Exam  >   Tests  >  Class X - Online Scholarship Test - MCQ

Class X - Online Scholarship Test - MCQ


Test Description

30 Questions MCQ Test - Class X - Online Scholarship Test

Class X - Online Scholarship Test - Question 1

Two plane mirrors are inclined at angles of 30º, 40°, 50° and 60°, turn by turn. At which angle of the mirrors, there would be the maximum number of images?

Class X - Online Scholarship Test - Question 2

Two thin convex lenses of focal lengths 10 cm and 20 cm are placed in contact. Then effective power of the combination is :

Detailed Solution for Class X - Online Scholarship Test - Question 2

Given:

  • Focal length of first lens, f1 = 10 cm
  • Focal length of second lens, f2 = 20 cm

To find:

  • Effective power of the combination

Solution:

  1. Calculate the power of each lens:

    • Power of a lens (P) is the reciprocal of its focal length (f) in meters.
    • P1 = 1/f1 = 1/0.1 = 10 Diopters (D)
    • P2 = 1/f2 = 1/0.2 = 5 Diopters (D)
  2. Calculate the effective power:

    • When lenses are in contact, the effective power (P) is the sum of individual powers.
    • P = P1 + P2 = 10 D + 5 D = 15 Diopters

Therefore, the effective power of the combination is 15 Diopters.

Class X - Online Scholarship Test - Question 3

A convex lens is made of a material having refractive index 1.2. If it is dipped into water (μ = 1.33), it will behave like :

Class X - Online Scholarship Test - Question 4

Three resistance each of 8 are connected to form a triangle. The resistance between any two terminals is :

Class X - Online Scholarship Test - Question 5

How will the reading in the ammeter A be affected if another identical bulb Q is connected in parallel to P? (Figure). The voltage in the mains is maintained at a constant value, then :

Class X - Online Scholarship Test - Question 6

Which of the following depicts an example of endothermic process ?

Detailed Solution for Class X - Online Scholarship Test - Question 6

An endothermic process is a chemical reaction or physical change that absorbs heat from its surroundings. Let's analyze each of the options provided:

  1. NaOH + HCl → NaCl + H₂O:

    • This is an exothermic reaction, where sodium hydroxide (NaOH) reacts with hydrochloric acid (HCl) to form sodium chloride (NaCl) and water (H₂O), releasing heat in the process.
  2. CuSO₄·5H₂O → CuSO₄ + 5H₂O:

    • This reaction represents the dehydration of copper(II) sulfate pentahydrate (CuSO₄·5H₂O) to anhydrous copper(II) sulfate (CuSO₄) by heating. This is an endothermic process because it requires heat to drive off the water molecules from the hydrated salt.
  3. 2Mg + O₂ → 2MgO:

    • This is an exothermic reaction where magnesium reacts with oxygen to form magnesium oxide, releasing a significant amount of heat and light.

Conclusion:

The reaction that depicts an endothermic process is:

2. CuSO₄·5H₂O → CuSO₄ + 5H₂O.

Class X - Online Scholarship Test - Question 7

A dilute solution of sodium carbonate was added to two test tubes one containing dil HCl (A) and the other containing dilute NaOH (B).The correct observation was :

Class X - Online Scholarship Test - Question 8

Addition of dilute HCl to separate samples containing magnesium (Mg), zinc (Zn) and lead
(Pb) results in formation of bubbles. The order of rate of formation of bubbles will be -

Class X - Online Scholarship Test - Question 9

Pair of CH3-COOH and H-COO-CH3 represents - 

Class X - Online Scholarship Test - Question 10

Which of the following remains unchanged on descending a group in the periodic table :

Class X - Online Scholarship Test - Question 11

A ladder of 15 m length reaches a window of a house which is 12 m above the ground on one side of the street. Keeping the foot of the ladder at the same point it is turned to the other side of the street and now it reaches the window of some other house which is 9 m high. The width of street is :

Class X - Online Scholarship Test - Question 12

In the following figure AE perpendicular to BC, D is the midpoint of BC, then x is equal to

Class X - Online Scholarship Test - Question 13

Two circles touch each other internally. Their radii are 4cm and 6cm. The length of the largest chord of the outer circle, if this chord lies outside the smaller circle will be :

Class X - Online Scholarship Test - Question 14

What must be added to 8x4 14x3 – 2x2 7x – 8 so that the resulting polynomial is exactly divisible by 4x2 3x –2.

