ngsfindia.org National Genius Search Main & Advanced Exam Class X Sample Question Paper

Organisation : National Genius Search Foundation
Exam : NGSE – Main & Advanced Exam
Document Type : Sample Question Papers
Class : X

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NGSE Main Class X : https://www.pdfquestion.in/uploads/9066-MainX.pdf
NGSE Advanced Class X : https://www.pdfquestion.in/uploads/9066-AdvancedX.pdf

NGSE Main & Advanced Exam Class X Sample Question Paper :

National Genius Search Examination : Mains :
Class : X
Time : 90 Minutes

Related : NGSE Main & Advanced Exam Class IX Sample Question Paper : www.pdfquestion.in/9062.html

Section 1 – Mathematics :
Important Note :
** Read the questions carefully and comprehend them correctly before you answer.
** Questions from 1 to 45 have one or more options right. To score full marks for each question, bubbles for all the right answer options should be shaded.
** Shading one or more wrong bubble/s make the answer wrong. No marks are given for partial answers.

01. Wisden posed a question to Vidya. The virus population on a patient reduces to half every hour. But why the reduction in virus population cannot be represented by a linear equation? Vidya couldn’t find the answer. What is your answer to help her?
(a) The rate of decrease is not in arithmetic progression
(b) We do not know the initial population
(c) We do not know the time taken
(d) The rate of decrease is a variable

02. During the class on real numbers, Vidya noted the following points in her notebook. What is / are the point/s she has wrongly noted?
(a) Factorize each of the given positive integers and express them as a product of powers of primes in ascending order of magnitudes of primes.
(b) To find the HCF, identify common prime factors and find the smallest exponent of these common factors. Raise these common prime factors to their exponents and multiply them to get the HCF.
(c) To find the LCM, list all prime factors once, occurring in the prime factorization of the given positive integers.
(d) For each of these factors, find the greatest exponent and raise each prime factor to the greatest exponent and multiply them to get the LCM.

03. In each of the following system of equations determine whether the system has a unique solution, no solution or infinitely many solutions. Mark ‘ P ’ for Unique solution, mark ‘ Q ’ No solution and mark ‘ R ’ for Infinitely many solutions.

04. The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the rath driver of Bheeshm. With one arrow each he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.
(a) 80
(b) 90
(c) 100
(d) 110

05. For some real number T, the first three terms of an arithmetic sequence are 2T,5T- 1, and 6T + 2. What is the numerical value of the fourth term?
(a) 27
(b) 19
(c) 13
(d) 7

06. In the figure, PQ is a tower standing vertically on the horizontal ground. From A, the angle of elevation of the top P of the tower is found to be 45??. On moving 50 meter up a slope of 15?? , the angle of elevation of P is found to be 75?? from B. The horizontal through B is BC. Find the height of the tower.
(a) 72 m
(b) 61 m
(c) 57 m
(d) 52 m

7. Which of the following can be proved?
(a) Diagonals of a trapezium divide each other proportionately
(b) Any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally
(c) The diagonals of a trapezium can be perpendicular to each other
(d) Two sides of trapezium can have the same length

8. Below are four questions Vidya put to Wisden – (a), (b), (c) and (d), which were asked for various exams during the last few years. The task for Wisden was to choose the parameter on which each of the following questions are framed. The parameters P, Q, R and S, are given among the answer options. Match the questions with the parameters given.
(a) A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. find the radius of the circle.
(b) In the figure below, if AB=AC, prove that BE = EC .
(c) A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA
(d) ABCD is a quadrilateral such that  90A circle  touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm, find r.

(P) Tangents from an exterior point to a circle are equal in length
(Q) Tangent lines at the end points of a diameter, of a circle are parallel
(R) Tangent to a circle is perpendicular to the radius through the point of contact
(S) Angles subtended at the centre by a pair opposite site are supplementary

9. What is the probability that a randomly selected two-digit number is a multiple of 14?
(a) 3/50
(b) 2/13
(c) 17/83
(d) 7/90

10. The mode of a frequency distribution can be determined graphically from
(a) Histogram
(b) Frequency polygon
(c) Ogive
(d) Frequency curve

National Genius Search Examination : Advanced
Section – 1: Mathematics
1. Vidya wonders why numbers one and zero are neither composite numbers nor prime numbers. Could you please explain to Vidya what can happen if they are either composite numbers or prime numbers? Use an example to punch your points

2. (a) There are two buildings with heights of 10 meter and 70 meter respectively that are 100 meter apart on a level surface. If a line ran from the top of each building to the bottom of the other, what would be the height of intersection from the ground?
(b) Determine the values of a and b for which the following system of linear equations has infinite solutions:

3. Without knowing the height and which sides are parallel, how would you find the area of a trapezium if all sides are given as 1m, 2m, 3m, and 4m? You need to explain the steps you take to solve the question. You need not find the numerical answer.

4. (a) The side of a square exceeds the side of the another square by 4 cm and the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares.
(b) If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral.

Section 2: Science
6. (a) A convex lens is used to form real image of an object on a screen. It is observed that even when the positions of the object and that screen are fixed there are two positions of the lens to form real images. If the heights of the images are 4 cm and 9 cm respectively. What will be the height of the object?
(b) A film projector magnifies a 100 film strip on a screen> if the linear magnification is 4. What is the area of magnified film on the screen?

7. (a) In the circuit shown, the value of each resistance is r. What will be the equivalent resistance of the circuit between points A and B?
(b) A cell of e. m. f. E is connected with an external resistance R, then potential difference across cell is V. What will be the internal resistance of cell?

8. Briefly explain human digestive system
9. Quana picked up a hot plate without knowing it is hot. She dropped the plate suddenly. Explain how Quana’s brain and her central nervous system worked to drop the plate