AD}{DB} = \frac{3}{2}$$ then $$\frac{AC}{AE} =$$

A

$$\frac{3}{7}$$

B

$$\frac{3}{2}$$

C

$$\frac{7}{6}$$

D

$$\frac{5}{3}$$

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IIT Ramaiah SAT April 29 2018 - Question 11

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The number of integral solutions of the equation $$\left[\frac{k}{1}\right] + \left[\frac{k}{2}\right] + \left[\frac{k}{3}\right] = 100$$, where $$[x]$$ is the greatest integer less than or equal to $$x$$, is

A

0

B

55

C

1

D

4

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IIT Ramaiah SAT April 29 2018 - Question 12

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If $$x > 2$$ then the number of values of $$x$$ satisfying $$\sqrt{|x - 2|} = \left|\sqrt{x - 2}\right|$$ is

A

0

B

less than 3000

C

2018

D

not finite

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IIT Ramaiah SAT April 29 2018 - Question 13

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In a triangle $$ABC$$, $$D$$ is a point on the side $$BC$$ such that $$AD$$ is the internal angle bisector of the angle $$A$$. The lengths of the sides $$AB$$, $$BC$$, $$AC$$ are 4, 6, 8 respectively. Then the area of triangle $$ACD$$ is

A

$$2\sqrt{15}$$

B

$$\sqrt{15}$$

C

$$3\sqrt{15}$$

D

2

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IIT Ramaiah SAT April 29 2018 - Question 14

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If $$a$$, $$b$$ are two real numbers such that $$a + 2b^{1/3} = 5$$, $$a^3 + 8b = 305$$ then

A

$$ab^{1/3} = -6$$

B

$$ab^{1/3} = 6$$

C

$$a^3 b = -216$$

D

$$2ab^{1/3} = 3$$

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IIT Ramaiah SAT April 29 2018 - Question 15

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The solution set of $$(3x)^{\log 3} = (5x)^{\log 5}$$ is

A

$$\{1, 3, 5, 15\}$$

B

$$\{1, 15\}$$

C

$$\left\{\frac{1}{15}\right\}$$

D

$$\{3, 5\}$$

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IIT Ramaiah SAT April 29 2018 - Question 16

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In triangle $$ABC$$, right angled at $$A$$, $$AD$$ is the altitude on to the side $$BC$$. If $$AD = 6$$ and $$BD = 9$$ then $$CD =$$

A

6

B

9

C

4

D

$$\frac{3}{2}$$

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IIT Ramaiah SAT April 29 2018 - Question 17

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$$P(x) = a_n x^n + a_{n-1}x^{n-1} + \cdots + a_1 x + a_0 = 0$$ is a polynomial equation. $$P(0)$$ is a root of the equation $$P(x) = 0$$. Then

A

$$P(0) = 0$$

B

$$P(a_0) = 0$$

C

$$P(P(0)) = 0$$

D

$$a_0$$ is a root of $$P(x) = 0$$

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IIT Ramaiah SAT April 29 2018 - Question 18

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Statement 1 - A function is possible from a set having 100 elements to a set having 2 elements.<br>Statement 2 - $$A$$, $$B$$ are two sets having 3 and 5 elements respectively. Number of functions from $$A$$ to $$B$$ such that the range of $$f$$ is equal to $$B$$ is 0.

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 19

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In a triangle $$ABC$$, $$AD$$ is the altitude onto the side $$BC$$. If angle $$B$$ is acute then $$AC^2 =$$

A

$$AB^2 + BC^2 + 2BC \cdot BD$$

B

$$AB^2 + BC^2 - 2BC \cdot BD$$

C

$$AB^2 + BC^2 + BC \cdot BD$$

D

$$AB^2 + BC^2$$

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IIT Ramaiah SAT April 29 2018 - Question 20

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$$x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 = (x - 1)(x - 2)(x - 3)(x - 4)$$ then

A

$$a_3 = -10$$

B

$$a_2 = 35$$

C

$$a_1 = -50$$

D

$$a_0 = 24$$

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IIT Ramaiah SAT April 29 2018 - Question 21

