MCQ Assessment Fakiragram College

Question 1 of 62

In the given figure, ABCD is a parallelogram and
CEFD is a rhombus. ∠ADF = 90° and ∠CFD = 24°.
Find ∠DAB.

A)

$48^\circ$

B)

$42^\circ$

C)

$56^\circ$

D)

$58^\circ$

Question 2 of 62

Ravi starts from his house and moves towards South.
He walks 100 m, then turns left and walks 200 m,
turns right and walks 500 m. How far is he from his
house?

A)

$400\sqrt{5}\,\text{m}$

B)

800\text{m}

C)

$200\sqrt{10}\,\text{m}$

D)

$200\sqrt{2}\,\text{m}$

Question 3 of 62

Study the following information and answer the question given below it.
A blacksmith has five iron articles A, B, C, D and E, each having a different weight.

A)

A

B)

B

C)

C

D)

D

Question 4 of 62

Choose the odd numeral pair / group.

A)

\text{2--8}

B)

$3\!-\!27$

C)

4\,\text{--}\,32

D)

5\,\text{--}\,125

Question 5 of 62

The bank balance of Puran is more than that of Sushma but less than the bank balance of Singh.
If the bank balance of Puran, Sushma and Singh be x, y and z respectively then which of the
following is correct?

A)

x < y < z

B)

y < x < z

C)

z < x < y

D)

x < z < y

Question 6 of 62

Find the number of triangles in the given figure.

A)

18

B)

20

C)

24

D)

None of the above

Question 7 of 62

Which number will replace the question mark?

A)

8

B)

4

C)

10

D)

6

Question 8 of 62

Group the given figures into three classes using each figure only once.

A)

3, 4, 9; 5, 7, 8; 1, 2, 6

B)

1, 5, 6; 2, 4, 8; 3, 7, 9

C)

4, 6, 8; 3, 5, 7; 1, 2, 9

D)

1, 2, 7; 3, 5, 9; 4, 6, 8

Question 9 of 62

$ \text{If a right triangle has sides of length 1 and}\sqrt{2}, \text{which of the following could be the length of the remaining side?}$

A)

I only

B)

II only

C)

III only

D)

I and III only

Question 10 of 62

Ravi starts from his house and moves towards South. He walks 100 m, then turns left and walks 200 m, turns right and walks 500 m. How far is he from is house?

A)

$400\sqrt{5}\text{m}$

B)

800 \text{m}

C)

$200\sqrt{10}\text{m}$

D)

$000\sqrt{2}\text{m}$

Question 11 of 62

If one leg of an isosceles right-angled triangle is increased by 6 cm and the other leg is increased by 4 cm, then change in area of the triangles is 24 sq cm. Find the length of the leg of the original triangle.

A)

$\frac{5}{12}\text{cm}$

B)

$\frac{12}{5}\text{cm}$

C)

$\frac{1}{5}\text{cm}$

D)

$\frac{1}{12}\text{cm}$

Question 12 of 62

Study the following information and answer the question given below it.
A blacksmith has five iron articles A, B, C, D and E, each having a different weight.
(i) A weighs twice as much as B. (ii) B weighs four and a half times as much as C.
(iii) C weighs half as much as D. (iv) D weighs half as much as E.
(v) E weighs less than A but more than C.
Which of the following is the lightest?

A)

A

B)

B

C)

C

D)

D

Question 13 of 62

Choose the odd numeral pair/group.

A)

9\, \text{--}\,3

B)

$\frac{1}{2}\,\text{--}\,\frac{1}{8}$

C)

$\frac{1}{3}\,\text{--}\,\frac{1}{12}$

D)

24\,\text{--}\,6

Question 14 of 62

Select a figure from amongst the options which will continue the same series as established by the five Problem Figures.

A)

B)

C)

D)

Question 15 of 62

Out of four figures marked (A), (B), (C) and (D) three are similar in a certain manner. However one figure is not like the other three. Choose the figure which is different from the rest.

A)

B)

C)

D)

Question 16 of 62

In the matrix there are eight designs and one space is left blank as shown by a question mark.
Which answer figures will replace the question mark?

A)

B)

C)

D)

Question 17 of 62

If 324 × 150 = 54, 251 × 402 = 48 and 523 × 345 = 120, then 651 × 345 = ?

A)

120

B)

85

C)

144

D)

60

Question 18 of 62

Find the figure which contains the Fig. (X) as its embedded part.

A)

B)

C)

D)

Question 19 of 62

In the number 5904627813 first and sixth digits are interchanged; and similarly the positions of second and seventh digits and so on are interchanged. Which of the following will be the 4th digit from the right after the new arrangement?

A)

1

B)

9

C)

4

D)

0

Question 20 of 62

$In the given matrix the values of A, B and C respectively are ____.$

A)

A = 13, B = 11, C = 9

B)

A = 13, B = 9, C = 11

C)

A = 9, B = 11, C = 13

D)

A = 9, B = 13, C = 11

Question 21 of 62

Two cars start from opposite places on a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and runs for another 25 km and then takes the direction to reach the main road. In the mean time, due to a minor break down the other car has run only 35 km along the main road. What would be the distance between the two cars at this point?