Detailed Solution for Class X - Online Scholarship Test - Question 14

We are tasked with determining what must be added to the polynomial 8x4 + 14x3 - 2x2 + 7x - 8 so that the resulting polynomial is exactly divisible by 4x2 + 3x - 2.

Step 1: Let the added polynomial be kx + c.

When we add kx + c to the given polynomial, the new polynomial becomes:

P(x) = 8x4 + 14x3 - 2x2 + 7x - 8 + kx + c

This P(x) must be exactly divisible by 4x2 + 3x - 2.

Step 2: Use the remainder theorem.

If P(x) is divisible by 4x2 + 3x - 2, then the remainder when P(x) is divided by 4x2 + 3x - 2 must be 0.

To determine k and c, we find the remainder when 8x4 + 14x3 - 2x2 + 7x - 8 is divided by 4x2 + 3x - 2.

Step 3: Perform polynomial long division.

Perform polynomial long division of 8x4 + 14x3 - 2x2 + 7x - 8 by 4x2 + 3x - 2. The division produces a quotient and a remainder. We are interested only in the remainder, as that determines the values of k and c.

Division Results:

  • Quotient: 2x2 + 2x - 1
  • Remainder: 14x - 10

Step 4: Determine k and c.

For the resulting polynomial to be exactly divisible by 4x2 + 3x - 2, the remainder must be 0. Therefore, we must add -14x + 10 to cancel out the remainder.

Final Answer:

The polynomial that must be added is: -14x + 10

This corresponds to option (c).

Class X - Online Scholarship Test - Question 15

If the mid-point of the line segment joining the points (–7, 14) and (k,4) is (a, b) where 2a 3b = 5, then the value of k will be :

Class X - Online Scholarship Test - Question 16

If sin x sin2x = 1, then the value of cos12x 3 cos10x 3 cos8x cos6x –1 is :

Class X - Online Scholarship Test - Question 17

l1, l2, l3 are three distinct non-concurrent lines in a plane with no two of them parallel. The number of circles for which all of l1, l2, and l3 are tangents is :

Class X - Online Scholarship Test - Question 18

Solve    :

Class X - Online Scholarship Test - Question 19

In the figure, ABC is a right angled triangle with    = 90�, BC = 21 cm and AB = 28 cm. With AC as diameter of a semicircle and with BC as radius, a quater circle is drawn. Find the area of the shaded portion (Approximately)

Class X - Online Scholarship Test - Question 20

Find the area of the triangle whose vertices are (a, b c), (a, b – c) and (– a, c).

Class X - Online Scholarship Test - Question 21

What is the sum of the following series?

 

Class X - Online Scholarship Test - Question 22

The sum of the first n terms of the arithmetic progression is equal to half the sum of the next n terms of the same progression. Find the ratio of the sum of the first 3n terms of the progression to the sum of its first n terms.

Class X - Online Scholarship Test - Question 23

Find the value of x in 

Detailed Solution for Class X - Online Scholarship Test - Question 23

Class X - Online Scholarship Test - Question 24

Let S be the set of integers x such that :

(i) 100 < x < 200

(ii) x is odd

(iii) x is divisible by 3 but not by 7

How many elements does S contain

Class X - Online Scholarship Test - Question 25

A rectangle contains three circles as shown in the diagram touches and to each other. If the width of the rectangle is 4 unit then the length of the rectangle is :

Class X - Online Scholarship Test - Question 26

In which part of chloroplast light reaction of photosynthesis occurs ?

Class X - Online Scholarship Test - Question 27

Leaves respire with the help of

Class X - Online Scholarship Test - Question 28

Pulmonary artery is an exception as it carries

Class X - Online Scholarship Test - Question 29

The functional unit of testis of man is

Class X - Online Scholarship Test - Question 30

Exophthalmic goitre is caused due to

View more questions
Download as PDF