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If $$\sum_{r=2}^{100} \frac{1}{1 + 2 + 3 + \cdots + r} = \frac{x}{y}$$, where $$x$$, $$y$$ are positive integers, GCD of $$x$$, $$y$$ is 1, then $$x + y =$$

A

200

B

99

C

101

D

111

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IIT Ramaiah SAT April 29 2018 - Question 22

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$$ABCD$$ is a cyclic quadrilateral inscribed in a circle of radius 5. $$E$$ is a point on the arc $$ADC$$. If angle $$AEC$$ is $$20^\circ$$ then

A

angle $$ABC$$ is $$160^\circ$$

B

angle $$ADC$$ is $$20^\circ$$

C

angle $$ABC$$ is $$100^\circ$$

D

angle $$ADC = 100^\circ$$

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IIT Ramaiah SAT April 29 2018 - Question 23

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Given $$\sin(A + B) = \sin A \cos B + \cos A \sin B$$, $$\sin 75^\circ =$$

A

$$\frac{2}{\sqrt{3}}$$

B

$$\frac{\sqrt{3} + 1}{2\sqrt{2}}$$

C

$$\frac{\sqrt{3} + 1}{\sqrt{2}}$$

D

$$\frac{\sqrt{3} - 1}{\sqrt{2}}$$

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IIT Ramaiah SAT April 29 2018 - Question 24

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Three of the vertices of a parallelogram are $$(2, -7)$$, $$(2, 0)$$ and $$(1, 8)$$ if the fourth vertex is

A

$$(1, 1)$$

B

$$(1, 15)$$

C

$$(3, -15)$$

D

$$(7, -8)$$

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IIT Ramaiah SAT April 29 2018 - Question 25

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In a rhombus lengths of the diagonals are 12 and 24. A circle C is inscribed in it. Then

A

radius of C is $$\frac{12}{\sqrt{5}}$$

B

radius of C is $$\frac{24}{\sqrt{5}}$$

C

area of the square inscribed in C is $$12\sqrt{\frac{2}{5}}$$

D

Area of square inscribed in C is $$6\sqrt{\frac{2}{5}}$$

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IIT Ramaiah SAT April 29 2018 - Question 26

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$$ax^2 + bx + c = 0$$ is a quadratic equation, $$a$$, $$b$$, $$c$$ are rational numbers. $$\Delta = b^2 - 4ac$$.

A

Roots of the equation are always real

B

If $$\Delta = k^2$$, $$k$$ is rational, then roots are rational

C

If $$\Delta \ne k^2$$, $$k$$ rational, then the roots are rational conjugates

D

Roots of the equation are always rational

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IIT Ramaiah SAT April 29 2018 - Question 27

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Statement 1 - If set $$A$$ has $$m$$ elements and set $$B$$ has $$n$$ elements then $$A \times B$$ has $$mn$$ elements.<br>Statement 2 - If $$A$$ has 5 elements and $$B$$ has 6 elements then the number of one-one functions from $$A$$ to $$B$$ is 6.

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 28

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Statement 1 - If a chord is drawn through the point of contact of a tangent to a circle, then the angles which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.<br>Statement 2 - If a line is drawn through an end point of a chord of a circle so that the angle formed with the chord is equal to the angle subtended by the chord in the alternate segment, then the line is a tangent to the circle.

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 29

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$$P(x) = a_n x^n + a_{n-1}x^{n-1} + \cdots + a_1 x + a_0 = 0$$ is a polynomial equation, $$a_0, a_1, \ldots, a_n$$ are integers. If $$\alpha$$ is an integer and $$P(\alpha) = 0$$ then

A

$$\alpha$$ divides $$a_0$$

B

$$a_0 = k\alpha$$, $$k$$ is an integer

C

$$a_0$$ divides $$\alpha$$

D

$$\alpha$$ divides $$a_n$$

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IIT Ramaiah SAT April 29 2018 - Question 30

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Number of values of $$x$$ such that $$|x| + \sqrt{x} + [x] = x$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is

A

1

B

0

C

more than 3

D

not finite

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IIT Ramaiah SAT April 29 2018 - Question 31

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$$C_1$$ and $$C_2$$ are two circles such that $$C_1$$ lies inside $$C_2$$. $$AB$$ is a chord of circle $$C_2$$ touching $$C_1$$ at $$P$$.