A)

65\, \text{km}

B)

75\, \text{km}

C)

80\, \text{km}

D)

85\, \text{km}

Question 22 of 62

Neelam, who is Rohit's daughter, says to Indu, "Your mother Reeta is the younger sister of my father, who is the third child of Sohanji." How is Sohanji related to Indu?

A)

Maternal uncle

B)

Father

C)

Grandfather

D)

Father-in-law

Question 23 of 62

If Moon is called Star, Star is Sun, Sun is Earth, Earth is Jupiter, Jupiter is Mars and Mars is Mercury, where does man live?

A)

Mars

B)

Jupiter

C)

Earth

D)

Sun

Question 24 of 62

In the given figure, square represents doctors, triangle represents ladies and circle represents surgeons. Which letter represents the ladies who are both doctors and surgeons?

A)

U

B)

T

C)

S

D)

P

Question 25 of 62

In the given question, which number will replace the question mark?

A)

0

B)

2

C)

11

D)

12

Question 26 of 62

If the positions of the third and tenth letters of the word DOCUMENTATION are interchanged, and likewise the positions of the fourth and seventh letters, the second and sixth letters, are also interchanged, then which of the following will be eleventh letter from the right end?

A)

C

B)

I

C)

T

D)

U

Question 27 of 62

If x < –1, then which of the following expressions holds?

A)

$x < x^2 < x^3$

B)

$x < x^3 < x^2$

C)

$x^2 < x^3 < x$

D)

$x^3 < x < x^2$

Question 28 of 62

If the perimeter of a rectangular garden plot is 80 metres, which of the following could be the length of one of its sides?

A)

I only

B)

II only

C)

III only

D)

I and II

Question 29 of 62

In the adjoining figure, circles with centres at L, M and N each have a radius of 2 units and are placed as shown here. If PQRS is the smallest rectangle that will enclose the 3 circles, what is the area of PQRS?

A)

8 sq.units

B)

12 sq.units

C)

16 sq.units

D)

32 sq.units

Question 30 of 62

If 3x + 2y = 17 and x and y are positive integers, then y could be which of the following?

A)

2

B)

3

C)

4

D)

5

Question 31 of 62

$\text{In the given figure } l_1 \parallel l_2. \text{ Which of the following must be true?}$

A)

\text{f = b}

B)

\text{b = c}

C)

\text{c = e}

D)

\text{d = f}

Question 32 of 62

In the adjoining figure, point P the intersection of lines l1 and l2 has coordinates (a, b) as shown here. Which of the following could be the ordered pair (a, b)?

A)

$\left(5,-\frac{5}{2}\right)$

B)

$\left(-1,\frac{5}{8}\right)$

C)

\left(0, 4\right)

D)

$\left(\frac{2}{3},\frac{1}{3}\right)$

Question 33 of 62

$In figure, \angle L = 62^\circ, \angle LMN = 54^\circ. If MO and NO are bisectors of \angle LMN and \angle LNM respectively of DLMN, find \angle ONM and \angle MON.$

A)

$27^\circ, 121^\circ$

B)

$64^\circ, 32^\circ$

C)

$64^\circ, 121^\circ$

D)

$32^\circ, 121^\circ$

Question 34 of 62

What should come next in the letter series given below?

A)

A

B)

I

C)

H

D)

B

Question 35 of 62

How many pairs of letters are there in the word NURSING which have as many letters between them as in the English alphabet?

A)

One

B)

Three

C)

Five

D)

Six

Question 36 of 62

Study the following arrangement carefully and answer the question given below :

A)

\text{F16}

B)

C)

D)

\text{F1Z}

Question 37 of 62

Four brothers go to a dance party. As they leave, each of the brothers accidentally takes a hat belonging to another brother and a coat belonging to a third brother. M takes the coat belonging to the brother whose hat is taken by P, while P's coat is taken by the brother who takes M's hat. S takes J's hat. Whose hat was taken by P?

A)

Can't say

B)

S

C)

M

D)

Either S or J

Question 38 of 62

In a certain code 'ring a bell' is written as '5 8 2', 'did not ring' is written as '3 5 9' and 'not a reason' is written as '7 2 9'. What is the code for 'ring?

A)

8

B)

2

C)

5

D)

3

Question 39 of 62

P, Q, R, S, T, U and W are sitting around a circle facing at the centre. S is third to the left of P who is second to the left of U. T is not a neighbour of
either U or S. R is third to left of Q. Which of the following information represents the first person sitting to the immediate right of the second person?

A)

PQ

B)

UW

C)

D)

PT

Question 40 of 62

A pile of cubes of equal size is arranged as shown in the figure. Now the block is dipped into a bucket full of red paint so that only the surfaces of the
block get coloured. How many cubes are coloured on four faces only?

A)

1

B)

0

C)

2

D)

4

Question 41 of 62

Find the missing character if the given matrix follows a certain rule row-wise or column-wise.

A)

2

B)

3

C)

4

D)

5

Question 42 of 62

In the given Venn diagram, triangle represents the healthy, square represents the old and circle represents the men. Which of the following
regions represents the men who are healthy but not old?

