Series RTEQ.P. Code 70/-1/-1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 2
Time allowed : 1½ HoursMaximum Marks : 40
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 20 questions. All questions are compulsory.
(ii)This question paper is divided into four sections – A, B, C and D.
(iii)In Section A, Question numbers 1 to 10 carry 1 mark each.
(iv)In Section B, Question numbers 11 to 14 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 15 to 18 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 19 to 20 are long answer (LA) type questions carrying 05 marks each.
(vii)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(viii)Use of calculators is not allowed.
SECTION A
This section comprises 10 questions of 1 mark each.
1.1
Do the roots of 3x² − 4x + 2 = 0 exist as real numbers? Give a reason.
2.1
Find the roots of x² − 5x = 0.
3.1
If x = −1 is a root of x² + kx − 6 = 0, find k.
4.1
Find the discriminant of x² − 6x + 9 = 0.
5.1
Is (x + 3)² = x² + 9 a quadratic equation? Give a reason.
6.1
Writing u = 1/x and v = 1/y, rewrite 3/x + 2/y = 7 as an equation in u and v.
7.1
Find x if x + y = 9 and x − y = 3.
8.1
For what value of k does the pair kx + 3y = 1 and 2x + 6y = 5 NOT have a unique solution?
9.1
Is the pair x − y = 2 and 2x − 2y = 5 consistent? Give a reason.
10.1
The lines 2x + 3y = 12 and 4x + 6y = 24 are intersecting, parallel or coincident?
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Show that 2x² − 6x + 9/2 = 0 has equal roots and find them.
12.2
Solve by factorisation: 2x² + x − 6 = 0.
13.2
Without solving, state whether the pair 5x − 4y + 8 = 0 and 7x + 6y − 9 = 0 has a unique solution, none, or infinitely many. Give the reason.
14.2
If x = 2, y = −1 is a solution of 4x + ky = 11, find k.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
The hypotenuse of a right triangle is 25 cm. One of the other two sides is 5 cm longer than the third side. Find the sides.
16.3
Find the roots of x² + 6x − 2 = 0 by the quadratic formula.
17.3
The denominator of a fraction exceeds its numerator by 2. If 1 is added to the numerator and 1 is subtracted from the denominator, the fraction becomes 1. If the denominator is increased by 1, the fraction becomes 1/2. Find the fraction.
18.3
Solve for u and v and then find x and y: 3/x + 2/y = 14 and 5/x − 3/y = 17.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Two taps running together can fill a tank in 6 hours. The tap with the smaller pipe takes 5 hours more than the tap with the larger pipe to fill the tank alone. Find the time each tap alone takes to fill the tank.
20.5
A boat goes 30 km upstream and 24 km downstream in 7 hours. It goes 18 km upstream and 48 km downstream in 7 hours. Find the speed of the boat in still water and the speed of the stream.
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