A

$$AP = PB$$

B

$$AP = \frac{1}{2}AB$$

C

$$AP = PB$$ if $$C_1$$ and $$C_2$$ are concentric

D

$$AP = PB$$ if $$C_1$$ and $$C_2$$ touch internally

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IIT Ramaiah SAT April 29 2018 - Question 32

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Statement 1 - Number of factors of 2018 is 2<br>Statement 2 - Sum of the squares of the factors of 2018 is 1018085

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 33

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$$\alpha, \beta, \gamma, \delta$$ are roots of the polynomial equation $$P(x) = a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 = 0$$. Then

A

$$\sum \alpha = a_3$$

B

$$\sum \alpha = \frac{a_3}{a_4}$$

C

$$\sum \alpha\beta = \frac{a_2}{a_4}$$

D

$$\alpha\beta\gamma\delta = \frac{a_0}{a_4}$$

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IIT Ramaiah SAT April 29 2018 - Question 34

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$$ABCD$$ is a rectangle region. $$P$$ is a point on the segment $$BC$$. $$PQRC$$ is also a rectangle region such that $$A$$, $$Q$$ lie on the opposite sides of the line $$BC$$. $$AD = 15$$, $$DR = 18$$. The perimeter of the region $$ABPQRDA$$ is

A

66

B

33

C

270

D

cannot be determined

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IIT Ramaiah SAT April 29 2018 - Question 35

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If $$x$$, $$y$$ are real numbers such that $$x^2 + y + 8 = 6x^{2/3}y^{1/3}$$, $$x^{2/3} + y^{1/3} > -2$$ then

A

$$x^{2/3} = 2$$

B

$$y = 8$$

C

$$y = 2\sqrt{2}$$

D

$$x = 2\sqrt{2}$$

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IIT Ramaiah SAT April 29 2018 - Question 36

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$$C_1, C_2, C_3, \ldots$$ are in A.P. $$C_1 = 8$$, $$C_2 = 10$$, $$C_3 = 12$$. If $$b_1 = 6$$ and $$b_n$$ be determined by $$b_n = b_{n-1} + C_n$$ then

A

$$b_4 = 42$$

B

$$b_7 = 96$$

C

$$b_5 = 58$$

D

$$b_6 = 76$$

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IIT Ramaiah SAT April 29 2018 - Question 37

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$$ABCD$$ is a rectangle having area 8051. Its side lengths are integers. Then minimum perimeter possible for such rectangle is

A

8051

B

16104

C

180

D

360

View Solution

IIT Ramaiah SAT April 29 2018 - Question 38

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For the function $$f(x) = \sqrt{x^2 - 3x + 2} + \sqrt{3x - x^2 - 2}$$

A

domain is $$[1, 2]$$

B

domain is $$\{1, 2\}$$

C

range is $$\{0\}$$

D

Range is $$[0, \infty)$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 39

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If $$A = (\cos x + \sin x)^2 + (\cos x - \sin x)^2$$, $$B = 2(\cos^6 x + \sin^6 x) - 3(\cos^4 x + \sin^4 x) + 1$$ then

A

$$A = B$$

B

$$A^2 + B = 4$$

C

$$A^2 - B^2 = 4$$

D

$$(1 + 2A - 5A^2 + 6A^3)(B^2 - 3B) = 0$$

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IIT Ramaiah SAT April 29 2018 - Question 40

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Statement 1 - If a trapezium is a cyclic quadrilateral, its non parallel sides are equal<br>Statement 2 - If a quadrilateral is cyclic then it is a trapezium