A)

1

B)

2

C)

3

D)

7

Question 43 of 62

Select the mirror image of Figure (X) from the given options, if the mirror is placed vertically to the right.

A)

B)

C)

D)

Question 44 of 62

Given below are the three figures (X), (Y) and (Z) showing a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded
paper has been cut. Identify the unfolded form of piece of paper.

A)

B)

C)

D)

Question 45 of 62

The given question consists of Problem Figures followed by option figures. Select a figure which will continue the series.

A)

B)

C)

D)

Question 46 of 62

There is a certain relationship between figures (i) and (ii). Establish the similar relationship between figures (iii) and (iv) by selecting a figure from the options which will replace the (?) in figure (iv).

A)

B)

C)

D)

Question 47 of 62

Select the figure from the options which can be formed from the pieces given in Figure (X).

A)

B)

C)

D)

Question 48 of 62

In a DABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm. The perimeter of the quad. ARPQ is

A)

\text{91 cm}

B)

\text{60\, cm}

C)

\text{51 cm}

D)

\text{70 cm}

Question 49 of 62

In the figure, it is given that

A)

$\text{75}^\circ$

B)

$\text{30}^\circ$

C)

$\text{60}^\circ$

D)

$\text{45}^\circ$

Question 50 of 62

$\text{The value of} \sqrt{6 + 2\sqrt{3} + 2\sqrt{2} + 2\sqrt{6}} \text{-} \frac{1}{\sqrt{5 - 2\sqrt{6}}}$

A)

2

B)

-1

C)

$\sqrt{6} + \sqrt{3}$

D)

\text{1}

Question 51 of 62

.

$\text{If } a + b + c = 15 \text{ and } a^2 + b^2 + c^2 = 83, \text{ find the value of } a^3 + b^3 + c^3 - 3abc.$

A)

180

B)

71

C)

128

D)

95

Question 52 of 62

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be K% lower than the volume of B. The value of K must be

A)

85.5

B)

92.5

C)

90.5

D)

87.5

Question 53 of 62

A bag contains 8 red and 4 green balls. Find the probability that the ball drawn is red when one ball is selected at random.

A)

$\frac{2}{3}$

B)

$\frac{1}{3}$

C)

$\frac{1}{6}$

D)

$\frac{5}{6}$

Question 54 of 62

In the given figure, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

A)

$\frac{1}{12}$

B)

$\frac{1}{6}$

C)

$\frac{1}{24}$

D)

$\frac{1}{8}$

Question 55 of 62

$\text{The value of the expression } \frac{(0.6)^0 - (0.1)^{-1}}{\left(\frac{2}{3}\right)^{-1} \cdot \left(\frac{3}{2}\right)^3 + \left(-\frac{1}{3}\right)^{-1}}$

A)

$-\frac{3}{2}$

B)

$\frac{2}{3}$

C)

$\frac{3}{2}$

D)

$\frac{9}{4}$

Question 56 of 62

In the given figure, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ?

A)

$\frac{(4\sqrt{2} + 1)a}{(4\sqrt{2} + 1)}\ \text{cm}$

B)

$\frac{5}{6}\, \text{a cm}$

C)

$(7 + 3\sqrt{2})\, \text{a cm} $

D)

None of these

Question 57 of 62

\text{In the given figure, } O \text{ is the centre of the circle. The distance between } P \text{ and } Q \text{ is } 4\,\text{cm. Find } \angle ROQ.

A)

$50^\circ $

B)

$60^\circ $

C)

$70^\circ $

D)

$35^\circ $

Question 58 of 62

In the given figure, CD || AE and CY || BA. Then ar(BCZY) =

A)

\text{ar}(\triangle CBY)

B)

\text{ar}(\triangle ZDC)

C)

\text{ar}(\triangle EDZ)

D)

All of these

Question 59 of 62

The given diagram is drawn on a cartesian plane.

A)

(-3, 3)

B)

(3, -3)

C)

(-3, -3)

D)

(-3, 2)

Question 60 of 62

The given diagram shows a cylinder with a diameter of 10 cm and height 15 cm. The shaded portion in the form of a cone, with base diameter 10 cm and height 6 cm, is hollowed out.

$\text{Find the volume of the remaining solid, in }\mathrm{cm}^3.$

A)

300\, \pi

B)

295\, \pi

C)

345\, \pi

D)

325\, \pi

Question 61 of 62

\[ \text{If } a - b = 3, \; a + b + x = 2, \text{ then the value of } (a - b)\left[x^3 + 3(a + b)x^2 + 3x(a + b)^2 + (a + b)^3\right] \text{ is:} \]

A)

84

B)

48

C)

32

D)

24

Question 62 of 62

\[ \text{ABCD is a trapezium in which } AB \parallel CD. \text{ Then } AC^2 + BD^2 \text{ is equal to:} \]

A)

\[ AD^2 + BC^2 - 2AB \cdot CD \]

B)

\[ AD^2 + BC^2 + 2AB \cdot CD \]

C)

\[ AD^2 - BC^2 + 2AB \cdot CD \]

D)

\[ AD^2 - BC^2 - 2AB \cdot CD \]

MCQ Assessment