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DPP 1

- The document discusses topics in mathematics including quadratic equations, sequences and series, trigonometric ratios, and more. - It provides 25 problems related to these math topics, asking learners to determine expressions, values, roots, and other relationships. - The problems cover skills like evaluating sums of series, finding common roots of equations, determining maximum/minimum values of expressions, and proving mathematical statements.

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DHRUV WORLD
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2K views2 pages

DPP 1

- The document discusses topics in mathematics including quadratic equations, sequences and series, trigonometric ratios, and more. - It provides 25 problems related to these math topics, asking learners to determine expressions, values, roots, and other relationships. - The problems cover skills like evaluating sums of series, finding common roots of equations, determining maximum/minimum values of expressions, and proving mathematical statements.

Uploaded by

DHRUV WORLD
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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MATHS

• Quadratic Equation (Common roots, Sum and product of roots)


• Sequences and Series (∑n, ∑n2, ∑n3, AGP, Vn method)
• Trigonometric Ratios, Multiple and Sub-Multiple angles, Compound
angles
__________________________________________________________________
1. The sum of n terms of the series 1 2 3
5.  2 2  2 2  .... up to n terms equals to
12  22  32  42  ...... is, where n is even 2 2
13 35 57
number n 1 nn  1
nn  1 (A) (B)
(A)  2n  1 22n  1
2

2
nn  1
n
(C) (D) None of these
(B) 2n  1
2
 5 7
(C)  nn  1 6. The numerical value of sin . sin . sin
(D) none of these
18 18 18
is equal to
3 5 7
2.  2  2  ...... to  is 1
1 1  2 1  23  33
2 3 (A) 1 (B)
(A) 3 (B) 4
8
(C) 5 (D) 6 1
(C) (D) None of these
4
The value of  r  n  2 is equal to
n
3
3.
r 2    
7. If tan  . tan   . tan     1 ,
n n  1 3  3 
2 2
9
(A)
4 0     / 2 , then value of 3
n 2 2n  1n  1 sin   4 cos 3  
(B) 9 (A) 1 (B) -1
6
n  1nn  12  9 (C) 1 / 2 (D)  1 / 2
(C) 8. The maximum value of
4
(D) none of these 4 sin 2 x  3 cos 2x  sin x / 2  cos x / 2 is
4. If  n  55 then  n 2 is equal to (A) 4  2 (B) 3  2
(A) 385 (B) 506 (C) 9 (D) 4
(C) 1185 (D) 3025
1 1 20. If 3x 2  2mx  4  0 and x 2  4m  2  0 have
9. If tan   , tan   , then    =
2 3 a common roots, then m is
(A) 0 (B)  / 2 1 1
(A)  (B) 
(C)  / 4 (D)  2 3
10. The value of tan 15 = 1 1
3 (C)  (D) 
11. If   2  , then 2  2  2 cos 4 3 2
2
21. If the equations ax  bx  c  0 and
2
equal to
(A)  2 cos  (B) -2 sin  cx 2  bx  a  0a  c have negative common
(C) 2 cos  (D) 2 sin  root then the value of a  b  c is
12. If  lies in fourth quadrant, then (A) 0 (B) 2
(C) 1 (D) none of these
  
4 cos 4   sin 2 2  4 cos 2    is equal 22. If ax  bx  c  0 and bx 2  cx  a  0 have a
2

 2 2
a 3  b3  c 3
to common root and a  0 , then is
(A) 1 (B) 2 abc
(C) -2 (D) 0 equal to ………
tan 70  tan 20 23. The equation x 2  ax  b  0 and
13. 
4 tan 50 x 2  bx  a  0 will have a common root. The
(A) 1 (B) ½ common root is
(C) -1 (D)-1/2 (A) -2 (B) 1
14. If sin x  sin x  1, then
2 (C) 2 (D) none of these
cos8 x  2 cos 6 x  cos 4 x 24. The equation ax  bx  a  0 ,
2

(A) 0 (B) -1 x3  2 x 2  2 x  1  0 have two roots in


(C) 2 (D) 1 common. Then a + b must be equal to
If tan   2 tan   1 , then cos 2  sin 2   (A) 1 (B) -1
2 2
15.
(C) 0 (D) none of these
(A) 1 (B) 2
25. Find the sum to infinity of the series
(C) 0 (D) -1
3 5 7 9
If  ,  roots of x  p x  1  c  0 then
 1      .....
2
16.
2 4 8 16
  1  1 is equal to
Find the value of 1  2  3  4  ........  9 .
3 3 3 3 3
(A) C (B) c-1 26.
(C) 1-c (D) none of these 27. Prove that the next term of the sequence 1, 5, 14,
30, 55, … is 91.
For a  b , if the equation x  ax  b  0 and
2
17. 28. Find the sum to n terms of each of the following
x 2  bx  a  0 have a common root, then the series
value of a  b  is 1. 1 2  2  3  3  4  4  5  ..........
2. 3 1  5  2  7  3  .........
2 2 2
(A) -1 (B) 0
(C) 1 (D) 2 2
2 2
 
3. 1  1  2  1  2  3  ........
2 2 2

x 2  bx   1
18. If the roots of the equation  are 29. Show that
ax  c   1 1 22  2  32  ....  n  n  1
2
3n  5
equal and opposite then the value of  is 
1  2  2  3  ....  n  n  1 3n  1
2 2 2
a b
(A) (B) C 30. Find the nth term and sum to n term of the
ab following series
(C)
1
(D)
ab 1  1  2  1  2  3  1  2  3  4  ........
c a b
19. If P and q are roots of the quadratic equation
x 2  mx  m2  a  0 , then the value of
p 2  q 2  pq is
(A) 0 (B) a
(C) –a (D)  m 2

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