A

Statement 1 is true

B

Statement 1 is false

C

Statement 2 is true

D

Statement 2 is false

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IIT Ramaiah SAT April 29 2018 - Question 41

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125 identical spherical drops merge to form one large spherical drop. Ratio of the surface area of the large drop to any one of the individual drops is

A

50

B

25

C

16

D

8

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IIT Ramaiah SAT April 29 2018 - Question 42

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A solid cube of side $$6\text{ cm}$$ and density $$2\text{ g cm}^{-3}$$ is floating in a liquid of density $$3\text{ g cm}^{-3}$$. Volume of the cube seen above the liquid surface is

A

$$18\text{ cm}^3$$

B

$$36\text{ cm}^3$$

C

$$72\text{ cm}^3$$

D

$$144\text{ cm}^3$$

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IIT Ramaiah SAT April 29 2018 - Question 43

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A tube of negligible mass and uniform cross section filled with a liquid of mass $$20\text{ g}$$ is floating in water as shown. When a lead shot is dropped in to the tube, the length of the submerged portion increases by $$L$$. The buoyant force on the tube after the lead shot is dropped is (Assume acceleration due to gravity $$= 10\text{ ms}^{-2}$$)
[image]

A

$$0.1\text{ N}$$

B

$$0.2\text{ N}$$

C

$$0.3\text{ N}$$

D

$$0.4\text{ N}$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 44

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A particle moving along a straight line covers $$60\%$$ of the distance at $$v$$. If the speed averaged for the entire distance is $$\frac{5v}{4}$$, then the speed with which the particle travelled for the remaining distance is

A

$$v$$

B

$$2v$$

C

$$3v$$

D

$$5v$$

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IIT Ramaiah SAT April 29 2018 - Question 45

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Figure shows velocity time graph for a particle in motion. Displacement made by the particle in $$12\text{ s}$$ is
[image]

A

$$9\text{ m}$$

B

$$15\text{ m}$$

C

$$12\text{ m}$$

D

$$18\text{ m}$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 46

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In the previous question the distance travelled by the particle in $$12\text{ s}$$ is
[image]

A

$$15\text{ m}$$

B

$$12\text{ m}$$

C

$$9\text{ m}$$

D

$$18\text{ m}$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 47

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A block A of mass $$m$$ moving with a constant velocity $$v$$ along a smooth horizontal floor collides with another block B of mass $$2m$$ and rebounds with a velocity $$\frac{2v}{5}$$, the velocity of block B after collision is

A

$$\frac{v}{3}$$

B

$$\frac{v}{5}$$

C

$$\frac{2v}{5}$$

D

$$\frac{3v}{5}$$

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IIT Ramaiah SAT April 29 2018 - Question 48

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A block of mass $$M$$ is displaced through $$s$$ from rest by applying a constant force $$F$$. If work done by the force equals increase in kinetic energy of the block, its velocity is

A

$$\frac{2FS}{M}$$

B

$$\sqrt{\frac{2FS}{M}}$$

C

$$\sqrt{\frac{FS}{M}}$$

D

$$\sqrt{\frac{FS}{2M}}$$

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IIT Ramaiah SAT April 29 2018 - Question 49

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$$n$$ samples of same liquid with masses $$m, 2m, 3m, \ldots, nm$$ at temperatures $$t, 2t, 3t, \ldots, nt$$ are mixed in an isolated system. The resultant temperature of the mixture is

A

$$nt$$

B

$$\frac{n(n + 1)t}{2}$$

C

$$\frac{n(n + 1)(2n + 1)t}{6}$$

D

$$\frac{(2n + 1)t}{3}$$

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IIT Ramaiah SAT April 29 2018 - Question 50

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$$20\text{ g}$$ of ice is dropped in to a calorimeter of water equivalent $$10\text{ g}$$ containing $$90\text{ g}$$ of water at $$40^\circ\text{C}$$. The resultant temperature of the mixture is (specific heat of water $$= 1\text{ cal g}^{-1}\,^\circ\text{C}^{-1}$$, Latent heat of ice $$= 80\text{ cal g}^{-1}$$)

