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Class XI Math Pre-Board Exam

This document contains a practice exam for Class 11 mathematics. It has 3 sections - multiple choice questions (MCQs), short answer questions, and long answer questions. The MCQ section has 20 questions testing concepts in algebra, trigonometry, sequences, series, and probability. The short answer section has 14 questions worth 5 marks each. Finally, the long answer section contains 4 questions worth 10 marks each, testing topics like linear algebra, arithmetic and geometric series, trigonometric equations, and probability.

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Syed Raza Hassan Gardezi
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161 views2 pages

Class XI Math Pre-Board Exam

This document contains a practice exam for Class 11 mathematics. It has 3 sections - multiple choice questions (MCQs), short answer questions, and long answer questions. The MCQ section has 20 questions testing concepts in algebra, trigonometry, sequences, series, and probability. The short answer section has 14 questions worth 5 marks each. Finally, the long answer section contains 4 questions worth 10 marks each, testing topics like linear algebra, arithmetic and geometric series, trigonometric equations, and probability.

Uploaded by

Syed Raza Hassan Gardezi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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UBIS INSTITUTE COACHING CLASSES

INSTITUTE OF INTELLECTUAL EXCELLENCE


PRE-BOARD EXAMINATION 2022-23
Paper: Mathematics Class: XI Dated: 17-05-2023
Time: 3 Hours Max Marks: 100
(SECTION - A)
(MCQs)
Q1. Choose the most appropriate answer:
i. The real part of is :
a) 2 b) -2 c) 1 d) -1
ii. ( ) is :
a) 0 b) 1 c) -1 d) i
iii. If A,B and C are matrices then ( )= :
a) b) c) ABC d) CBA
iv. :
a) b) c) | | d) | |
v. If ⃗ ⃗ are two vectors such that ⃗ ⃗ , then :
a) ⃗ b) ⃗
c) ⃗ d) N.O.T
vi. If points A and B are points with position vectors ⃗ ⃗ ⃗⃗⃗⃗⃗⃗ :
a) ⃗ b) ( ⃗ ) c) ⃗ d) ⃗
vii. If a,b,c are three consecutive terms of a sequence such that b-a = c-b then that sequence is:
a) Arithmetic b) Geometric c) Harmonic d) N.O.T
viii. An infinite geometric series is convergent if :
a) | | b) | | c) | | d) | |
ix. ∑ = :
(
a) n b) c) d) ( )
x. The product 15.14.13 can be written as :
a) 15C4 b) 15C13 c) 15C3 d) 15P3
xi. If a fair coin is tossed then probability of getting a head is :
a) b) c) d)
xii. If f(x) is an even function then:
a) f(-x) = - f(x) b) f(-x) = 0 c) f(-x) = f(x) d) N.O.T
xiii. The domain of the function f(x) = is :
a) ℝ b) ℝ - {+2} c) ℝ -{2} d) ℝ - , -
xiv. ( )= :
a) Sin θ b) – Sin θ c) Cos θ d) – Cos θ
xv. Cos 2θ = :
a) b) c) d) All of these
xvi. = :

a) √ b) √ c) d)
xvii. A circle which touches each side of the triangle from inside is called:
a) b) c) d) N.O.T
xviii. The value off circum – radius R is:
a) b) c) d)
xix. :
a) b) c) d)
xx. The solution of 3tan θ - 3 = 0 is radius:
a) b) c) d)
(SECTION - B)
(SHORT ANSWERS)
Note: Answer any 10 of the following question, each carries 05 marks:
Q2. Simplify : (√ ) .

Q3. [ ] then find

Q4. If * +, prove that ( ) .


Q5. Find the vector ⃗⃗⃗⃗⃗ |⃗⃗⃗⃗⃗ | ⃗⃗⃗⃗⃗
(8,1,-4).
Q6. Find λ if the vectors ̂ ̂ ̂ ̂ ̂ ̂ ̂ ̂ ̂ :
Q7. Find the vulgar fraction equivalent to the given recurring decimal 2. ̇ ̇ .
Q8. Prove that ( ) ( ) ( )
Q9. Prove the given proposition by using mathematical induction:
( )

Q10. A man 1.8m tall observes that the angle of elevation of the top of a tree at a distance of 12m from him is
31o45’. What is the height of tree
Q11. Sum the series up to infinity: | |
Q12. Prove that:
( )
Q13. Prove that:
Q14. Show that: ( ) ( ) ( )

(SECTION - C)
(LONG ANSWERS)
Note: Attempt any 3 of the following questions, each question carries 10 marks.
Q12. a) Solve by using Gauss-Jordan method

b) The measure of two sides of a triangle are 4 and 5 units, find the measure of third side so that area of the
triangle i 6 square units.

Q13. a) If ( ) ( ) then show that .

b) Find n so that may become the arithmetic mean between a and b.

Q14. a) Find the sum of the series using partial fractions ∑


b) Two events A and B are such that ( ) ( ) ( ) . Find (A∩ ) P( )
Q15. a) Find the general solution of the trigonometric equation
b) Show that : .

Best Of Luck

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