A

$$0^\circ\text{C}$$

B

$$20^\circ\text{C}$$

C

$$10^\circ\text{C}$$

D

$$30^\circ\text{C}$$

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IIT Ramaiah SAT April 29 2018 - Question 51

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A convex lens of focal length $$20\text{ cm}$$ and a convex mirror are arranged as shown. A point object is located on the principal axis at a distance of $$30\text{ cm}$$ to the left of the lens. If the final image coincides with the object, focal length of the mirror must be
[image]

A

$$5\text{ cm}$$

B

$$10\text{ cm}$$

C

$$15\text{ cm}$$

D

$$30\text{ cm}$$

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IIT Ramaiah SAT April 29 2018 - Question 52

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In the previous question if the convex mirror is removed, the distance of the image from the object would be
[image]

A

$$30\text{ cm}$$

B

$$60\text{ cm}$$

C

$$90\text{ cm}$$

D

$$120\text{ cm}$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 53

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The image produced by a convex mirror of an extended object is

A

diminished, virtual

B

real, magnified

C

magnified, virtual

D

real, diminished

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IIT Ramaiah SAT April 29 2018 - Question 54

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A biconvex lens of focal length $$20\text{ cm}$$ has curved surfaces whose radii are in the ratio $$1 \colon 2$$. Refractive index of the material of the lens is 1.5. Smaller of the radii of curvatures is

A

$$30\text{ cm}$$

B

$$15\text{ cm}$$

C

$$10\text{ cm}$$

D

$$20\text{ cm}$$

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IIT Ramaiah SAT April 29 2018 - Question 55

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A long horizontal straight conductor carries a current from north to south. Points A and B are to east and west of the conductor and points C, D are vertically above and below the conductor. Direction of magnetic field at

A

A is downward

B

B is upward

C

C is westward

D

D is westward

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IIT Ramaiah SAT April 29 2018 - Question 56

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Readings of ammeter in the circuit shown is (Consider ammeter, voltmeter and battery as ideal)
[image]

A

$$\frac{E}{2R}$$

B

$$\frac{E}{3R}$$

C

$$\frac{E}{R}$$

D

$$\frac{E}{4R}$$

View Solution

IIT Ramaiah SAT April 29 2018 - Question 57

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In the previous question the reading of the voltmeter is
[image]

A

$$E$$

B

$$\frac{E}{2}$$

C

$$\frac{E}{3}$$

D

$$\frac{E}{4}$$

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IIT Ramaiah SAT April 29 2018 - Question 58

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Two resistances of $$6\,\Omega$$ and $$3\,\Omega$$ are connected in parallel. The ratio of the rate of heat production in the $$6\,\Omega$$ and $$3\,\Omega$$ resistances is

A

$$2 \colon 1$$

B

$$1 \colon 2$$

C

$$3 \colon 1$$

D

$$1 \colon 3$$

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IIT Ramaiah SAT April 29 2018 - Question 59

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In the previous question if the combined current in the two resistors is $$3\text{ A}$$, the rate of heat production in the combination is

A

$$18\text{ W}$$

B

$$12\text{ W}$$

C

$$36\text{ W}$$

D

$$24\text{ W}$$

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IIT Ramaiah SAT April 29 2018 - Question 60

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An electric bulb rated $$60\text{ W}$$ at $$220\text{ V}$$. If the bulb is used on $$110\text{ V}$$ supply, its power would be

A

$$60\text{ W}$$

B

$$30\text{ W}$$

C

$$15\text{ W}$$

D

$$240\text{ W}$$

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IIT Ramaiah SAT April 29 2018 - Question 61

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A long straight vertical conductor is carrying some current. Magnetic field lines in the neighbourhood of the conductor are

A

straight lines parallel to the conductor

B

straight lines perpendicular to the conductor

C

concentric circles in horizontal plane

D

concentric circles in vertical plane

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IIT Ramaiah SAT April 29 2018 - Question 62

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A charged ion of mass $$m$$ and charge $$q$$ is moving in circular path of radius $$r$$ in a plane at right angles to a magnetic field of strength $$B$$. Frequency of revolution of the particle is

A

$$\frac{qB}{2\pi m}$$

B

$$\frac{2\pi m}{qB}$$

C

$$\frac{2qB}{\pi m}$$

D

$$\frac{\pi m}{2qB}$$

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IIT Ramaiah SAT April 29 2018 - Question 63

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Nucleus A decays in to nucleus C in a two-step process. $$A \rightarrow B + {}^4_2\text{He}$$ and $$B \rightarrow C + 2e^-$$. Then

A

A and C are isotopes

B

A and C are isobars

C

A and B are isotopes

D

A and B are isobars

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IIT Ramaiah SAT April 29 2018 - Question 64

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In a nuclear reactor $$94\text{ g}$$ of uranium ($$\text{U}^{235}$$) undergoes fission every 160 minutes. Number of reactions occurring every minute is (Avogadro number is $$6 \times 10^{23}$$ per mole)

A

$$1.5 \times 10^{21}$$

B

$$1.5 \times 10^{22}$$

C

$$1.5 \times 10^{20}$$

D

$$1.5 \times 10^{19}$$

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IIT Ramaiah SAT April 29 2018 - Question 65

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In the previous question, if the energy released from the fission of one $$\text{U}^{235}$$ nucleus is $$200\text{ MeV}$$, assuming $$100\%$$ efficiency the power output of the reactor is

A

$$200\text{ MW}$$

B

$$300\text{ MW}$$

C

$$400\text{ MW}$$

D

$$800\text{ MW}$$

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IIT Ramaiah SAT April 29 2018 - Question 66

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The electronic configuration with the highest ionization enthalpy is

A

$$[\text{Ne}]3s^2 3p^1$$

B

$$[\text{Ne}]3s^2 3p^2$$

C

$$[\text{Ne}]3s^2 3p^3$$

D

$$[\text{Ne}]3d^{10} 4s^2 3p^3$$

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IIT Ramaiah SAT April 29 2018 - Question 67

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For the following reactions ZnO respectively acting as a/an<br>i) $$\text{ZnO} + \text{Na}_2\text{O} \rightarrow \text{Na}_2\text{ZnO}_2$$ ii) $$\text{ZnO} + \text{CO}_2 \rightarrow \text{ZnCO}_3$$

A

acid and acid

B

acid and base

C

base and acid

D

base and base

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IIT Ramaiah SAT April 29 2018 - Question 68

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The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal<br>$$\text{Fe}_2\text{O}_3(s) + 3\text{CO}(g) \rightleftharpoons 2\text{Fe}(l) + 3\text{CO}_2(g)$$<br>Using the LeChatelier's principle, predict which of the following will disturb the equilibrium?

A

removal of CO

B

removal of $$\text{CO}_2$$

C

addition of $$\text{CO}_2$$

D

addition of $$\text{Fe}_2\text{O}_3$$

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IIT Ramaiah SAT April 29 2018 - Question 69

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The group(s) in which all are not having triangular planar structures is/are

A

$$\text{BF}_3$$, $$\text{NF}_3$$, $$\text{CO}_3^{2-}$$

B

$$\text{CO}_3^{2-}$$, $$\text{NO}_3^-$$, $$\text{SO}_3$$

C

$$\text{NH}_3$$, $$\text{SO}_3$$, CO $$\text{CO}_3^{2-}$$

D

$$\text{NCl}_3$$, $$\text{BCl}_3$$, $$\text{SO}_3$$

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IIT Ramaiah SAT April 29 2018 - Question 70

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Assuming ideal behavior the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is (Cl = 35.5 amu)

A

0.64

B

1.64

C

1.46

D

0.46

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IIT Ramaiah SAT April 29 2018 - Question 71

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When $$\text{XO}_2$$ is fused with an alkali metal hydroxide in the presence of an oxidizing agent such as $$\text{KNO}_3$$, a dark green product is formed which disproportionate in acid solution to afford a dark purple solution. X is

A

Ti

B

Cr

C

V

D

Mn

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IIT Ramaiah SAT April 29 2018 - Question 72

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A group 13 element X reacts with chlorine gas to produce compound $$\text{XCl}_3$$. $$\text{XCl}_3$$ is electron deficient and easily reacts with $$\text{NH}_3$$ to form $$\text{Cl}_3\text{X} \leftarrow \text{NH}_3$$ adduct. However, $$\text{XCl}_3$$ does not undergo dimerization. X is

A

Ga

B

Al

C

In

D

B

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IIT Ramaiah SAT April 29 2018 - Question 73

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In which of the following conversions involves change in both shape and hybridization?

A

$$\text{BF}_3 \rightarrow \text{BF}_4^-$$

B

$$\text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+$$

C

$$\text{CH}_4 \rightarrow \text{C}_2\text{H}_6$$

D

$$\text{NH}_3 \rightarrow \text{NH}_4^+$$

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IIT Ramaiah SAT April 29 2018 - Question 74

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1 g of a carbonate ($$\text{M}_2\text{CO}_3$$) an treatment with excess HCl produces 0.01186 moles of $$\text{CO}_2$$. The molar mass of $$\text{M}_2\text{CO}_3$$ in $$\text{g mol}^{-1}$$ is

A

118.6

B

11.86

C

1186

D

84.3

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IIT Ramaiah SAT April 29 2018 - Question 75

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Which of the following salts is/are the basic in aq. solution

A

$$\text{FeCl}_3$$

B

$$\text{Pb(NO}_3)_2$$

C

$$\text{Na}_2\text{CO}_3$$

D

$$\text{CH}_3\text{COOK}$$

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IIT Ramaiah SAT April 29 2018 - Question 76

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Metal M is treated with NaOH, a white gelatinous precipitate X is formed. X is soluble in excess of NaOH solution. X when heated strongly gives an oxide, which is also one of the products of alumino thermite process. The metal M is

A

Fe

B

Al

C

Zn

D

Ca

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IIT Ramaiah SAT April 29 2018 - Question 77

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The compound(s) that produces nitrogen gas by thermal decomposition is/are

A

$$\text{NH}_4\text{NO}_2$$

B

$$(\text{NH}_4)_2\text{SO}_4$$

C

$$(\text{NH}_4)_2\text{Cr}_2\text{O}_7$$

D

$$\text{NH}_4\text{NO}_3$$

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IIT Ramaiah SAT April 29 2018 - Question 78

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Which of the following compounds contain(s) no covalent bond(s)<br>$$\text{KCl}$$, $$\text{PH}_3$$, $$\text{O}_2$$, $$\text{B}_2\text{H}_6$$, $$\text{H}_2\text{SO}_4$$

A

$$\text{KCl}$$

B

$$\text{KCl}$$; $$\text{B}_2\text{H}_6$$

C

$$\text{KCl}$$; $$\text{B}_2\text{H}_6$$; $$\text{PH}_3$$

D

$$\text{KCl}$$; $$\text{H}_2\text{SO}_4$$

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IIT Ramaiah SAT April 29 2018 - Question 79

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In $$\text{KO}_2$$, the nature of oxygen species and oxidation state of oxygen atom are respectively

A

superoxide, and $$-\frac{1}{2}$$

B

peroxide and $$-\frac{1}{2}$$

C

superoxide and $$-1$$

D

oxide and $$-2$$

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IIT Ramaiah SAT April 29 2018 - Question 80

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At a certain temperature in a $$5\text{ L}$$ vessel, 2 moles of CO and 3 moles of $$\text{Cl}_2$$ gas were allowed to reach equilibrium according to the reaction $$\text{CO} + \text{Cl}_2 \rightleftharpoons \text{COCl}_2$$<br>At equilibrium of one mole of CO is present then equilibrium constant $$K_c$$ for the reaction is

A

2.5

B

3

C

4

D

2

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IIT Ramaiah SAT April 29 2018 - Question 81

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Correct order of electronic affinity is

A

$$\text{F} > \text{Cl} > \text{O}$$

B

$$\text{Cl} > \text{F} > \text{O}$$

C

$$\text{O} > \text{F} > \text{Cl}$$

D

$$\text{F} > \text{O} > \text{Cl}$$

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IIT Ramaiah SAT April 29 2018 - Question 82

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The decreasing order of bond angles in $$\text{BF}_3$$, $$\text{NH}_3$$, $$\text{H}_2\text{O}$$, $$\text{I}_3^-$$

A

$$\text{BF}_3 > \text{NH}_3 > \text{H}_2\text{O} > \text{I}_3^-$$

B

$$\text{BF}_3 > \text{I}_3^- > \text{H}_2\text{O} > \text{NH}_3$$

C

$$\text{I}_3^- > \text{BF}_3 > \text{NH}_3 > \text{H}_2\text{O}$$

D

$$\text{I}_3^- > \text{NH}_3 > \text{H}_2\text{O} > \text{BF}_3$$

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IIT Ramaiah SAT April 29 2018 - Question 83

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A white sodium salt dissolves readily in water to give a solution neutral to litmus. A silver nitrate solution is added to the above solution white ppt is formed which does not dissolve in dil. nitric acid. The anion is

A

$$\text{SO}_4^{2-}$$

B

$$\text{CO}_3^{2-}$$

C

$$\text{Cl}^-$$

D

$$\text{S}^{2-}$$

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IIT Ramaiah SAT April 29 2018 - Question 84

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In graphite and diamond the percentage of P-character of the hybrid orbital's in hybridization are respectively

A

33 and 25

B

67 and 75

C

33 and 75

D

50 and 75

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IIT Ramaiah SAT April 29 2018 - Question 85

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When a electric current is passed though acidified water, $$112\text{ ml}$$ of $$\text{H}_2$$ gas at NTP was collated at cathode in 965 seconds. The current passed in ampheres is

A

0.1

B

2.0

C

0.5

D

1.0

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IIT Ramaiah SAT April 29 2018 - Question 86

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Which of the following correct for $$\text{P}_4$$ molecular structure

A

total no. of $$\alpha$$-bonds in $$\text{P}_4$$ molecule is 6

B

the bond angles in $$\text{P}_4$$-molecule is $$60^\circ$$

C

each P-atom linked to 4-other P-atoms

D

each P-atom carry one lone pair of electron

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IIT Ramaiah SAT April 29 2018 - Question 87

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A solution containing 1 mole of NaCl and 1.5 mole of $$\text{H}_2\text{SO}_4$$ will be neutralized by

A

1.5 mole of NaOH

B

3 mole of NaOH

C

1.5 mole of $$\text{Ba(OH)}_2$$

D

5 mole of NaOH

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IIT Ramaiah SAT April 29 2018 - Question 88

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Which of the following statements is/are true about the quantum numbers $$n$$, $$l$$, $$m$$ and $$s$$?

A

$$l$$ gives an idea of the shape of the orbital

B

$$n$$ gives an idea of the size of the orbital

C

$$m$$ gives an idea of the structure of orbital

D

$$s$$ gives an idea of spinning nature of electron

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IIT Ramaiah SAT April 29 2018 - Question 89

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In which of the following molecules the octet rule is not violated?

A

$$\text{Cl}_2\text{O}$$

B

$$\text{BF}_3$$

C

$$\text{SF}_6$$

D

$$\text{NH}_4^+$$

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IIT Ramaiah SAT April 29 2018 - Question 90

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Which of the following statements are not correct for alkanes

A

all C-H and C-C bonds have a length of $$1.112\,\mathring{A}$$ and $$1.54\,\mathring{A}$$ respectively

B

all bond angles ae tetrahedral having a value of $$109^\circ 28'$$

C

the C-C chain is linear and not Zig-Zag

D

all alkanes exhibit isomerism

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